AN INTEGRATED FUZZY APPROACH FOR DETERMINING ENGINEERING CHARACTERISTICS IN CONCRETE INDUSTRY

Abstract

This paper deals with the modeling of conceptual knowledge to capture the major customer requirements effectively and to transform these requirements systematically into the relevant design requirements. Quality Function Deployment (QFD) is a well-known planning and problem-solving tool for translating customer needs (CNs) into the engineering characteristics (ECs) and can be employed for this modeling. In this study, an integrated methodology is presented to rank ECs for implementing QFD in a fuzzy environment. The proposed methodology uses fuzzy weighted average method as a fuzzy group decision making approach to fuse multiple preference rankings for determining the weights of the customer needs. It adopts a fuzzy Analytic Network Process (ANP) approach which enables the consideration of inner dependencies in a cluster as well as the interdependencies between the clusters to determine the importance of ECs. The proposed approach is illustrated through a case study in ready-mixed concrete industry.

INTRODUCTION

Manufacturing industries need to introduce new products or a new version of an existing product at minimum cost with a short lead time in order to cope with intense competition in global markets. In a highly competitive environment, the customer oriented production encompasses a lot of comprehensive activities from idea generation to final product's constitution and considers not only a valuable technological knowledge but also an effective quality management system. Quality Function Deployment (QFD) is an effective quality system aimed at satisfying the customers. It has been an important tool that is applied in many industries (Raharjo et al. 2008; Karsak and Ozogul 2009; Celik et al. 2009; Kuijt-Evers et al. 2009; Ahmed and Amagoh 2010; Sweet et al. 2010), since many years however only a few researchers addressed its use in construction industry. Some of the applications include the determination of design characteristics of internal layouts of building apartments, the construction design of low-cost housing and the processing of customer requirements (Mallon and Mulligan 1993; Serpell and Wanger 1994; Rhman et al. 1999; Kamara and Anumba 1999).

In this study, QFD is implemented to translate the customer needs for plasticizers used in concrete, into engineering characteristics (ECs). The customer requirements for plasticizers are rapidly changing that, the need for a systematic tool like QFD is inevitable to reflect these changes to the ECs in a timely manner. Some researchers used ANP to take into account the inner-relationship and interrelationship among the CRs and ECs in QFD (Karsak et al. 2002; Partovi and Corredoira 2002). Analytic Network Process (ANP) is a powerful approach that includes all the possible relations among all the parameters in a product development which considers not only the interdependencies between customer needs and engineering characteristics but also the inner dependencies among the customer requirements and among the engineering characteristics.

It is important to note that in QFD most of input variables are considered to be inherently vague and ambiguous, for this reason, this situation presents a special challenge to the effective calculation of the importance of ECs. In general, CNs that are expressed by subjective and qualitative terms should be translated into ECs. Fuzzy approach developed by Zadeh (1965) is particularly useful to translate linguistic variables expressed by the customers or experts into fuzzy numbers. In the literature, several researchers employed QFD together with the fuzzy approach. Chen and Ngai (2008) propose a novel fuzzy-QFD program modeling approach to complex product planning which integrates fuzzy set theory and QFD framework in order to optimize the values of engineering characteristics by considering the design uncertainty and financial considerations. Jia and Bai (2010) use QFD for manufacturing strategy development and integrate fuzzy set theory and house of quality, to capture the imprecision and vagueness of decision-relevant inputs and to facilitate the analysis of decision- relevant QFD information.

Some of the studies have extended the use of ANP by employing linguistic parameters to consider impreciseness and vagueness present in QFD. Büyüközkan et al. (2004) proposed a fuzzy ANP model to determine the importance for the design requirements. Ertay et al. (2005) used linguistic data as the input for the QFD process and prioritized ECs based on the fuzzy ANP approach and illustrated the proposed approach in automotive industry. Kahraman et al. (2006) developed an integrated fuzzy ANP approach to determine the importance of ECs in product design based on both fuzzy QFD and fuzzy optimization models. The application is illustrated via a PVC window system producer. In another work, an advanced QFD model based on fuzzy analytic network process is proposed by Liu and Wang (2010) to take into account the interrelationship between and within the components of QFD.

