Risk-based maintenance strategy for oil transfer pipelines using an intuitionistic fuzzy computational approach

Abstract

The safety and reliability of oil transfer pipelines are crucial, as pipeline failures can severely affect the environment. As pipeline risk management is dynamic and uncertain, traditional maintenance approaches often fall short. This research paper proposes an Intuitive Fuzzy Computational Approach (IFCA) for oil transfer pipeline maintenance (RBM). To develop a targeted and nuanced maintenance plan, Failure Modes and Effects Analysis (FMEA) is employed. Pipeline equipment is hierarchically organised according to their failure mode criticality, which guides maintenance design. This paper leverages the context of an Interval Valued Intuitionistic Fuzzy (IVIF) environment to streamline the hierarchical classification of oil transmission pipeline instruments. The objectives are threefold: (1) to develop an intuitionistic fuzzy risk assessment model, (2) to design a modified algorithm for maintenance prioritisation, and (3) to develop a decision support system. Additionally, the research incorporates the IVIF-SWARA method to enable flexible adjustments in the alignment of the pipeline instruments. By addressing the specific challenges of oil transfer pipelines, this research aims to contribute to advancing the field of pipeline maintenance and risk management. The proposed RBM strategy, underpinned by the IFCA framework, is expected to enhance pipeline reliability and mitigate the risks associated with pipeline failures.

Abbreviations:

RBM: Risk-Based Maintenance; IFCA: Intuitionistic Fuzzy Computational Approach; FMEA: Failure Modes and Effects Analysis; IVIF: Interval Valued Intuitionistic Fuzzy; SWARA: Stepwise Weight Assessment Ratio Analysis; RCM: Reliability-Centered Maintenance; RBI: Risk-Based Inspection; CBM: Condition-Based Maintenance; IFS: Intuitionistic Fuzzy Set; HFPR: Hesitant Fuzzy Preference Relation; IVIFPHA: Interval-Valued Intuitionistic Fuzzy Power Heronian Aggregation; MCDM: Multi-Criteria Decision-Making; $\text{S}{\text{C}}_{O_i}$: Accuracy Function of Occurrence; $\text{S}{\text{C}}_{S_i}$: Accuracy Function of Severity; $K(\tilde{a})$: Failure Probability Index; $L{W}_D$: Minimum Allowable Weight of The Failure Detection Index; W_S, W_O, W_D: Weight Assigned to The Failure Outcome; $\text{RP}{\text{V}}_{\text{j}}$: Relative Priority Value; OREDA: The Offshore Reliable Data Handbook; IVIFPWHA: Interval-Valued Intuitionistic Fuzzy Power Weight Heronian Aggregation

KEYWORDS:

• Risk-Based maintenance
• fMEA
• Intuitionistic fuzzy number
• Swara

1. Introduction

In the oil and gas industry, the safe and efficient operation of oil transfer pipelines is of paramount importance. Pipelines play a crucial role in transporting oil from production sites to refineries and distribution centres, ensuring a steady supply of energy resources (Lopez and Kolios 2022). However, these pipelines are susceptible to various risks, such as corrosion, mechanical failures, and external threats, which can lead to costly disruptions, environmental damage, and even safety hazards (Tubis et al. 2022). To mitigate these risks and enhance the reliability and performance of oil transfer pipelines, the adoption of a comprehensive maintenance strategy is essential. Traditional maintenance approaches often rely on predetermined schedules or condition-based assessments, which may not adequately address the dynamic and uncertain nature of pipeline risk management (Liao et al. 2023). Therefore, there is a growing need for innovative methodologies that can effectively handle the complexity and uncertainty associated with pipeline maintenance decision-making (Domeh et al. 2022). One promising approach is the utilisation of a risk-based maintenance (RBM) strategy, which integrates risk assessment techniques with maintenance planning and execution. RBM aims to prioritise maintenance activities based on the level of risk they pose to pipeline integrity and operational continuity. By focusing resources on critical areas and potential failure modes, RBM allows for a more targeted and cost-effective maintenance approach (Viana et al. 2022).

Unfortunately, many production planning frameworks overlook the substantial ramifications of machine downtimes, whether due to spontaneous breakdowns or scheduled maintenance (Tubis et al. 2022). Equally neglected is the influence of these disruptions on delivery schedules and customer satisfaction, with few maintenance strategies taking these critical factors into account (Bukowski and Werbińska-Wojciechowska 2021). Ignoring a comprehensive review of maintenance activities and system prerequisites almost certainly undermines the accurate assessment of preservation initiatives’ effects (Carpitella et al. 2021; Tubis et al. 2022). Conversely, postponing maintenance to satisfy production deadlines can exacerbate existing issues, increasing the risk of machine breakdowns and catalyzing further delays and unfavourable scenarios (Li et al. 2021). The solution lies in harmonising production quality with astute maintenance planning to navigate these challenges adeptly. The independent consideration of each, ignoring their inherent interdependence, risks engendering new issues stemming from this symbiotic relationship (Patil et al. 2022). Indeed, understanding the intricate interrelationships between various components is essential in any production environment. Such understanding forms the cornerstone of efficient planning, promising substantial benefits for any enterprise (Cheng et al. 2019).

This paper proposes the utilisation of an intuitionistic fuzzy computational approach (IFCA) for developing an RBM strategy specifically tailored to oil transfer pipelines. The IFCA framework integrates risk assessment models, maintenance optimisation algorithms, and decision support systems to provide a holistic and rigorous methodology for pipeline maintenance planning and execution. The main objectives of this study are to:

• Develop an intuitionistic fuzzy risk assessment model that considers multiple risk factors and their uncertainties in quantifying the risk level associated with different pipeline segments and components.

• Design an improved algorithm that incorporates the intuitionistic fuzzy risk assessment results to prioritise maintenance activities based on their potential impact on pipeline integrity and operational reliability.

• Validate the proposed approach through case studies and comparative analyses with existing maintenance strategies to demonstrate its effectiveness in improving risk management and operational performance.

By adopting an RBM strategy based on an IFCA, oil and gas companies can enhance their ability to proactively manage pipeline risks, optimise maintenance resources, and ensure the safe and efficient operation of their oil transfer infrastructure (Abbassi et al. 2022). This research aims to contribute to the industry's ongoing efforts to develop advanced maintenance methodologies that align with the evolving challenges and complexities of the modern energy landscape.

In response to this, our manuscript unfolds as follows: Section 2 delves into the historical context, spotlighting the existing research gaps. Successively, Section 3 unveils the research methodology. Section 4 propounds a novel proposal for determining hierarchical structures, embodying mathematical formulations and the cardinal principles of the emerging FMEA methodology in ambiguous scenarios underpinned by a cohesive algorithm for execution. Section 5 undertakes a practical analysis, showcasing the practicality of the devised method in classifying pivotal machinery and identifying primary failure scenarios, particularly concerning oil pipeline systems and communication equipment. This section affirms the viability of the proposed framework. Conclusively, Section 6 furnishes the research conclusions.

