Dominance based fuzzy decision support framework for g-resilient (ecosilient) supplier selection: an empirical modelling

Figures & data

Figure 1. Resilience triangle as described by (Tierney and Bruneau 2007).

Figure 2. Trapezoidal fuzzy number .

Figure 3. Triangular fuzzy number .

Table 1.1. Pertinent attributes relevant to g-resilient supplier selection.

Dimensions	Criteria	Citations
Green criteria	Use of environment-friendly technology, C1	Awasthi, Chauhan, and Goyal (2010), Handfield et al. (2002), Lee et al. (2009), Nielsen et al. (2014)
	Use of environment-friendly materials, C2	Awasthi, Chauhan, and Goyal (2010), Humphreys, McIvor, and Chan (2003), Handfield et al. (2002), Handfield, Sroufe, and Walton (2005), Nielsen et al. (2014)
	Green market share, C3	Awasthi, Chauhan, and Goyal (2010), Handfield, Sroufe, and Walton (2005), Nielsen et al. (2014)
	Partnership with green organisations, C4	Awasthi, Chauhan, and Goyal (2010), Humphreys, McIvor, and Chan (2003), Handfield, Sroufe, and Walton (2005), Nielsen et al. (2014)
	Management commitment, C5	Awasthi, Chauhan, and Goyal (2010), Handfield, Sroufe, and Walton (2005), Nielsen et al. (2014)
	Adherence to environmental policies, C6	Awasthi, Chauhan, and Goyal (2010), Humphreys, McIvor, and Chan (2003), Handfield, Sroufe, and Walton (2005), Nielsen et al. (2014)
	Green R & D projects, C7	Awasthi, Chauhan, and Goyal (2010), Lee et al. (2009), Tseng and Chiu (2013), Orji and Wei (2014), Amindoust et al. (2012), Nielsen et al. (2014)
	Staff Training, C8	Barbarosoglu and Yazgac (1997), Humphreys, McIvor, and Chan (2003), Awasthi, Chauhan, and Goyal (2010), Handfield, Sroufe, and Walton (2005)
	Green process planning, C9	Ghadimi and Heavey (2014), Nielsen et al. (2014), Hashemi, Karimi, and Tavana (2015), Awasthi, Chauhan, and Goyal (2010), Nielsen et al. (2014)
	Design for environment, C10	Akili (2009), Awasthi, Chauhan, and Goyal (2010), Humphreys, McIvor, and Chan (2003), Handfield et al. (2002), Nielsen et al. (2014)
	Environmental certification, C11	Humphreys, McIvor, and Chan (2003), Nielsen et al. (2014), Hashemi, Karimi, and Tavana (2015), Lee et al. (2009), Awasthi, Chauhan, and Goyal (2010), Nielsen et al. (2014)
	Pollution control initiatives, C12	Tseng and Chiu (2013), Yeh and Chuang (2011), Awasthi, Chauhan, and Goyal (2010), Zhu, Dou, and Sarkis (2010), Orji and Wei (2014), Bai and Sarkis (2010), Amindoust et al. (2012), Azadnia et al. (2012), Humphreys, McIvor, and Chan (2003), Lee et al. (2009), Nielsen et al. (2014)
Resiliency criteria	Investment in capacity buffers, C13	Chou and Chang (2008), Hervani, Helms, and Sarkis (2005), Epstein and Wisner (2001), Yazlali and Erhun (2009), Li and Debo (2009)
	Responsiveness, C14	Özgen et al. (2008), Handfield, Sroufe, and Walton (2005), Yazlali and Erhun (2009), Tang and Musa (2011), Haldar et al. (2012)
	Capacity for holding strategic inventory stocks for crises, C15	Chopra and Sodhi (2004), Jüttner, Peck, and Christopher (2003), Yazlali and Erhun (2009), Tang (2006), Haldar et al. (2012)

Table 1.2. Definitions of criteria in relation to g-resilient supplier selection.