In this study, we consider a Fuzzy ANP approach in which CNs in QFD is converted into ECs by pairwise comparison matrices. We also show how the importance of CNs can be expressed by using fuzzy set theory and then we employ a group decision making technique in which the prioritization of CNs is realized by aggregating multiple expressions in a fuzzy environment.

To the best of our knowledge, this work will be the first attempt to manage the problem of new product development in concrete industry by using an integrated methodology which includes fusion algorithms and a fuzzy ANP.

The rest of the paper is organized as follows. The next section gives a preliminary in construction industry. In QFD Literature Review and Ready–Mixed Concrete Industry section, a brief literature review on QFD is provided and the importance of QFD in construction industry is discussed. The proposed methodology is explained in the Proposed Methodology section. Then, we provide a case study in the concrete industry to illustrate the proposed methodology. We conclude and outline the future research in the Discussions and Concluding Remarks section.

PRELIMINARY

In recent years, construction industry is gaining more importance particularly in countries located on an earthquake risk belt, including Turkey. In earthquake-zones, not only the soil quality but also the construction quality is significant. In some cases, soil properties can be adequate to construct durable buildings, whereas construction quality may be insufficient to allow the endurance against destructive earthquakes. Hence, it is indispensable to respect not only the soil properties where the building is located, but also the construction of the building itself. Construction quality is contingent upon the sufficiency of the construction procedure, upon the quality of the chosen materials and equipments, and upon the labor quality all of which can be assured by means of continuous audits. Among these factors, the quality of concrete as the primal material of reinforced concrete buildings has a primary effect on the construction industry.

Concrete is a mixture of cement paste and aggregates. Cement paste being composed of cement and water coats the surface of fine and coarse aggregates which are inert granular materials such as sand, gravel, and crushed stone. Through chemical reaction called hydration, cement paste congeals and gains strength to be transformed into concrete. Chemical admixtures are the ingredients in concrete other than cement paste and aggregates which are added to the mixture of cement paste either in the concrete mixture station or in the construction site. Plasticizers as one of the admixtures are linear polymers containing sulfuric acid groups attached to the polymer at regular intervals. They can be added to concrete to increase viscosity and strength. The effect of plasticizers continues only 30 to 60 minutes depending on the properties and dosage rate, and the process is followed by a rapid loss in employability (Atac et al. 2003).

Creating concrete with high quality is important such that the quality of its ingredients such as aggregates and plasticizers should comply with quality standards. Therefore, several quality standards such as ISO 9001, OHSAS, ISO 14001 and Quality function deployment (QFD) have been implemented in civil engineering projects. The more detailed information about these subjects is given in the following section.

QFD LITERATURE REVIEW AND READY-MIXED CONCRETE INDUSTRY

The roots of quality function deployment (QFD) go back to the late 1960s. Akao (1990) defined QFD as “a method for developing a design quality aimed at satisfying the customer and then deploying (translating) the consumer's demands into design targets and major quality assurance points to be used throughout the production phase.” Since 1990s till today, many firms operating in different industries had adapted QFD for their products and service development. Akao reported that QFD was most frequently used in the automotive, electronics and aerospace industry (Akao 1990).

In recent years, there have been also some applications in construction industry. Kamara et al.(1999, 2000) and Kamara and Anumba (2001) proposed a computerized model to be used in construction industry which incorporates Client Requirements Processing Model (CPRM) as a tool to facilitate the systematic definition, analysis and mapping of client requirements to design specifications in a collaborative and concurrent manner. Arditi and Lee (2003) proposed a QFD model to measure the corporate service quality of Design/Build (D/B) firms to be evaluated by construction owners, while Pheng and Yeap (2001) provided a study to assess the awareness of QFD methodology and to highlight the benefits of QFD approach in D/B contracts. In their study, Eldin et al. (2003) involved the preparation of a conceptual design for a modern large-size classroom for college students. Ahmed et al.(2003) proposed a model to be used in civil engineering capital project planning process in design stage. Yang et al. (2003) developed a fuzzy QFD system to support buildable design decision making. Dikmen et al. (2005) proposed to use the QFD system further after the construction stage as a decision-making tool during marketing. In another research, Malekly et al. (2010) integrated QFD with the TOPSIS method in a fuzzified decision making process for bridge superstructure design. Luu et al. (2010) used QFD to improve the basic layout and basic specifications of middle-grade apartment project in Vietnam.