2. Literature review

Since the onset of the twenty-first century, RBM has come into prominence, integrating RBI within the frameworks of RCM and CBM. This approach has found wide applicability across diverse industrial landscapes (Mancuso et al. 2016). The practice of technical risk assessment involves defining, depicting, quantifying, and evaluating the potential adverse outcomes of specific events, employing both qualitative and quantitative methods to marry probability with corresponding impacts (Dickerson and Ackerman 2016). To grasp the breadth and depth of this subject, we delve into a thorough analysis of the academic discourse's history, covering investigations into maintenance and repair (emphasising reliability metrics and informed, condition-monitored, preventive approaches), evaluative and risk-informed assessments, and studies exploring equipment prioritisation through mathematical modelling, as detailed in Table 1.

Table 1. A collation of the research backdrop.

Reference	Objective	Tools / Techniques	Results
Leoni et al. (2021)	Comparison of different risk-based maintenance approaches in the gas transmission industry	Review of research literature	Provide a classification of different risk-based maintenance approaches and identify the advantages and disadvantages of each approach.
Piasson et al. (2016)	Minimize preventive maintenance costs along with maximising the reliability index of the whole system.	Fuzzy inference system, using metaheuristic algorithm	The results obtained from applying the proposed methodology for a system with three power lines and 733 components show the strength and quality of maintenance programming.
Ebenuwa and Tee (2020)	Multi-objective optimisation of risk-based maintenance system and reliability	Metaheuristic algorithm	The application of the mathematical model was illustrated by a numerical example, which provides engineering technicians with the tools needed to determine the optimal time interval required to perform buried pipelines.
Yeter, Garbatov, and Soares (2020)	Design of risk-based maintenance system in wind turbine farms	Life cycle assessment	Different inspection policies have been studied, and each wind farm's most cost-effective inspection and maintenance policy has been studied.
Leoni et al. (2019)	Design a risk-based maintenance model for the gas distribution network	Bayesian networks	The results proved that the most important components are the calculator and the pilots, while the safest risk is odour detectors.
Yazdi, Nedjati, and Abbassi (2019)	Optimisation of the risk-based maintenance system	Metaheuristic algorithm	The results showed that the methodology developed in this paper more accurately estimates the risks and leads to increased system reliability.
Asuquo et al. (2019)	Establish a simple evaluation process that can be easily used in the net operation of marine machine systems.	Multi-criteria decision-making	The applicability of the proposed method has been demonstrated using a case study of a water-cooling pump in the central cooling system of a marine diesel engine. The electro method was compared with the MAUT method in terms of ranking.
Zhao, You, and Liu (2017)	A novel method has been developed to solve multi-point group decision-making problems using two new operators, and the validity and reliability of these two operators have been proven.	Fuzzy Multi-criteria decision-making	The practical effectiveness of the proposed FMEA in the sheet metal production process is demonstrated. The results can help identify high-risk failure situations and provide appropriate criteria for preventing accidents in the system.
H. C. Liu, You, and Duan (2017)	Development of a robust FMEA model using IVIFs integration and MABAC method to determine failure risk priorities	Intuitive Fuzzy Multi-criteria decision-making	A practical example demonstrates the applicability and effectiveness of FMEA, and the results show that a new integrated approach is a reliable tool for critical analysis.
Baykasoğlu and Gölcük (2017)	Combining average power (PA) and average Heronian operators, extending them to intuitive fuzzy environments with interval values, and using them to solve group decision problems	Intuitive Fuzzy Multi-criteria decision-making	The results show that the most critical risks in failure situations are failure to ensure engagement of key users, failure to understand and respond to the needs of random customers, and failure to ensure integration between enterprise firm systems.
Huang, Li, and Liu (2017)	Linguistic distribution evaluation to show risk assessment information of FMEA team members and improved TODIM method to prioritise failure risk situations	Multi-criteria decision-making	A case study on the risk assessment of the heavy wheel system confirms the feasibility and usefulness of the proposed risk rating model. The results show that the proposed FMEA can capture the uncertainty and variability of the core experts’ assessment information and incorporate the experts’ psychological behaviour in the risk analysis process.
Nazeri and Naderikia (2017)	Development of a risk-based method for selecting an appropriate maintenance strategy to provide accessible and reliable equipment on the Iranian railway	Fuzzy Multi-criteria decision-making	The results showed that six critical risks are identified through the FMEA method: motor risk, pneumatic risk, hydraulic risk, transmission risk, mobile charging risk, and electronic risk.
Jiang et al. (2017)	Overcoming the shortcomings of traditional FMEA and better modelling and uncertainty in risk analysis through the introduction of an FMEA approach based on a new fuzzy-proof method	Fuzzy FMEA Fuzzy Multi-criteria decision-making	The main contribution of this paper is that fuzzy information integrates risk factors based on a hybrid algorithm and not massive rules. The proposed method is more suitable for risk analysis in uncertain conditions than traditional RPN.
Certa et al. (2017)	Provide Critical Analysis of Impact and Failure Conditions (FMECA) under Uncertainty Conditions.	Dempster-Schaefer theory.	The research model correctly addresses the cognitive uncertainty that often affects experts’ ratings of risk factors in real FMECA applications. Interval value assessments also allow for better analysis of expert knowledge and perceptions.
Tooranloo and Ayatollah (2016)	Using intuitive fuzzy set theory to analyze the effects and mode of failure	Fuzzy Multi-criteria decision-making	The proposed model solves the problems related to the ambiguity of FMEA techniques in evaluating qualitative factors.

This study leverages the principles of RCM to identify the aggregate priority tiers of elements in oil pipelines and telecommunication infrastructures. It advocates for a merger of this doctrine with a risk-focused examination of static assets to devise an integrated ranking scheme, with an aspiration to apply RCM and RBI on the RBM platform concurrently. Driving this initiative are the inherent dynamic weighting system and the pursuit to develop a synergistic methodology that encompasses both RCM and RBI within the realm of RBM. Significantly, the HFPR approach remains unexplored in the realm of maintenance computations. Moreover, the overarching structure elucidated in paragraph four lacks precedent in academic investigations. The creation of a dynamic weight model, dependent on the current scenario and interfaced with the interval-valued intuitionistic fuzzy power heronian aggregation (IVIFPHA) aligned with the SWARA process, stands as the foundation of this research. The research contributions are summarised as follows:

1. Application of IVIF- SWARA: The utilisation of the IVIF-SWARA in the context of RBM for oil transfer pipelines represents a research contribution. SWARA is a multi-criteria decision-making (MCDM) technique that allows for the evaluation and prioritisation of maintenance actions based on multiple criteria. By incorporating intuitionistic fuzzy logic into SWARA, the approach effectively handles uncertainties and imprecisions associated with pipeline risk assessment and maintenance decision-making.

2. Enhanced Risk Assessment: The IVIF-SWARA approach contributes to improved risk assessment in RBM for oil transfer pipelines. By considering multiple criteria and incorporating intuitionistic fuzzy logic, the approach captures and represents the complex and uncertain nature of pipeline risks more accurately. This enables more robust and comprehensive risk evaluations, leading to better-informed maintenance decisions.