Criteria	Definitions
Use of environment-friendly technology	In order to protect the environment from industrial wastes (or residuals), a clean and environment-friendly technology must be explored. This emphasises the use of environment-friendly technology that conserves energy and fossil fuel resources (Awasthi, Chauhan, and Goyal 2010). This must ensure enhancement of manufacturing capabilities, design capabilities, and ability to cope up with latest technology (Chou and Chang 2008). It facilitates new product/process development of the supplier’s side that can provide new and upgraded products to the firm (Lee et al. 2009; Shaik and Abdul-Kader 2011)
Use of environment-friendly materials	Organisations must encourage their suppliers to provide environment friendly materials to avoid any after effects. Green purchasing can address issues such as reduction of waste produced, material substitution through environmental sourcing of raw materials, and waste minimisation of hazardous material (Rao and Holt 2005). Therefore, companies are increasingly managing their suppliers’ environmental performance to ensure that the products supplied by them are environmentally-friendly; and these are produced using environmentally-friendly processes
Green market share	It can be evaluated in view of the effort of suppliers in producing green products. It includes green image of the supplier and better stake holder relationship. It also includes the extent of retention of customers with green purchasing habits (Awasthi, Chauhan, and Goyal 2010)
Partnership with green organisations	This criterion reflects a strong affection towards organisations working under green manufacturing practice. It includes association, collaboration and partnership with green suppliers, environmental organisations (Awasthi, Chauhan, and Goyal 2010).
Management commitment	This refers to the involvement of management towards implementation of green programs in order to improve the environmental performance (Awasthi, Chauhan, and Goyal 2010). Environmental management improves quality of products with regard to environmental and value management such as environmental policies, their implementation and respective certifications (Shaik and Abdul-Kader 2011)
Adherence to environmental policies	It is basically the conformance to environmental regulatory standards (Awasthi, Chauhan, and Goyal 2010). This criterion also includes the necessity of reviewing the supplier’s environmental policy to obtain a condition of zero environmental harm
Green R & D projects	It is the movement of R&D projects and production habits from being conventional to green. It is also defined as the supplier’s green R&D capability to meet current and future demand of the firm (Shaik and Abdul-Kader 2011). Green R&D projects should focus on green product and green process planning (Awasthi, Chauhan, and Goyal 2010)
Staff Training	It is the availability of adequate information to the workers in regard to green production system and applicability of green policies into the manufacturing practices. Suppliers should emphasise on staff training to fulfill environmental targets (Awasthi, Chauhan, and Goyal 2010).
Lean process planning	The main focus of lean process planning is to improve green attributes (namely resource consumption and environmental impacts) of production processes by optimising process elements, process courses, and process projects (Cao et al. 2002; He et al. 2007). Green process planning for manufacturing system emphasises on reducing energy and resource consumption, avoid wastage, reduce noise and harmful environmental effects during manufacturing without sacrificing productivity, quality, and efficiency (Gogoi and Hazarika 2014)
Design for environment	It is the emphasis on environment-friendly design for manufacturing practices so that the product can be recycled, reused, re-manufactured along with disassembly as well as disposal. It necessitates checking of supplier’s design for environment capability (e.g. design for disassembly) so that the product becomes more environmental-friendly (Humphreys, McIvor, and Chan 2003)
Environmental certification	Suppliers should achieve environment-related certifications, such as ISO 14000 (Shaik and Abdul-Kader 2011). For suppliers claiming to be green, the most tangible activity is to get environmental certificate or labels like ISO14000, eco-friendly label and carbon footprint label, etc. (Banaeian et al. 2015)
Pollution control initiatives	This shows the effort or extent of pollution minimisation initiatives related to air emissions, waste water disposal, solid wastes, energy consumption, use of harmful materials and hazardous wastes etc. (Awasthi, Chauhan, and Goyal 2010). It is the extent of technology available to control all kind of pollutions like average volume of air pollutants, waste water, solid waste, and harmful materials released (Hashemi, Karimi, and Tavana 2015)
Investment in capacity buffers	Buffer (also called safety stock) capacity is defined as the level of additional stock preserved to mitigate the risk of stock-outs due to uncertainties in supply and demand (Haldar et al. 2012). A buffer stock scheme (commonly implemented as intervention storage, the ‘ever-normal granary’) is an attempt to use commodity storage for the purposes of stabilising prices in an entire economy or, more commonly, an individual (commodity) market. Specifically, commodities are bought when there is a surplus in the economy, stored, and are then sold from these stores when there are economic shortages in the economy. The volume of buffer capacity should be the optimal
Responsiveness	Responsiveness is the ability of suppliers to respond with the fluctuating market demands in minimal possible time. It is also known as the response speed of suppliers towards unpredictable market demand, which necessitates supply of more variety (mass-customised product) at shorter notice. It helps suppliers’ firms for gaining competitive advantage in the market (Haldar et al. 2012)
Capacity for holding strategic inventory stocks for crises	It shows zero availability loss replenishment and stock turn (Handfield, Sroufe, and Walton 2005). The strategic inventory stock must be at its defined level as protective capacity is essential to cope up with any uncertain demand. Inventory stock should be at optimum level as it will create a huge loss if maintained above/below the level prescribed so far. Strategic inventory stock is essential for the assurance of prompt delivery performance even in crisis (like strike, natural disaster, transport delay etc.). The resilience performance of the firm can be enhanced by ensuring delivery in case of emergency. An optimal (economic) volume of inventory should be maintained to survive in adverse situations