Besides some implementations of the QFD approach in some stages of the construction, none of the implementations in the literature have concentrated on the quality of concrete or its ingredients, i.e., concrete additives such as plasticizers used in concrete. Therefore, there exists a gap in the literature in determining the impact of construction chemicals in reinforcement of concrete.

It is important to handle rigorously the problems of reinforced concrete in ready mixed concrete industry. This study presents a novel approach to apply the QFD method to plasticizers production used in concrete in order to enable their production according to the rapidly changing demands of customers, namely ready-mixed concrete producers. The proposed methodology can be used as a cross-functional planning tool to help the plasticizer development team.

PROPOSED METHODOLOGY

The proposed methodology to determine the overall priorities of the ECs is composed of three main stages: Questionnaire Survey, Fusion Algorithm and Fuzzy ANP. The schematic representation of the proposed methodology is illustrated in Figure 1.

FIGURE 1 The schematic representation of the proposed methodology.

Stage 1. Questionnaire Survey

We suppose that there are a group of experts, E = {E ₁, E ₂, … , E _m }, in other words, customers of plasticizers firms that produce concrete, provide fuzzy opinions about a set of requirements, χ = {x ₁, x₂, x ₃, ……… x _n }, and the importance of CNs is determined according to questions in survey analysis . The experts' individual preferences for the determination of importance values of CNs are expressed as fuzzy triangular numbers such that h = {h _i , i = 1,2, …… 5} where h ₁ = partly important h ₂ =partly more important, h ₃ = important, h ₄ = very important, and h ₅ = extremely important. Linguistic scales for CN importance values are shown in Table 1. The membership function representation of triangular fuzzy numbers for each linguistic scale is provided in Figure 2.

FIGURE 2 Triangular fuzzy numbers.

TABLE 1 Linguistic Scales for CN Importance Values

Linguistic scale for importance	Triangular fuzzy scale	Triangular fuzzy reciprocal scale
Partly important	(1,2,3)	(1/3, 1/2, 1)
Partly more important	(2,3,4)	(1/4, 1/3, 1/2)
Important	(3,4,5)	(1/5, 1/4, 1/3)
Very important	(4,5,6)	(1/6, 1/5, 1/4)
Extremely important	(5,6,7)	(1/7, 1/6, 1/5)

Stage 2. Fusion Algorithm: Determining the Importance Values of CNs (ω₁)

In the Questionnaire Survey, the experts express their fuzzy opinions about the importance values of CNs using linguistic terms. In this stage, the experts' individual preferences are combined into a group collective one by using Chen's (1998) fusion algorithm which is based on the method of Hsu and Chen (1996).

The steps of the Chen's (1998) fusion algorithm can be summarized as follows. The interested reader can refer to Chen (1998) and Olcer and Odabasi (2005) for more details.

Step 1: Assume that R _k denotes the fuzzy opinion of expert E _k . Let R _k  = (a _k , b _k , c _k ) be a triangular fuzzy number given by expert k to represent the importance value of a CN with respect to a subjective attribute. Then the standardized form of the fuzzy number R _k can be obtained as follows:

where and y is the maximum value of non-standardized triangular fuzzy numbers given by experts for the same attribute.

Step 2: Assume that the degree of importance of expert E_k (k = 1,2,…,M) is we _k , where we _k  ∈ [0,1] and .