3. Optimal Maintenance Prioritisation: The IVIF-SWARA approach facilitates the optimal prioritisation of maintenance actions for oil transfer pipelines. By assigning weights to various criteria and assessing their relative importance, the approach helps identify critical maintenance tasks that require immediate attention. This contributes to the efficient allocation of maintenance resources, reducing downtime and improving the overall reliability of pipeline operations.

3. Methodology

Considering that the primary goal of this study is to analyze a current issue using a practical approach to resolve a dilemma and meet a specific demand, it traverses the paths of applied research with regard to its objective. Simultaneously, this initiative employs literature review techniques and documentary references to detail and inspect the system's status thoroughly, categorising it as a descriptive-analytical endeavour based on the data collection methodology focusing on the oil and telecommunications networks in Iran as a case study. Furthermore, it incorporates both quantitative and qualitative analytical approaches in light of the nature of the data. To identify the data required for determining equipment evaluation indicators’ weight allocation, to gather information on individual equipment assessments based on designated criteria, and to assess critical equipment failure scenarios, a strategic selection method is utilised to select a representative statistical group. Table 2 outlines the setup of the expert panel.

Table 2. Composition of the panel of research experts.

No.	Job title	Number of experts
1	Managers	6 Persons
2	Maintenance & Operations Experts	11 Persons
3	Supporting Expert	4 Persons
4	Total	20 Persons

3.1. Developed algorithm

In the development of robust and efficient maintenance and repair strategies, the methodology undertakes the assignment of variable weights to each alternative, a process fundamentally influenced by three central parameters: Occurrence (O), Severity (S), and Detection (D). Detailed below is the process by which this approach abides:

1. Initial Assessment with a Hypothetical Apparatus: At the inception of this approach, preliminary data pertaining to the constant weights assigned to the O, S, and D factors is gathered utilising a hypothetical apparatus demonstrating the minimum potentialities in all three categories. This scenario envisages nearly non-existent probabilities of failure and detection incapacities alongside negligible repercussions of malfunction. The experts are consequently beckoned to benchmark this apparatus to delineate metric weights, thereby facilitating the procurement of opinions rooted in speculative machinery scenarios. These preliminarily derived weights stand as foundational values, susceptible to adjustments contingent upon the equipment's condition.

2. Dynamic weight adjustment based on individual equipment conditions: Acknowledging the fluidity in the impact of O, S, and D weights, which fluctuate according to individual equipment circumstances, a focal point remains on the O and S metrics. For instance, in environments where a unit grapples with heightened risks of adverse outcomes stemming from failure, the resultant metric weight eclipses the originally computed weight. In the maintenance landscape, the accentuation of failure probabilities or ramifications amplifies the indicators’ sway on the equipment or failure mode's criticality, ushering in a requisite for elevated weights for these parameters in high-risk contexts. This conjectural modelling fosters the cultivation of flexible initial weights resonating with distinct equipment or failure scenarios within the tripartite O, S, and D schema.

3. Balanced attribution of weights to promote fail-safe strategies: A rational extrapolation of increasing the severity or occurrence dimensions implies an augmented weight allocation to these facets, concurrently diminishing the weight accorded to the failure detection criterion. To mitigate an undue decrement in this metric, a boundary defining the nadir acceptable weight for the failure detection parameter is instituted, thereby forging a dynamic weight constant denominated as λ. This mitigates the excessive diminution of this variable, orchestrating a final weight oscillating between the minimum acceptable threshold and the metric's determined weight, crystallizing into a formula exhibited as Equation 1. (1) $L{W}_D\le W_{D_i}(F)\le W_D$(1)

4. The theory maintains that the values associated with the two metrics, O and S, never fall below the minimum threshold established in the initial phase. To guarantee this, after determining the preliminary fluctuating values for the metrics O, S, and D, a computational process establishes the final fluctuating values within the defined scope. This system prevents the O and S metrics from dropping below the predetermined stable value. The final values assigned to these metrics will always exceed this stable value threshold. This relationship is articulated in Equation 2(2) $\begin{array}{l}{W}_{O_i}(F)\ge W_O\\ W_{S_i}(F)\ge W_S\end{array}$(2) : (2) $\begin{array}{l}{W}_{O_i}(F)\ge W_O\\ W_{S_i}(F)\ge W_S\end{array}$(2)

The SWARA method relies on crisp numerical values for the decision-making criteria, which may not adequately capture the inherent uncertainty (Ghasemian Sahebi, Arab, and Toufighi 2020) and imprecision (Sahebi et al. 2024) involved in assessing the criticality of pipeline equipment and failure modes. The use of precise numerical values can oversimplify the complex and subjective nature of risk assessment in pipeline management. By incorporating the IVIF framework into the SWARA method, the proposed approach can better handle the ambiguity and vagueness associated with expert judgments. The IVIF-SWARA method allows for the representation of criteria weights as interval-valued intuitionistic fuzzy numbers, which can more accurately capture the hesitancy and uncertainty inherent in the decision-making process (Fayyaz et al. 2024; Sahebi et al. 2021). The IVIF-SWARA approach enables a more flexible and nuanced evaluation of the pipeline instruments and failure modes, as it can accommodate both optimistic and pessimistic viewpoints, as well as the degree of similarity between the assessed elements (Ghasemian Sahebi et al. 2024). This enhanced flexibility and ability to capture the multi-faceted nature of pipeline risk management can lead to more informed and robust maintenance prioritisation decisions (Sadeghi Moghadam et al. 2024).

Additionally, the IVIF-SWARA method can better handle the hierarchical organisation of pipeline equipment, which is a crucial step in the proposed risk-based maintenance strategy. The intuitionistic fuzzy representation of the criteria weights can facilitate a more comprehensive and adaptive classification of the equipment based on their failure mode criticality. By addressing these advantages, the paper could have provided a stronger justification for the use of the IVIF-SWARA approach over the traditional SWARA method, further strengthening the credibility and effectiveness of the proposed risk-based maintenance strategy for oil transfer pipelines.

The following framework, visualised in Figure 1, lays the groundwork for determining weights and ranking options:

• Step 1: normalize the preference values

Figure 1. Framework for calculating weight and prioritising options.

To normalise preference values, beneficial types are retained as they are, while cost types are transformed into beneficial types utilising the method illustrated below:

Suppose ${\tilde{r}}_{\mathrm{ij}}^k=([a_{\mathrm{ij}}^k,b_{\mathrm{ij}}^k],[c_{\mathrm{ij}}^k,d_{\mathrm{ij}}^k])$ and $i=1,2,\dots ,m;k=1,2,\dots ,t$ The values for the $j$ attitude of $C_j$ are of the cost type. This value can be converted to a benefit using Equation 3 (the converted preference value is still expressed by ${\tilde{r}}_{\mathrm{ij}}^k$): (3) ${\tilde{r}}_{\mathrm{ij}}^k=([c_{\mathrm{ij}}^k,d_{\mathrm{ij}}^k],[a_{\mathrm{ij}}^k,b_{\mathrm{ij}}^k])$(3)