Table 2. 7-point linguistic scales and corresponding fuzzy numbers representation.

Linguistic terms for criteria ratings	Linguistic terms for assigning criteria weights	Generalised trapezoidal fuzzy numbers (Chen, Lin, and Huang 2006) (Fuzzy representation 1)	Combination of generalised triangular as well as trapezoidal fuzzy numbers (Fuzzy representation 2)
Very Poor, VP	Very Low, VL	(0, 0, 0, 0.125)	(0, 0, 0.125)
Poor, P	Low, L	(0, 0.125, 0.125, 0.25)	(0, 0.125, 0.25)
Medium Poor, MP	Medium Low, ML	(0.125, 0.25, 0.25, 0.375)	(0.125, 0.25, 0.375)
Fair, F	Medium/ Moderate, M	(0.25, 0.375, 0.5, 0.625)	(0.25, 0.375, 0.5, 0.625)
Medium Good, MG	Medium High, MH	(0.5, 0.625, 0.625, 0.75)	(0.5, 0.625, 0.75)
Good, G	High, H	(0.625, 0.75, 0.75, 0.875)	(0.625, 0.75, 0.875)
Very Good, VG	Very High, VH	(0.75, 0.875, 0.875, 1)	(0.75, 0.875, 1)

Table 3. Priority weight of criteria.

Criteria	Linguistic priority weight as given by the decision-makers
	DM1	DM2	DM3	DM4	DM5
C1	H	H	H	H	H
C2	VH	VH	H	H	VH
C3	MH	MH	H	H	H
C4	H	H	H	H	MH
C5	VH	VH	VH	H	VH
C6	MH	H	H	H	MH
C7	H	H	H	H	H
C8	MH	H	VH	VH	VH
C9	H	H	VH	VH	VH
C10	H	H	H	H	H
C11	VH	VH	VH	VH	H
C12	H	VH	H	VH	H
C13	H	H	H	H	H
C14	H	MH	MH	MH	VH
C15	VH	VH	VH	VH	VH

Table 4.1. Appropriateness rating of supplier alternative S₁ with respect to evaluation criteria.