In situations where the relative importance of experts is widely different for each attribute of the problem, the weight of each expert is taken into consideration. Firstly, the most important expert is selected among experts and a value of one is assigned to him/her, i.e., re _k  = 1. Then, the lth expert is compared with the most important expert and a relative weight for the lth expert re _l is obtained. Therefore, the max{re ₁ , re ₂ , … , re _M } = 1 and min{re ₁ , re ₂ , … , re _M } > 0 and the degree of importance we _k is defined as follows:

Step 3: Calculate the degree of similarity of the opinions between each pair of experts E _u and E _v , where  ∈ [0,1], 1 ≤ u ≤ M, 1 ≤ v ≤ M, and u ≠ v. The degree of similarity between each pair of experts E _u and E _v is calculated as follows:

Let A and B be two standardized triangular fuzzy number, A = (a ₁ ,a ₂ , a ₃ ) and B = (b ₁ ,b ₂ , b ₃ ) where 0 ≤ a ₁  ≤ a ₂  ≤ a ₃  ≤ 1 and 0 ≤ b ₁  ≤ b ₂  ≤ b ₃  ≤ 1. Then, the degree of similarity between the standardized triangular fuzzy numbers A and B can be measured by the similarity function S,

where S(A,B) ∈ [0,1].

Step 4: Construct the agreement matrix (AM), after all the similarity degrees between experts are measured.

where , if u ≠ v and S _uv  = 1, if u = v.

Step 5: After calculating the degrees of similarity , the average degree of consensus AA(E _u ) of expert E _u (u = 1,2, … , M) and the relative degree of consensus RA(E _u ) of each expert E _u can be defined as follows:

Step 6: In this step, the consensus degree coefficient CC(Eu) of expert Eu (u = 1,2,…,M) is calculated by combining the weight of the opinion of expert Eu (u = 1,2,…,M) with the relative average degree of consensus RA(E_u) as follows:

where β (0 ≤ β ≤ 1) is a relaxation factor. When β = 0, a homogenenous group of experts problem is considered.

Step 7: The aggregation result of the fuzzy opinions R_AG is obtained as follows:

where operators ⊗ and ⊕ are the fuzzy multiplication operator and the fuzzy addition operator, respectively. The fuzzy multiplication and addition of triangular fuzzy numbers are also triangular fuzzy numbers. Therefore, these fuzzy numbers should be converted into the crisp importance values by using Chang's Extent Analysis (Chang 1996). The detailed information about Chang's Extent Analysis will be given in the next section.

Stage 3. Fuzzy ANP Approach for Translating CNs into ECs

This stage is based on determining both the relationship between CNs and ECs, and the correlation among CNs and the correlation among ECs. ANP is a process in which inner dependencies within clusters are taken into consideration as well as the interdependencies among clusters. From a general point of view, ANP consists of two stages: the first one is the construction of the network, and the second is the calculation of the priorities of the elements. In order to construct the structure of the problem, all of the interactions among the elements should be considered. When the elements of a component Y depend on another component X, we represent this relation with an arrow from component X to Y. All of these relations are evaluated by pairwise comparisons and a supermatrix, which is a matrix of influence among the elements, is obtained by these priority vectors. The supermatrix is raised to limiting powers to calculate the overall priorities, and thus the cumulative influence of each element on every other element with which it interacts, is obtained.

The general principle of ANP as a representation of QFD can be illustrated graphically in a way that the inner dependencies within “criteria” and “alternatives” clusters can be indicated with a looped arc and the inter dependencies between the two clusters can be indicated with a directed arc as in Figure 3.

FIGURE 3 The analytic network process representation of quality function deployment.

When a network embraces only two clusters as in the case of QFD, namely CNs and ECs, then the matrix manipulation approach, in other words, the supermatrix of a hierarchy is as follows:

where ω₁, which has already been determined in stage 2, is a vector on the CNs that represents the impact of the goal. W ₂ is a matrix that includes the impact of the CNs on each of the ECs. W ₃ and W ₄ are the matrices that represent the inner dependencies among the CNs and among the ECs, respectively. Here “impact” denotes the potential of the ECs to satisfy the requirements implicitly in each of the CNs and in a similar way for the CNs in terms of the goal. The calculation details of these matrices are provided in Ertay et al. (2005).

In order to calculate W ₂, W ₃, and W ₄ values, Fuzzy AHP (Analytic Hierarchy Process) technique can be used. Besides, there are various types of fuzzy AHP in the literature. Among them, Chang's (1996) extent analysis will be opted for the study because of its simplicity compared to other fuzzy AHP approaches. In this study, triangular fuzzy numbers are used to build pairwise comparison matrices for ANP to improve the quality of responsiveness to CNs and ECs. The steps of Chang's extent analysis [see, (Chang, 1996)] are as follows.