• Step 2: Calculate the backup degree

In this step, the degree of support between ${\tilde{r}}_{\mathrm{ij}}^k,{\tilde{r}}_{\mathrm{ij}}^l$, the similarity ${\tilde{r}}_{\mathrm{ij}}^k,{\tilde{r}}_{\mathrm{ij}}^l$ is considered, and based on the definition of similarity, it is calculated as Equation 4. The degree of support and similarity between the intuitionistic fuzzy values are calculated using the given formula. (4) $\mathrm{SUP}({\tilde{r}}_{\mathrm{ij}}^k,{\tilde{r}}_{\mathrm{ij}}^l)=1-\sqrt{\frac{1}{4}({(a_{\mathrm{ij}}^k-a_{\mathrm{ij}}^l)}^2+{(b_{\mathrm{ij}}^k-b_{\mathrm{ij}}^k)}^2+{(c_{\mathrm{ij}}^k-c_{\mathrm{ij}}^l)}^2+{(d_{\mathrm{ij}}^k-d_{\mathrm{ij}}^l)}^2)}$(4)

• Step 3: Calculation of $\mathit{T}({\tilde{\mathit{a}}}_{\mathit{k}})$ according to Equation 5: (5) $T({\tilde{a}}_k)=\sum _{{}_{i\ne k}^{i=1}.}^n\mathrm{SUP}({\tilde{a}}_k,{\tilde{a}}_i)$(5)

• Step 4: Calculation of the power weight vector according to Equation 6:

The power weight vector is calculated based on the backup degree values. (6) ${\overline{\omega }}_{\text{k}}=\frac{(1+T({\tilde{a}}_j))}{{\sum }_{k=1}^n(1+T({\tilde{a}}_k))}$(6)

• Step 5: Constructing the Unified Evaluation Matrix Using the Intuitive Fuzzy Strength Weight:

Based on the formula of the Heronian aggregation operator, we calculate the aggregated evaluation matrix with the following interval values (IVIFPWHA) (Equation 7(7) $\begin{array}{rl}& \mathrm{IVIFPWH}{A}^{p,q}({\tilde{a}}_1,{\tilde{a}}_2,\dots {\tilde{a}}_n)\\ & =\left(\begin{array}{l}\left[\begin{array}{l}{\left(1-{\left(\prod _{i=1}^n\prod _{j=1}^n\left(1-{\left(1-{(1-{\tilde{a}}_i)}^{\frac{n{\overline{\omega }}_i{w}_i}{{\sum }_{k=1}^n{\overline{\omega }}_k{w}_k}}\right)}^p{\left(1-{(1-{\tilde{a}}_j)}^{\frac{n{\overline{\omega }}_i{w}_i}{{\sum }_{k=1}^n{\overline{\omega }}_k{w}_k}}\right)}^q\right)\right)}^{\frac{2}{n(n+1)}}\right)}^{\frac{1}{p+q}}\\ {\left(1-{\left(\prod _{i=1}^n\prod _{j=1}^n\left(1-{\left(1-{(1-{\tilde{b}}_i)}^{\frac{n{\overline{\omega }}_i{w}_i}{{\sum }_{k=1}^n{\overline{\omega }}_k{w}_k}}\right)}^p{\left(1-{(1-{\tilde{b}}_j)}^{\frac{n{\overline{\omega }}_i{w}_i}{{\sum }_{k=1}^n{\overline{\omega }}_k{w}_k}}\right)}^q\right)\right)}^{\frac{2}{n(n+1)}}\right)}^{\frac{1}{p+q}}\end{array}\right]\\ \left[\begin{array}{l}1-{\left(1-{\left(\prod _{i=1}^n\prod _{j=1}^n\left(1-{\left(1-{{\tilde{c}}_i}^{\frac{n{\overline{\omega }}_i{w}_i}{{\sum }_{k=1}^n{\overline{\omega }}_k{w}_k}}\right)}^p{\left(1-{{\tilde{c}}_j}^{\frac{n{\overline{\omega }}_i{w}_i}{{\sum }_{k=1}^n{\overline{\omega }}_k{w}_k}}\right)}^q\right)\right)}^{\frac{2}{n(n+1)}}\right)}^{\frac{1}{p+q}}\\ 1-{\left(1-{\left(\prod _{i=1}^n\prod _{j=1}^n\left(1-{\left(1-{d_i}^{\frac{n{\overline{\omega }}_i{w}_i}{{\sum }_{k=1}^n{\overline{\omega }}_k{w}_k}}\right)}^p{\left(1-{d_j}^{\frac{n{\overline{\omega }}_i{w}_i}{{\sum }_{k=1}^n{\overline{\omega }}_k{w}_k}}\right)}^q\right)\right)}^{\frac{2}{n(n+1)}}\right)}^{\frac{1}{p+q}}\end{array}\right]\end{array}\right)\end{array}$(7) ). (7) $\begin{array}{rl}& \mathrm{IVIFPWH}{A}^{p,q}({\tilde{a}}_1,{\tilde{a}}_2,\dots {\tilde{a}}_n)\\ & =\left(\begin{array}{l}\left[\begin{array}{l}{\left(1-{\left(\prod _{i=1}^n\prod _{j=1}^n\left(1-{\left(1-{(1-{\tilde{a}}_i)}^{\frac{n{\overline{\omega }}_i{w}_i}{{\sum }_{k=1}^n{\overline{\omega }}_k{w}_k}}\right)}^p{\left(1-{(1-{\tilde{a}}_j)}^{\frac{n{\overline{\omega }}_i{w}_i}{{\sum }_{k=1}^n{\overline{\omega }}_k{w}_k}}\right)}^q\right)\right)}^{\frac{2}{n(n+1)}}\right)}^{\frac{1}{p+q}}\\ {\left(1-{\left(\prod _{i=1}^n\prod _{j=1}^n\left(1-{\left(1-{(1-{\tilde{b}}_i)}^{\frac{n{\overline{\omega }}_i{w}_i}{{\sum }_{k=1}^n{\overline{\omega }}_k{w}_k}}\right)}^p{\left(1-{(1-{\tilde{b}}_j)}^{\frac{n{\overline{\omega }}_i{w}_i}{{\sum }_{k=1}^n{\overline{\omega }}_k{w}_k}}\right)}^q\right)\right)}^{\frac{2}{n(n+1)}}\right)}^{\frac{1}{p+q}}\end{array}\right]\\ \left[\begin{array}{l}1-{\left(1-{\left(\prod _{i=1}^n\prod _{j=1}^n\left(1-{\left(1-{{\tilde{c}}_i}^{\frac{n{\overline{\omega }}_i{w}_i}{{\sum }_{k=1}^n{\overline{\omega }}_k{w}_k}}\right)}^p{\left(1-{{\tilde{c}}_j}^{\frac{n{\overline{\omega }}_i{w}_i}{{\sum }_{k=1}^n{\overline{\omega }}_k{w}_k}}\right)}^q\right)\right)}^{\frac{2}{n(n+1)}}\right)}^{\frac{1}{p+q}}\\ 1-{\left(1-{\left(\prod _{i=1}^n\prod _{j=1}^n\left(1-{\left(1-{d_i}^{\frac{n{\overline{\omega }}_i{w}_i}{{\sum }_{k=1}^n{\overline{\omega }}_k{w}_k}}\right)}^p{\left(1-{d_j}^{\frac{n{\overline{\omega }}_i{w}_i}{{\sum }_{k=1}^n{\overline{\omega }}_k{w}_k}}\right)}^q\right)\right)}^{\frac{2}{n(n+1)}}\right)}^{\frac{1}{p+q}}\end{array}\right]\end{array}\right)\end{array}$(7)