Criteria	Ratings expressed in linguistic terms as given by the DMs
	DM1	DM2	DM3	DM4	DM5
C1	P	P	P	P	MP
C2	MP	P	F	F	F
C3	P	P	MP	MP	MG
C4	F	MG	MG	MG	G
C5	MP	F	MG	MG	F
C6	F	F	F	F	G
C7	MG	F	G	G	F
C8	MP	F	F	F	MP
C9	F	F	F	F	MP
C10	MP	F	F	MP	G
C11	MG	F	MG	F	F
C12	F	F	F	F	MP
C13	MP	F	F	F	MG
C14	F	MP	F	MP	MP
C15	F	F	F	F	MG

Table 4.2. Appropriateness rating of supplier alternative S₂ with respect to evaluation of criteria.

Criteria	Ratings expressed in linguistic terms as given by the DMs
	DM1	DM2	DM3	DM4	DM5
C1	F	F	F	MG	MG
C2	F	MG	MG	F	F
C3	MP	F	F	F	MP
C4	F	F	F	F	MG
C5	MG	F	MG	F	F
C6	F	F	F	F	MP
C7	MP	F	F	F	MP
C8	MG	G	F	F	G
C9	F	F	F	MP	F
C10	MP	MP	MP	MP	F
C11	F	MP	F	MP	F
C12	F	F	F	F	MP
C13	MG	F	F	MG	G
C14	G	MG	MG	MG	MG
C15	MG	MG	F	F	MG

Table 4.3. Appropriateness rating of supplier alternative S₃ with respect to evaluation criteria.

Criteria	Ratings expressed in linguistic terms as given by the DMs
	DM1	DM2	DM3	DM4	DM5
C1	F	F	MG	G	F
C2	G	G	G	G	MG
C3	MG	MG	G	G	MG
C4	G	G	G	G	F
C5	F	MG	MG	MG	F
C6	F	F	F	F	MG
C7	G	G	G	MG	G
C8	VG	G	VG	G	G
C9	G	G	G	G	MG
C10	MG	G	G	G	MG
C11	G	G	MG	MG	G
C12	F	F	MG	MG	F
C13	F	F	F	F	MG
C14	MG	MG	MG	MG	G
C15	G	G	MG	G	MG

Table 4.4. Appropriateness rating of supplier alternative S₄ with respect to evaluation criteria.

Criteria	Ratings expressed in linguistic terms as given by the DMs
	DM1	DM2	DM3	DM4	DM5
C1	G	G	G	G	VG
C2	VG	G	G	MG	G
C3	G	MG	MG	G	G
C4	VG	VG	VG	VG	G
C5	MG	F	G	G	MG
C6	G	G	G	MG	VG
C7	VG	VG	G	VG	G
C8	G	G	G	G	VG
C9	F	MG	MG	MG	G
C10	G	G	G	G	MG
C11	G	MG	G	MG	VG
C12	F	F	F	F	MG
C13	MG	MG	G	G	G
C14	G	G	G	G	VG
C15	VG	G	G	G	VG

Table 5. Aggregated fuzzy rating of supplier alternatives with respect to criteria: The initial decision-making matrix.