Let X = {x ₁ ,x ₂ ,…,x _n } be an object set, and U = {u ₁ ,u ₂ ,…,u _m } be a goal set. According to the method of Chang's (1992) extent analysis, each object is taken and extent analysis for each goal, g _i , is performed, respectively. Therefore, m extent analysis values for each object can be obtained, with the following signs:

Step 1: The value of fuzzy synthetic extent with respect to the ith object is computed with

where every represents the extent analysis of ith object for m goals, j = 1,2, … …… m.

If we consider only two fuzzy numbers such as M ₁ = (l ₁, m ₁, u ₁) and M ₂ = (l ₂, m ₂, u ₂), then the following operational laws are to be performed to obtain S _i :

Step 2: The degree of possibility of M ₂ ≥ M ₁ is defined as:

To compare M ₁ and M ₂, both V(M ₁ ≥ M ₂) and V(M ₂ ≥ M ₁) values are to be computed.

Step 3: The degree possibility for a convex fuzzy number to be greater than k convex fuzzy numbers M _i (i = 1, 2, ……… , k) can be defined as:

When we assume that

Then the weight vector is given by:

where A_i(i = 1,2,…,n) are elements

Step 4: Via normalization, the normalized weight vectors are obtained as:

where W is a nonfuzzy number.

Finally, The crisp results of W₂, W₃ and W₄ are determined using Chang's extent analysis. Later we obtain the interdependent priorities of the CNs, w_c = W₃ ∗ w₁ and the interdependent priorities of the ECs, W_A = W₄ ∗ W₂. The overall priorities of the ECs are obtained as follows: w^ANP = W_A∗w_c.

A CASE STUDY IN READY-MIXED CONCRETE INDUSTRY

In our case study, in order to identify the CNs regarding plasticizer production, we interview with three Turkish leading concrete firms, which are the main customers of the company Degussa which provides construction chemicals to these leading concrete firms. CNs are identified as Water Reduction (WR), Water Disgorgement (WD), Early High Resistance (EHR); Dosage (D), Consistency (CON); Placing, Vibrating Leveling (PVL); Aggregates (A); Segregation (S); Flash Point (FP); Viscosity (V); Compatibility of Concrete and Steel (CCS); Endurance of the Concrete Against Temperature (ECAT); Watering Frequency (WF); Shrinkage and Cracking (SC). For confidential purposes, in this paper, the names of the three concrete firms will be represented by letters A, B and C, respectively. ECs considered in this study are determined after interviewing with the experts of Degussa. These are Optimal Cement Quantity (OCQ); Loss of Consistency (LOC); Corrosion (CO); Liquidity (LI); Water Reduction (WR); Freezing Point (FrP); Specific Gravity (SG); Mineral Mixtures (MM); Chlorine (CH); Usability in Different Types of Cement (UDTC).

In order to acquire “Voice of Customer”, a survey has been prepared and these firms were asked to fill out the survey, which is given Table 2.

TABLE 2 Survey to Acquire “Voice of Customer”

Questionnaire	Partly important	Partly more important	Important	Very important	Extremely important
1. How important is proportion of water reduction required for especially residential buildings?	□	□	□	□	□
2. How important is the realization of the fact that the consistency of the concrete be preserved.	□	□	□	□	□
3. How important is that the flash point is under the acceptable levels?	□	□	□	□	□
4. How important is the early high resistance?	□	□	□	□	□
5. How important is for you the fact that the concrete is very viscose?	□	□	□	□	□
6. How important is the quantity of the plasticizers for the segregation?	□	□	□	□	□
7. How important is the dosage of the cement for the concrete quality?	□	□	□	□	□
8. How important is for the prospective plasticizers to provide the compatibility of the concrete with the steel?	□	□	□	□	□
9. The quality of the aggregates for the concrete quality is crucial. For the prospective concrete, what do you think about the contributions of the plasticizers to solve the problems related to the quality problems of the aggregates?	□	□	□	□	□
10. How important is the reduction of the need for watering, especially important for the concrete quality?	□	□	□	□	□
11. What do you think about the contributions of the plasticizers for the reduction of shrinkage and cracking?	□	□	□	□	□
12. How important is the contribution of the plasticizers in the preventation of water-disgorgement?	□	□	□	□	□
13. What do you think about the contribution of the plasticizers to the easy implementation of placing, vibrating, and leveling?	□	□	□	□	□
14. What do you think about the contribution of the plasticizers related to the endurance of the concrete to the temperature?	□	□	□	□	□