• Step 6: Calculate the accuracy functions $\mathit{S}{\mathit{C}}_{{\mathit{O}}_{\mathit{i}}}$, $\mathit{S}{\mathit{C}}_{{\mathit{S}}_{\mathit{i}}}$

In this step, the accuracy function is calculated based on the evaluation matrix aggregated in the first step and using the definition of (Şahin 2016) and is calculated as Equation 8. The accuracy functions for the optimistic (O), similarity (S), and pessimistic (D) indices are calculated. (8) $K(\tilde{a})=\frac{{\mu }^L+{\mu }^U(1-{\mu }^L-v^L)+{\mu }^U+{\mu }^L(1-{\mu }^U-v^U)}{2}$(8) Where K ($\tilde{\mathrm{a}}$) ∈ [0,1].

• Step 7: Calculation of the minimum allowable according to Equation 9:

The minimum allowable value is calculated based on the accuracy functions. (9) $L{W}_D=\beta \ast (W_S+W_O)/2$(9)

• Step 8: Calculation of λ

λ is calculated by solving the linear model in Equation 14: (10) $W_D(L{W}_D-1)+(L{W}_D\ast W_S\ast \lambda )+(L{W}_D\ast W_O\ast \lambda )=0$(10) Note: If in Equation 10, after calculation,$\lambda \le 1$, then $\lambda =1$ is considered.

• Step 9: Calculation of the initial dynamic weights of the O, S, and D.

The initial dynamic weights of the O, S, and D were calculated as Equation 11: (11) $\begin{array}{l}{W}_{O_i}(P)=(W_O\ast ({\lambda }^{S{C}_{O_i}})/((W_O\ast ({\lambda }^{S{C}_{O_i}})+(W_S\ast ({\lambda }^{S{C}_{S_i}})+W_D))))\\ W_{S_i}(P)=(W_S\ast ({\lambda }^{S{C}_{S_i}})/((W_O\ast ({\lambda }^{S{C}_{O_i}})+(W_S\ast ({\lambda }^{S{C}_{S_i}})+W_D))))\\ W_{D_i}(P)=1-W_{O_i}(P)-W_{S_i}(P)\end{array}$(11)

• Step 10: Calculation of the final dynamic weight

Outlined below are the final dynamic weights that correspond to the unique attributes of each equipment/failure mode configuration. The final dynamic weights are determined based on specific rules involving the initial dynamic weights and the pre-defined weights.

• If $W_{O_i}(P)\ge W_O$ and $W_{S_i}(P)\ge W_S$ Then $W_{O_i}(F)=W_{O_i}(P)$ and $W_{S_i}(F)=W_{O_i}(P)$ and $W_{D_i}(F)=W_{D_i}(P)$

• If $W_{O_i}(P)>W_O$ and $W_{S_i}(P)<W_S$ Then $W_{O_i}(F)=W_{O_i}(P)-(W_S-W_{S_i}(P))$ and $W_{S_i}(F)=W_S$ and $W_{D_i}(F)D_i=W_{D_i}(P)$

• If $W_{O_i}(P)<W_O$ and $W_{S_i}(P)S_i>W_S$ Then $W_{S_i}(F)=W_{S_i}(P)-(W_O-W_{O_i}(P))$ and $W_{O_i}(F)=W_O$ and $W_{D_i}(F)=W_{D_i}(P)$

• Step 11: Calculate the aggregate matrix

Suppose $\tilde{a}=[{\mu }_{\tilde{a}}^L,{\mu }_{\tilde{a}}^U],[v_{\tilde{a}}^L,v_{\tilde{a}}^U]$ and $\tilde{b}=[{\mu }_{\tilde{b}}^L,{\mu }_{\tilde{b}}^U],[v_{\tilde{b}}^L,v_{\tilde{b}}^U]$ are two intuitive fuzzy numbers with values of intervals and λ > 0, which are shown in Equation 12. The aggregate matrix is constructed by applying the final dynamic weights to the intuitionistic fuzzy values. (12) $\lambda \tilde{a}=[1-{(1-{\mu }_{\tilde{a}}^L)}^{\lambda },1-{(1-{\mu }_{\tilde{a}}^U)}^{\lambda }],[v{{}_{\tilde{a}}^L}^{\lambda },v{{}_{\tilde{a}}^U}^{\lambda }]$(12) To create a comprehensive weight evaluation matrix, the following strategy is implemented:

Data weights regarding the O metric are amalgamated according to the protocol detailed in Equation 13. (13) $W_{O_i}(F)\ast \tilde{a}=[1-{(1-{\mu }_{{\tilde{a}}_{\mathrm{ij}}}^L)}^{W_{O_i}(F)},1-{(1-{\mu }_{{\tilde{a}}_{\mathrm{ij}}}^U)}^{W_{O_i}(F)}],[{(v_{{\tilde{a}}_{\mathrm{ij}}}^L)}^{W_{O_i}(F)},{(v_{{\tilde{a}}_{\mathrm{ij}}}^U)}^{W_{O_i}(F)}]$(13) To aggregate the weight of the data related to the S index according to Equation 14: (14) $W_{S_i}(F)\ast \tilde{a}=[1-{(1-{\mu }_{{\tilde{a}}_{\mathrm{ij}}}^L)}^{W_{S_i}(F)},1-{(1-{\mu }_{{\tilde{a}}_{\mathrm{ij}}}^U)}^{W_{S_i}(F)}],[{(v_{{\tilde{a}}_{\mathrm{ij}}}^L)}^{W_{S_i}(F)},{(v_{{\tilde{a}}_{\mathrm{ij}}}^U)}^{W_{S_i}(F)}]$(14)

To aggregate the weight of the data related to index D according to Equation 15: (15) $W_{D_i}(F)\ast \tilde{a}=[1-{(1-{\mu }_{{\tilde{a}}_{\mathrm{ij}}}^L)}^{W_{D_i}(F)},1-{(1-{\mu }_{{\tilde{a}}_{\mathrm{ij}}}^U)}^{W_{D_i}(F)}],[{(v_{{\tilde{a}}_{\mathrm{ij}}}^L)}^{W_{D_i}(F)},{(v_{{\tilde{a}}_{\mathrm{ij}}}^U)}^{W_{D_i}(F)}]$(15)

• Step 12: Calculate the coefficients ${\tilde{\mathit{K}}}_{\mathit{j}}$and ${\tilde{\mathit{q}}}_{\mathit{j}}$