Criteria	Aggregated fuzzy rating of supplier alternatives with respect to criteria
	S1	S2	S3	S4
C1	(0.1000, 0.2200, 0.2400, 0.5000)	(0.4000, 0.5400, 0.5800, 0.8000)	(0.4000, 0.5800, 0.6000, 0.9000)	(0.7000, 0.8200, 0.8400, 1.0000)
C2	(0.1000, 0.4000, 0.4200, 0.6000)	(0.4000, 0.5400, 0.5800, 0.8000)	(0.5000, 0.7600, 0.7800, 0.9000)	(0.5000, 0.7800, 0.8200, 1.0000)
C3	(0.1000, 0.3200, 0.3800, 0.8000)	(0.2000, 0.4200, 0.4600, 0.6000)	(0.5000, 0.6800, 0.7400, 0.9000)	(0.5000, 0.7200, 0.7600, 0.9000)
C4	(0.4000, 0.6200, 0.6800, 0.9000)	(0.4000, 0.5200, 0.5400, 0.8000)	(0.4000, 0.7400, 0.7400, 0.9000)	(0.7000, 0.8800, 0.9600, 1.0000)
C5	(0.2000, 0.5000, 0.5600, 0.8000)	(0.4000, 0.5400, 0.5800, 0.8000)	(0.4000, 0.5600, 0.6200, 0.8000)	(0.4000, 0.6600, 0.7000, 0.9000)
C6	(0.4000, 0.5600, 0.5600, 0.9000)	(0.2000, 0.4600, 0.4800, 0.6000)	(0.4000, 0.5200, 0.5400, 0.8000)	(0.5000, 0.7800, 0.8200, 1.0000)
C7	(0.4000, 0.6400, 0.6600, 0.9000)	(0.2000, 0.4200, 0.4600, 0.6000)	(0.5000, 0.7600, 0.7800, 0.9000)	(0.7000, 0.8600, 0.9200, 1.0000)
C8	(0.2000, 0.4200, 0.4600, 0.6000)	(0.4000, 0.6400, 0.6600, 0.9000)	(0.7000, 0.8400, 0.8800, 1.0000)	(0.7000, 0.8200, 0.8400, 1.0000)
C9	(0.2000, 0.4600, 0.4800, 0.6000)	(0.2000, 0.4600, 0.4800, 0.6000)	(0.5000, 0.7600, 0.7800, 0.9000)	(0.4000, 0.6200, 0.6800, 0.9000)
C10	(0.2000, 0.4800, 0.5200, 0.9000)	(0.2000, 0.3400, 0.4200, 0.6000)	(0.5000, 0.7200, 0.7600, 0.9000)	(0.5000, 0.7600, 0.7800, 0.9000)
C11	(0.4000, 0.5400, 0.5800, 0.8000)	(0.2000, 0.4200, 0.4600, 0.6000)	(0.5000, 0.7200, 0.7600, 0.9000)	(0.5000, 0.7400, 0.8000, 1.0000)
C12	(0.2000, 0.4600, 0.4800, 0.6000)	(0.2000, 0.4600, 0.4800, 0.6000)	(0.4000, 0.5400, 0.5800, 0.8000)	(0.4000, 0.5200, 0.5400, 0.8000)
C13	(0.2000, 0.4800, 0.5200, 0.8000)	(0.4000, 0.6000, 0.6400, 0.9000)	(0.4000, 0.5200, 0.5400, 0.8000)	(0.5000, 0.7200, 0.7600, 0.9000)
C14	(0.2000, 0.3800, 0.4400, 0.6000)	(0.5000, 0.6400, 0.7200, 0.9000)	(0.5000, 0.6400, 0.7200, 0.9000)	(0.7000, 0.8200, 0.8400, 1.0000)
C15	(0.4000, 0.5200, 0.5400, 0.8000)	(0.4000, 0.5600, 0.6200, 0.8000)	(0.5000, 0.7200, 0.7600, 0.9000)	(0.7000, 0.8400, 0.8800, 1.0000)

Table 6. Aggregated fuzzy weight of criteria.

Criteria	Aggregated fuzzy criteria weight
C1	(0.7000, 0.8000, 0.8000, 0.9000)
C2	(0.7000, 0.8600, 0.9200, 1.0000)
C3	(0.5000, 0.7200, 0.7600, 0.9000)
C4	(0.5000, 0.7600, 0.7800, 0.9000)
C5	(0.7000, 0.8800, 0.9600, 1.0000)
C6	(0.5000, 0.7200, 0.7600, 0.9000)
C7	(0.7000, 0.8000, 0.8000, 0.9000)
C8	(0.5000, 0.8200, 0.9000, 1.0000)
C9	(0.7000, 0.8600, 0.9200, 1.0000)
C10	(0.7000, 0.8000, 0.8000, 0.9000)
C11	(0.7000, 0.8800, 0.9600, 1.0000)
C12	(0.7000, 0.8400, 0.8800, 1.0000)
C13	(0.7000, 0.8000, 0.8000, 0.9000)
C14	(0.5000, 0.7000, 0.7800, 1.0000)
C15	(0.8000, 0.9000, 1.0000, 1.0000)

Table 7. The normalised decision matrix.