According to the survey conducted above, for example, when the importance of Early High Resistance (EHR) is asked to ready-mixed concrete firms, all of the answers were given as “very important.” Since the firms interviewed had different views, the linguistic terms which represent the importance values of CNs differ from firm to firm. Therefore, it is necessary to aggregate these importance values by using a fusion algorithm. The example below illustrates step by step how the fusion algorithm can help to aggregate importance values of the fourth customer need “Early High Resistance (EHR)”.

Step 1: The answers of the three concrete firms for the fourth question related to the importance of the customer need “Early High Resistance (EHR)” were “Very Important”, “Important” and “Extremely Important”, respectively, which can be represented by generalized fuzzy numbers

If we translate each generalized fuzzy number representing the linguistic opinions of customers into standardized triangular fuzzy numbers

Step 2: To obtain the degree of importance of concrete firms, the most important concrete firm is selected and a value of one is assigned to it, i.e., re _k  = 1 by the experts of Degussa. Then, the 2nd and 3rd firms are compared with the most important firm and relative weights for these firms re ₂ and re ₃ are obtained as 0.6 and 0.4, respectively. Therefore, the degree of importance we ₁ , we ₂ and we ₃ are determined based on equation (2) as follows:

Step 3: In order to compute the average consensus and the relative average degree of consensus among the three participants, pairwise similarity degrees have to be calculated based on the opinions between each pair of experts.

Step 4: After calculating the degrees of similarity, the average degree of consensus AA(E _u ) of expert E _u (u = 1,2, … ,M) and the relative degree of consensus RA(E _u ) of each expert E _u are obtained as follows:

Step 5: In order to take the relative average degree of consensus among the three participants into account, we assume that β = 0.80. In this way, the relative weights of the experts are smoothed in some extent with regard to their relative average consensus degrees. The consensus degree coefficient CC(E _u ) of expert E _u (u = 1,2, … ,M) is calculated as follows;

Step 6: The fusion result of the three linguistic opinions of each customer for the first question in survey is obtained by using the consensus degree coefficients as follows:

Finally, the calculation results for each question in the survey are given in Table 3.

TABLE 3 Aggregation Results Based on Chen's (1998) Fusion Algorithm

Customer needs	Triangular fuzzy number
Water reduction(WR)	0,571	0,714	0,857
Consistency (CON)	0,505	0,648	0,791
Flash point (FP)	0,460	0,603	0,746
Early hirResistance (EHR)	0,560	0,703	0,846
Viscosity (V)	0,603	0,746	0,889
Segregation (S)	0,560	0,703	0,846
Dosage (D)	0,540	0,682	0,825
Compatibility of concrete and steel (CCS)	0,615	0,758	0,900
Aggregates (A)	0,486	0,629	0,772
Watering frequency (WF)	0,560	0,703	0,846
Shrinkage and cracking (SC)	0,603	0,746	0,889
Water-Disgorgement (WD)	0,505	0,648	0,791
Placing, vibrating, leveling (PVL)	0,571	0,714	0,857
Endurance of concrete against temperature (ECAT)	0,305	0,448	0,590

After obtaining the aggregated results for each question in the survey by Chen's(1998) fusion algorithm, Chang's Extent Analysis is applied to determine the importance weights of the customer needs. The results are represented by vector w ₁ .

Assuming that there is no inner dependence among the ECs, they are compared with respect to each CN yielding the column eigenvectors of W ₂. Hence, ECs will be determined to be equivalent to the CNs considering the technological possibilities and peculiarities of the plasticizer producer company (Degussa) as related to how to procure the CNs. For example, one of the possible questions for determining the relative importance of the ECs for “Water Reduction (WR)” can be as follows: “What is the relative importance of Loss of Consistency (LOC) when compared to Flash Point (FP) with respect to WR?” which yields “Very Important” as answer. For the purpose of brevity, the details of the pairwise comparison matrices were not discussed in this paper.