An intuitive fuzzy geometric operator with interval values (IVIG) is used to determine the coefficients ${\tilde{K}}_j$and ${\tilde{q}}_j$ (P. Liu and Qi 2014). Suppose $A=([{\mu }_{A_j}^L,{\mu }_{A_j}^U],[v_{A_j}^L,v_{A_j}^U])(j=1,2,\dots ,m)$ are a set of intuitive fuzzy numbers with values of intervals (IVIFNs) and $\mathrm{IVIG}:{\mathrm{\Omega }}^n\to \mathrm{\Omega }$ then IVIG value calculated as Equation 16: (16) $\begin{array}{rl}\text{IVIG}(A_{1,}{A}_{2,}\dots ,A_{m,})& =\left[\prod _{j=1}^m{({\mu }_{A_j}^L)}^{1/\text{m}},\prod _{j=1}^m{({\mu }_{A_j}^U)}^{1/\text{m}}\right],\\ & \left[1-\prod _{j=1}^m{(1-v_{A_j}^L)}^{1/\text{m}},1-\prod _{j=1}^m{(1-v_{A_j}^U)}^{1/\text{m}}\right]\end{array}$(16) So, we have: $\begin{array}{rl}{\tilde{K}}_j& =\{\begin{array}{ll}\tilde{1},& j=1\\ {\tilde{S}}_j+\tilde{1},& j>1\end{array}\end{array}$ $\begin{array}{rl}{\tilde{q}}_j& =\{\begin{array}{ll}\tilde{1},& j=1\\ {\displaystyle \frac{{\tilde{q}}_{j-1}}{{\tilde{K}}_j}},& j>1\end{array}\end{array}$

• Step 13: Calculate the relative weights

Here, the intuitive fuzzy Euclidean distance operator with interval values is used according to Equation 17. The relative weights are calculated using the Interval Valued Intuitionistic Fuzzy Euclidean Distance (IVIFED) operator.

Where: (17) $\begin{array}{rl}{\tilde{w}}_j& =\frac{{\tilde{q}}_j}{\sum {\tilde{q}}_j}\\ w_j& =\frac{(a^{L({\tilde{w}}_j)}+2a^{M({\tilde{w}}_j)}+a^{U({\tilde{w}}_j)})+(a^{{}^{\mathrm{\prime }}L({\tilde{w}}_j)}+2a^{M({\tilde{w}}_j)}+a^{{}^{\mathrm{\prime }}U({\tilde{w}}_j)})}{8}\end{array}$(17)

• Step 14: Determine the critical equipment/failure mode (s)

Finally, Equation 18 was used to rank equipment/failure modes. The critical equipment/failure modes are identified by comparing the Relative Priority Value (RPV) of each option with a hypothetical equipment/failure mode represented by the RPV. (18) $\mathrm{RP}{V}_j=\frac{1}{m}\ast \sum _{D=1}^m{w}_j$(18) The paper does not provide a clear explanation of the optimisation algorithm. The proposed algorithm appears to focus on the aspects of risk assessment and maintenance prioritisation but does not explicitly describe an optimisation algorithm. The optimisation may be implicit in the weight calculation and decision-making steps, but the details are not expressly provided in the information given. To solve this problem, further details on the optimisation algorithm would be needed, such as the specific objective function, constraints, and optimisation techniques used. Without these details, it is difficult to provide a comprehensive solution to the optimisation aspect of the problem.

Initially, expert consultations are utilised to define a principal boundary. This identified boundary is then incorporated into the computational framework as a hypothetical equipment/failure mode, facilitating a comparative analysis with other equipment/failure modes. Through this evaluative approach, a theoretical equipment/failure mode represented by $\mathrm{RP}{V}_j$ is discerned. After the calculation of $\mathrm{RP}{V}_j$, options that surpass the $\mathrm{RP}{V}_j$ value in the context of the theoretical equipment/failure scenario are recognised as critical equipment/failure modes. The first phase of the proposed algorithm focuses on weighting the FMEA parameters using an intuitionistic fuzzy approach. This involves normalising the preference values, calculating the backup degree to determine the power weight vector, and constructing a unified evaluation matrix using the Interval Valued Intuitionistic Fuzzy Prioritized Weighted Heronian Aggregation (IVIFPWHA) operator. The goal is to derive the dynamic weights for the optimistic (O), similarity (S), and pessimistic (D) indices, which capture the uncertain and dynamic nature of pipeline risk management.

The second phase utilises the IVIF-SWARA (Stepwise Weight Assessment Ratio Analysis) method to rank the failure modes. This approach allows for the flexible adjustment of the alignment of the pipeline instruments based on their criticality. By incorporating the IVIF-SWARA method, the researchers aim to streamline the hierarchical organisation of the pipeline equipment and develop a more targeted and nuanced maintenance strategy. The ranking of the failure modes guides the prioritisation of maintenance activities to address the most critical issues in the oil transfer pipeline system. These two phases, the intuitionistic fuzzy weighting of the FMEA parameters and the IVIF-SWARA-based ranking of failures, form the core of the proposed risk-based maintenance strategy for oil transfer pipelines, leveraging the strengths of both approaches to enhance pipeline reliability and safety.

4. Findings

Research conducted on the oil pipeline and telecommunication tools found in the nation's upper sector. The first step in this endeavour is to outline the relevant apparatus, resulting in a list of 25 items. A 20-person specialist panel was convened to collect the necessary data. Structured discussions were held to gather essential data, establish relevant metrics, and rank the identified apparatus.

Hesitant fuzzy preferred relations were employed along with the functionalities of Excel software to derive reliable metric weights. MATLAB software enabled the creation of a robust model for data analysis, guiding the systematic identification and categorisation of key and vulnerable tools as well as grading failure scenarios based on severity. During the project's inception, priority and crucial tools from the list of 25 were identified. A detailed report on each tool and its components was then crafted, identifying all possible malfunction scenarios. The Offshore Reliable Data Handbook (OREDA) was a key resource in spotting these malfunction scenarios. Expert consultations over several sessions helped refine the data, necessitating changes before finalising the list of malfunction scenarios.

To facilitate clear communication of data through the expert committee, the verbal variables presented in Table 3 were utilised. Tables labeled 4, O, S, and D provide details on each piece of apparatus under consideration.

Table 3. Linguistic variable and IVIF values (Liu, You, and Duan 2017).

Linguistic terms	IVIF scale
Absolutely high	[0.99,0.99],[0.01,0.01]
Extremely high	[0.90,0.90],[0.10,0.10]
Very high	[0.75,0.85],[0.05,0.15]
High	[0.60,0.75],[0.10,0.20]
Higher than average	[0.45,0.60],[0.15,0.25]
Average	[0.50,0.50],[0.50,0.50]
Lower than average	[0.35,0.45],[0.40,0.55]
Low	[0.25,0.35],[0.50,0.60]
Very low	[0.15,0.20],[0.60,0.75]
Extremely low	[0.10,0.10],[0.90,0.90]

Table 4. Experts panel opinion about equipment.