Criteria	Normalised fuzzy rating of supplier alternatives with respect to criteria
	S1	S2	S3	S4
C1	(0.1000, 0.2200, 0.2400, 0.5000)	(0.4000, 0.5400, 0.5800, 0.8000)	(0.4000, 0.5800, 0.6000, 0.9000)	(0.7000, 0.8200, 0.8400, 1.0000)
C2	(0.1000, 0.4000, 0.4200, 0.6000)	(0.4000, 0.5400, 0.5800, 0.8000)	(0.5000, 0.7600, 0.7800, 0.9000)	(0.5000, 0.7800, 0.8200, 1.0000)
C3	(0.1111, 0.3556, 0.4222, 0.8889)	(0.2222, 0.4667, 0.5111, 0.6667)	(0.5556, 0.7556, 0.8222, 1.0000)	(0.5556, 0.8000, 0.8444, 1.0000)
C4	(0.4000, 0.6200, 0.6800, 0.9000)	(0.4000, 0.5200, 0.5400, 0.8000)	(0.4000, 0.7400, 0.7400, 0.9000)	(0.7000, 0.8800, 0.9600, 1.0000)
C5	(0.2222, 0.5556, 0.6222, 0.8889)	(0.4444, 0.6000, 0.6444, 0.8889)	(0.4444, 0.6222, 0.6889, 0.8889)	(0.4444, 0.7333, 0.7778, 1.0000)
C6	(0.4000, 0.5600, 0.5600, 0.9000)	(0.2000, 0.4600, 0.4800, 0.6000)	(0.40000.5200, 0.5400, 0.8000)	(0.5000, 0.7800, 0.8200, 1.0000)
C7	(0.4000, 0.6400, 0.6600, 0.9000)	(0.2000, 0.4200, 0.4600, 0.6000)	(0.5000, 0.7600, 0.7800, 0.9000)	(0.7000, 0.8600, 0.9200, 1.0000)
C8	(0.2000, 0.4200, 0.4600, 0.6000)	(0.4000, 0.6400, 0.6600, 0.9000)	(0.7000, 0.8400, 0.8800, 1.0000)	(0.7000, 0.8200, 0.8400, 1.0000)
C9	(0.2222, 0.5111, 0.5333, 0.6667)	(0.2222, 0.5111, 0.5333, 0.6667)	(0.5556, 0.8444, 0.8667, 1.0000)	(0.4444, 0.6889, 0.7556, 1.0000)
C10	(0.2222, 0.5333, 0.5778, 1.0000)	(0.2222, 0.3778, 0.4667, 0.6667)	(0.5556, 0.8000, 0.8444, 1.0000)	(0.5556, 0.8444, 0.8667, 1.0000)
C11	(0.4000, 0.5400, 0.5800, 0.8000)	(0.2000, 0.4200, 0.4600, 0.6000)	(0.5000, 0.7200, 0.7600, 0.9000)	(0.5000, 0.7400, 0.8000, 1.0000)
C12	(0.2500, 0.5750, 0.6000, 0.7500)	(0.2500, 0.5750, 0.6000, 0.7500)	(0.5000, 0.6750, 0.7250, 1.0000)	(0.5000, 0.6500, 0.6750, 1.0000)
C13	(0.2222, 0.5333, 0.5778, 0.8889)	(0.4444, 0.6667, 0.7111, 1.0000)	(0.4444, 0.5778, 0.6000, 0.8889)	(0.5556, 0.8000, 0.8444, 1.0000)
C14	(0.2000, 0.3800, 0.4400, 0.6000)	(0.5000, 0.6400, 0.7200, 0.9000)	(0.5000, 0.6400, 0.7200, 0.9000)	(0.7000, 0.8200, 0.8400, 1.0000)
C15	(0.4000, 0.5200, 0.5400, 0.8000)	(0.4000, 0.5600, 0.6200, 0.8000)	(0.5000, 0.7200, 0.7600, 0.9000)	(0.7000, 0.8400, 0.8800, 1.0000)