The general crisp results of W ₂ are as follows in Table 4.

TABLE 4 The Matrix Related to the Importance Degrees of ECs with Respect to Each CN

W2	WR	CON	FP	EHR	V	S	D	CCS	A	WF	SC	WD	PVL	ECAT
WR	0.321	0.284	0.294	0.307	0.280	0.245	0.253	0	0.245	0.376	0.371	0.336	0.121	0.074
CH	0	0	0.079	0	0	0.219	0	0	0.219	0.005	0	0.262	0	0.013
OCQ	0.112	0.263	0.157	0.275	0.194	0.189	0.479	0.264	0.189	0.273	0.268	0.221	0.134	0.285
UDT	0	0	0	0	0	0.155	0	0	0.155	0	0	0.054	0	0
LOC	0.081	0.273	0	0.199	0.152	0.115	0	0.227	0.115	0.238	0.209	0.122	0.314	0.263
LI	0.091	0.179	0	0.096	0.283	0.067	0	0.195	0.067	0	0.06	0.007	0	0
SG	0	0	0	0	0	0.010	0.0023	0	0.010	0	0	0	0	0
FrP	0	0	0.470	0.119	0.0911	0	0	0.167	0	0.108	0.0909	0	0.225	0.229
MM	0.395	0	0	0.003	0	0	0.265	0.146	0	0	0	0	0.202	0.137
CO	0	0	0	0	0	0	0	0	0	0	0	0	0	0

The inner dependence among the CNs is determined through analyzing the impact of each CN on other CNs by using pairwise comparisons. The relationship between the CNs is shown in Figure 4. For example, one of the possible questions for determining the inner dependence of CNs can be as follows: “What is the relative importance of “Water Reduction” (WR) when compared to “Watering Frequency” (WF) on controlling WR?” yielding “Very Important” as answer.

FIGURE 4 The inner dependence among the customer needs.

The general crisp results of W ₃ are as follows in Table 5.

TABLE 5 The Matrix Related to the Inner Dependencies Among CNs Based on Linguistic Evaluation

W3	WR	CON	FP	EHR	V	S	D	CCS	A	WF	SC	WD	PVL	ECAT
WR	1	0.268	0.315	0	0	0	0	0	0	0.266	0.275	0	0	0
CON	0	0.363	0.075	0	0	0	0	0	0	0	0	0	0	0
FP	0	0.23	0.61	0	0	0	0	0	0	0	0	0	0	0
EHR	0	0	0	1	0	0	0	0	0	0	0	0	0	0
V	0	0	0	0	1	0	0	0	0	0	0	0	0	0
S	0	0	0	0	0	0.735	0	0	0	0	0	0	0	0
D	0	0.138	0	0	0	0	1	0	0	0	0	0	0	0
CCS	0	0	0	0	0	0	0	1	0	0	0	0	0	0
A	0	0	0	0	0	0.265	0	0	1	0	0	0	0	0
WF	0	0	0	0	0	0	0	0	0	0.734	0	0	0	0
SC	0	0	0	0	0	0	0	0	0	0	0.725	0	0	0
WD	0	0	0	0	0	0	0	0	0	0	0	1	0	0
PVL	0	0	0	0	0	0	0	0	0	0	0	0	1	0
ECAT	0	0	0	0	0	0	0	0	0	0	0	0	0	1

In the following stage, we consider the dependencies among the ECs which are represented in Figure 5. The relative importance weights obtained from pairwise comparisons are given in Table 6. We can utilize questions such as “What is the relative importance of Loss of Consistency (LOC) when compared to Water Reduction (WR) on controlling Freezing Point (FP)?”.

FIGURE 5 The inner dependence among the engineering characteristics.