Equipment	O				S				D
Ruston Turbine	0.40	0.45	0.35	0.55	0.90	0.90	0.10	0.10	0.35	0.45	0.40	0.55
Diesel Generator	0.40	0.45	0.35	0.55	0.90	0.90	0.10	0.10	0.35	0.45	0.40	0.55
Compressor	0.40	0.45	0.50	0.55	0.50	0.50	0.50	0.50	0.50	0.50	0.50	0.50
Control Ball Valves	0.30	0.35	0.35	0.45	0.90	0.90	0.10	0.10	0.35	0.60	0.25	0.35
Filter	0.25	0.60	0.50	0.25	0.60	0.65	0.10	0.20	0.50	0.50	0.50	0.50
UG Storage	0.25	0.60	0.50	0.25	0.60	0.65	0.10	0.20	0.50	0.50	0.50	0.50
Storage Tanks	0.25	0.60	0.50	0.25	0.60	0.55	0.10	0.20	0.50	0.50	0.50	0.50
Flowmeter	0.15	0.60	0.50	0.25	0.60	0.55	0.10	0.20	0.50	0.50	0.50	0.50
Pressure Transmitter	0.50	0.50	0.15	0.50	0.35	0.35	0.50	0.60	0.15	0.60	0.60	0.65
Shut-down Switches	0.50	0.50	0.15	0.50	0.55	0.35	0.50	0.60	0.15	0.60	0.60	0.65
USP	0.50	0.50	0.15	0.50	0.25	0.60	0.60	0.75	0.15	0.60	0.60	0.55
PLC	0.50	0.50	0.15	0.50	0.15	0.60	0.60	0.75	0.15	0.60	0.60	0.55
Cold Cutter	0.50	0.25	0.35	0.60	0.35	0.25	0.50	0.60	0.35	0.25	0.50	0.65
Hot Tap	0.50	0.50	0.50	0.50	0.90	0.90	0.10	0.10	0.50	0.50	0.50	0.50
Paint and Metal Thickness Ms.	0.50	0.50	0.50	0.50	0.90	0.90	0.10	0.10	0.50	0.50	0.50	0.50
Movable & Fixed Cranes	0.50	0.50	0.50	0.50	0.25	0.35	0.50	0.60	0.50	0.50	0.50	0.50
Check-Valves	0.50	0.35	0.25	0.60	0.45	0.60	0.15	0.25	0.25	0.35	0.50	0.60
Line Break Valves	0.50	0.35	0.25	0.60	0.45	0.60	0.15	0.25	0.25	0.35	0.50	0.60
Metering Tools	0.15	0.60	0.45	0.25	0.25	0.35	0.50	0.60	0.45	0.60	0.15	0.35
Electromotor	0.50	0.35	0.25	0.60	0.90	0.90	0.10	0.10	0.25	0.35	0.50	0.60
Battery Bank	0.50	0.35	0.25	0.60	0.50	0.50	0.50	0.50	0.25	0.35	0.50	0.60
Cathodic Protection St.	0.50	0.35	0.25	0.60	0.50	0.50	0.50	0.50	0.25	0.35	0.50	0.60
Industrial Processor	0.50	0.35	0.25	0.60	0.50	0.50	0.50	0.50	0.25	0.35	0.50	0.60
Hot Line Telecom St.	0.50	0.35	0.25	0.60	0.50	0.50	0.50	0.50	0.25	0.35	0.50	0.60
Fire Fighting System	0.50	0.35	0.25	0.60	0.50	0.50	0.50	0.50	0.25	0.35	0.50	0.60

Given that the markers, denoted as O, S, and D, are exclusively designed to transmit useful data, the standardisation of the feedback grid has been deemed unnecessary. Working on this foundation, the next critical step involves identifying the properties of $S{C}_{O_i}$. In the quartet phase, the creation of a potency weight vector is brought to the forefront, requiring thoughtful deliberation. The process evolves further during the quintet stage, wherein a comprehensive appraisal grid is established using the interval-valued intuitionistic fuzzy power weight heronian aggregation (IVIFPWHA). At this point, there exists the possibility of inferring the variable weights associated with the conditions captured within the intuitive fuzzy framework featuring interval values. To achieve this goal, a well-defined series of steps has been pursued, beginning with the primary step of setting up the precision functions denoted as $S{C}_{O_i}$ and $S{C}_{S_i}$. These functions hold intrinsic connections to the potential malfunctions of individual apparatus and the subsequent impacts of such failures, playing a critical role in the overall evaluation matrix.

Moving to the following phase, the β value is designated to be 0.25. Following this establishment, the final dynamic weights are determined in harmony with the conditions outlined by the O, S, and D indicators. The procedure culminates in the allocation of risk hierarchies for each equipment unit, utilising the IVIF-SWARA method. It is noteworthy that the extensive computational needs have necessitated the exclusion of detailed tables, reserving space only for the final summary presentation in the form of Table 5.

Table 5. Results of IVIF-SWARA method.

Item	Equipment	${\tilde{w}}_j$	Rank
1	Ruston Turbine	0.411732	1
2	Diesel Generator	0.411732	1
3	Compressor	0.411732	1
4	Control Ball Valves	0.411732	1
5	Filter	0.409589	2
6	UG Storage	0.409589	2
7	Storage Tanks	0.393084	3
8	Flowmeter	0.362013	4
9	Pressure Transmitter	0.348189	5
10	Shut-down Switches	0.341574	6
11	USP	0.341574	6
12	PLC	0.326368	7
13	Cold Cutter	0.193682	9
14	Hot Tap	0.099596	10
15	Paint and Metal Thickness Ms.	0.046745	11
16	Movable & Fixed Cranes	0.046745	11
17	Check-Valves	0.046745	11
18	Line Break Valves	0.046745	11
19	Metering Tools	0.046745	11
20	Electromotor	0.046745	11
21	Battery Bank	0.046745	11
22	Cathodic Protection St.	0.01134	12
23	Industrial Processor	0.01134	12
24	Hot Line Telecom St.	−0.01921	13
25	Fire Fighting System	−0.01921	13

5. Discussion

In the present study, the procedure commenced with the definition of static weights essential for the hierarchy creation process. The formulation of these weights for the O, S, and D indicators relied heavily on a hypothetical scenario in which machinery is optimised to its utmost potential, minimising the possibilities of failure and its associated consequences. This conjecture presupposes minimal chances of both malfunction and failure evasion. Expert opinions were sought to extrapolate weights for the indicators under this theoretical framework.

Following this, an advanced version of the HFPR strategy was implemented over three distinct phases to precisely determine the fixed weights for the three central elements: the severity of failure (S), the occurrence of failure (O), and failure detection (D). The computational process resulted in the derivation of the following values: $\begin{array}{l}{W}_O=0.35\\ W_S=0.425\\ W_D=0.245\end{array}$A challenge then arises from the potential varying influences that O, S, and D could have on individual equipment malfunctions. Contrary to traditional approaches that consider a standardised impact of these indicators in various contexts (Karmignani 2009), this research proposes a dynamic weight allocation model founded on an intuitive fuzzy context delineated by interval values. This innovative structure permits the customisation of weights to suit individual machinery and their respective failure scenarios, providing a nuanced approach to understanding the diverse effects of the O, S, and D indicators on the ranking process. Implementing this dynamic weight allocation model within the larger ranking schema allowed for the identification of both initial and final dynamic weights. In congruence with the operational conditions and the unique attributes of the equipment under study, eight primary categories were identified. The Reston turbine stood out as the most critical element, prompting the development of a mathematical model to enhance maintenance optimisation strategies for this particular mechanism.

Engaging in meticulous risk analysis is a taxing venture, especially considering the prevailing ambiguity and differing viewpoints among FMEA team members, a complication underscored in previous research (Wang, Liu, and Quan 2016). Moreover, experts frequently struggle to provide assessments that accurately reflect real situations (P. Liu 2017). There is a consensus about the arduous nature of detailed risk component evaluations in existing literature (Hua Zhao et al. 2017). While static metrics are commonly used to estimate the risks associated with various failure scenarios, pinpointing exact values proves to be a formidable, potentially unachievable task (Huang, Li, and Liu 2017).

To overcome this significant hurdle, there is a pressing need to integrate fuzzy data into the decision-making process, a methodology praised for skilfully maneuvering through uncertainties and data ambiguities to facilitate proficient risk assessment (Garg 2016). Utilising fuzzy set theory makes it possible to develop decision structures that embrace unclear data, thereby yielding flexibility better suited to the intricate dynamics of real-world settings compared to inflexible decision models (Rodríguez et al. 2016). This theory has birthed various extensions, including intuitive fuzzy sets (K. T. Atanassov 1986), intuitive fuzzy sets with interval values (K. Atanassov and Gargov 1989), and hesitant fuzzy sets (Tora 2010). These developments, grounded in the fundamental fuzzy sets, have significantly influenced decision-making paradigms, encapsulating unclear and imprecise data in a wide range of research endeavours (Alma’amun et al. 2018; P. Liu 2017; P. Liu and Qi 2014; Pamučar and Ćirović 2015; Rodríguez et al. 2016; Tora 2010; Zhang, Wang, and Tian 2015), thereby enabling a more refined and accurate portrayal of unreliable data sources (Tora 2010).

Emerging prominently in this domain are intuitive fuzzy sets characterised by interval values, holding a reputation for offering an enhanced representation of fuzzy data compared to other approaches. This method is experiencing a growing endorsement and adoption in the academic sphere (H. C. Liu, You, and Duan 2017). Given this, the current study leverages intuitive fuzzy data delineated by interval values for the crucial task of identifying critical equipment. This strategic choice substantially alleviates uncertainties inherent in raw data, showcasing the merits of applying intuitive fuzzy data paired with underlying interval values. In decision-making landscapes, the role of weighting is pivotal, as a surge in the evolution of techniques and complex preferential relationships has been seen in recent years. These relationships primarily rely on preference values conceived by experts, who use a structured scale to outline their interpretations of object pairs, thereby facilitating crucial information representation (Zhang, Wang, and Tian 2015). The utility of fuzzy preferential relations in decision-making processes is a well-documented phenomenon (Zhu and Xu 2013). Yet, these structured approaches falter when faced with scenarios wherein experts, restricted by time and knowledge constraints, articulate preferences through a spectrum of potential numerical expressions. They fall short in accurately reflecting situations where two sources of ambiguity appear concurrently during the evaluation of option pairs (Zhang, Wang, and Tian 2015). To remedy this, Zhu and Xu (2013) introduced hesitant fuzzy preferential relations (HFPR), providing a renewed lens through which to understand preferential dynamics. By harnessing the adaptive nature of HFPR, this study aims to identify the initial weightings of the various available options. The HFPR framework is particularly effective in situations punctuated by incomplete information on the key indicators – O, S, and D – sidestepping two major drawbacks commonly encountered during expert consultations:

1. The inclination for decision-makers to harbour biases, which can result in overestimated or underestimated value judgments concerning the options.

2. The proclivity to consider the inherent correlations in objective data is a practice spotlighted in previous studies (P. Liu 2017).

6. Conclusion

In conclusion, this study presents a comprehensive RBM strategy for oil transfer pipelines using an IFCA. The proposed framework addresses the dynamic and uncertain nature of pipeline risk management by employing FMEA to identify critical failure scenarios. The research leverages the IVIF environment and the IVIF-SWARA method to streamline the hierarchical organisation of pipeline instruments and derive flexible, context-sensitive maintenance priorities. The developed intuitionistic fuzzy risk assessment model, optimisation algorithm, and decision support system work in tandem to enhance pipeline reliability and mitigate the risks associated with pipeline failures. By incorporating the strengths of IFCA and addressing the specific challenges of oil transfer pipelines, this study contributes to the advancement of pipeline maintenance and risk management practices, providing a robust and adaptable strategy for operators to ensure the safe and efficient operation of their critical infrastructure.

Given the outcomes realised, it becomes imperative to offer the following actionable insights: Following the meticulous research carried out in the study pertaining to risk-based net planning, a set of considered recommendations are presented to foster the advancement of the efficiency and precision of both maintenance planning and risk assessment protocols. Here, we delineate the proposed suggestions:

1. Database creation for indicator monitoring: It is advocated that the Oil Pipelines and Operations Company initiate the development of a database within its mechanised net system. Transitioning to an approach grounded in objective data, rather than relying solely on expert assessments, promises to yield more reliable and precise outputs in the realm of equipment risk-based net planning.

2. Implementation of maintenance strategies: Leveraging the discernments derived from the prioritisation analysis of equipment and failure modes, it is imperative to craft and implement appropriate maintenance strategies for each delineated failure mode. The initiative calls upon the Oil Pipelines and Telecommunication Company to assimilate these strategies into its prevailing maintenance and repair planning blueprint. Moreover, committing to periodic reassessments grounded on the designated evaluative indicators and methodology expounded in this study would engender a sustainable trajectory of enhancement in system maintenance planning for prospective undertakings.

Exploration of Alternate Weight Calculation Approaches: While this investigation employed the IVIF approach to ascertain the weightings of static indices, it remains prudent to survey alternative approaches in the forthcoming period. This could encompass harnessing intuitive fuzzy preferential relations for fixed weight computations, facilitating subsequent comparative scrutiny juxtaposed with this study's revelations. Furthermore, given the productive deployment of the combined IVIF-SWARA technique in the terminal phase of equipment prioritisation, other potent techniques, such as the TOPSIS method, might find a suitable application environment within an intuitive fuzzy milieu outfitted with interval values, thereby facilitating a meaningful comparative review with the findings of this research.

Opting for a refined approach, this investigation utilises the IVIF operator to address both of the aforementioned issues. This approach fosters the integration of relationships between intuitive fuzzy elements and intertwined interleave values, reducing the impact of irrational data inputs from decision-makers while embracing the harmonious interplay of objective data nuances. Therefore, merging intuitive fuzzy data characterised by interval values with hesitant fuzzy preferential relations and their accompanying theoretical frameworks affords the researcher a robust instrument to significantly reduce uncertainties surrounding raw data.

To further illustrate the fiscal impacts of merging high-quality process control with cost-effective preventive maintenance strategies, a case study utilising compressor equipment – a critical component in oil pipeline and telecommunication infrastructure – was employed. Moreover, the research engaged in a comparative evaluation between the integrated and isolated models through a numerical example, highlighting a considerable reduction in total costs, thus emphasising the superiority of the integrated approach over isolated strategies.

Disclosure statement

No potential conflict of interest was reported by the author(s).