TABLE 6 The Matrix Related to Inner Dependencies Among ECs Based on Linguistic Evaluation

W4	WR	CH	OCQ	UDTC	LOC	LI	SG	FrP	MM	CO
WR	1	0	0	0	0.231	0	0	0.282	0	0
CH	0	1	0	0	0	0	0	0	0	0
OCQ	0	0	1	0	0	0	0	0.076	0	0
UDTC	0	0	0	1	0	0	0	0	0	0
LOC	0	0	0	0	0.769	0.232	0	0	0	0
LI	0	0	0	0	0	0.768	0.293	0	0	0
SG	0	0	0	0	0	0	0.707	0	0	0
FrP	0	0	0	0	0	0	0	0.642	0	0
MM	0	0	0	0	0	0	0	0	1	0
CO	0	0	0	0	0	0	0	0	0	1

Later we obtain the interdependent priorities of the CNs, w_c = W₃ ∗ w₁ as follows:

The interdependent priorities of the ECs, W_A = W₄ ∗ W₂, are presented in Table 7.

TABLE 7 The Interdependent Priorities of the Engineering Characteristics

WA	WR	CON	FP	EHR	V	S	D	CCS	A	WF	SC	WD	PVL	ECAT
WR	0.339	0.348	0.426	0.387	0.341	0.272	0.253	0.1	0.272	0.461	0.445	0.362	0.258	0.199
CH	0	0	0.079	0	0	0.219	0	0	0.219	0.005	0	0.262	0	0.013
OCQ	0.112	0.263	0.193	0.285	0.201	0.189	0.479	0.276	0.189	0.281	0.276	0.221	0.151	0.302
UDTC	0	0	0	0	0	0.155	0	0	0.155	0	0	0.054	0	0
LOC	0.083	0.252	0	0.175	0.182	0.104	0	0.22	0.104	0.183	0.175	0.095	0.241	0.202
LI	0.07	0.138	0	0.073	0.217	0.055	0.001	0.15	0.055	0	0.046	0.006	0	0
SG	0	0	0	0	0	0.007	0.002	0	0.007	0	0	0	0	0
FrP	0	0	0.302	0.077	0.059	0	0	0.107	0	0.069	0.058	0	0.145	0.147
MM	0.395	0	0	0.003	0	0	0.265	0.146	0	0	0	0	0.205	0.137
CO	0	0	0	0	0	0	0	0	0	0	0	0	0	0

The overall priorities of the ECs, w^ANP = W_A ∗ w_c, are obtained as follows:

After applying Chang's extent analysis method to find the weights of the customer needs, the most important customer need has been found as “Water Reduction” with a relative importance value of 0.l63 and the least important customer need has been found as “Endurance of the Concrete Against Temperature” with a relative importance value of 0. The ANP analysis results indicate that the most important design attribute is “Water Reduction” with a relative importance value of 0.316, and corrosion is the least important attribute with a relative importance value of 0. In order to meet the CNs with the above importance values, the production process should particularly focus on the ECs Water Reduction and Optimal Cement Quantity.

DISCUSSIONS AND CONCLUSION REMARKS

In this paper, an integrated methodology based on fuzzy fusion algorithm and FANP was proposed and its applicability was illustrated by means of a real-life case study for ready-mixed concrete firms. The results of the study showed that the proposed methodology is an effective tool in determining the relative importance of ECs, which is a fundamental problem in QFD applications and an important task to ensure the success of new product development.

The proposed approach determines the relative importance of ECs by considering not only the outer dependencies between CNs and ECs, but also the inner dependencies among CNs and among ECs. It comprises three main stages. The first stage is the development of a survey analysis to determine the CNs and the second is the aggregation of the fuzzy opinions of the customers by means of a fuzzy fusion algorithm. In the last stage the overall relative importance values of ECs have been determined by means of fuzzy ANP approach.

The proposed approach was applied on a civil engineering problem to determine the relative importance of ECs for a plasticizer producer company. The results indicate that the proposed approach can be implemented in practice and can provide satisfactory solutions in determining the relative importance of ECs. Furthermore, the results also revealed that, in creating concrete of the future, the plasticizer producer company may focus on improving the features of “Water Reduction” and “Optimum Cement Quantity” for high quality ready-mixed concrete. Although applied in concrete production process, the proposed methodology is flexible enough to be used for other product development processes as well.