Table 8. The weighted normalised decision matrix.

Criteria	Weighted normalised rating of supplier alternatives with respect to criteria
	S1	S2	S3	S4
C1	(0.0700, 0.1760, 0.1920, 0.4500)	(0.2800, 0.4320, 0.4640, 0.7200)	(0.2800, 0.4640, 0.4800, 0.8100)	(0.4900, 0.6560, 0.6720, 0.9000)
C2	(0.0700, 0.3440, 0.3864, 0.6000)	(0.2800, 0.4644, 0.5336, 0.8000)	(0.3500, 0.6536, 0.7176, 0.9000)	(0.3500, 0.6708, 0.7544, 1.0000)
C3	(0.0556, 0.2560, 0.3209, 0.8000)	(0.1111, 0.3360, 0.3884, 0.6000)	(0.2778, 0.5440, 0.6249, 0.9000)	(0.2778, 0.5760, 0.6418, 0.9000)
C4	(0.2000, 0.4712, 0.5304, 0.8100)	(0.2000, 0.3952, 0.4212, 0.7200)	(0.2000, 0.5624, 0.5772, 0.8100)	(0.3500, 0.6688, 0.7488, 0.9000)
C5	(0.1556, 0.4889, 0.5973, 0.8889)	(0.3111, 0.5280, 0.6187, 0.8889)	(0.3111, 0.5476, 0.6613, 0.8889)	(0.3111, 0.6453, 0.7467, 1.0000)
C6	(0.2000, 0.4032, 0.4256, 0.8100)	(0.1000, 0.3312, 0.3648, 0.5400)	(0.2000, 0.3744, 0.4104, 0.7200)	(0.2500, 0.5616, 0.6232, 0.9000)
C7	(0.2800, 0.5120, 0.5280, 0.8100)	(0.1400, 0.3360, 0.3680, 0.5400)	(0.3500, 0.6080, 0.6240, 0.8100)	(0.4900, 0.6880, 0.7360, 0.9000)
C8	(0.1000, 0.3444, 0.4140, 0.6000)	(0.2000, 0.5248, 0.5940, 0.9000)	(0.3500, 0.6888, 0.7920, 1.0000)	(0.3500, 0.6724, 0.7560, 1.0000)
C9	(0.1556, 0.4396, 0.4907, 0.6667)	(0.1556, 0.4396, 0.4907, 0.6667)	(0.3889, 0.7262, 0.7973, 1.0000)	(0.3111, 0.5924, 0.6951, 1.0000)
C10	(0.1556, 0.4267, 0.4622, 0.9000)	(0.1556, 0.3022, 0.3733, 0.6000)	(0.3889, 0.6400, 0.6756, 0.9000)	(0.3889, 0.6756, 0.6933, 0.9000)
C11	(0.2800, 0.4752, 0.5568, 0.8000)	(0.1400, 0.3696, 0.4416, 0.6000)	(0.3500, 0.6336, 0.7296, 0.9000)	(0.3500, 0.6512, 0.7680, 1.0000)
C12	(0.1750, 0.4830, 0.5280, 0.7500)	(0.1750, 0.4830, 0.5280, 0.7500)	(0.3500, 0.5670, 0.6380, 1.0000)	(0.3500, 0.5460, 0.5940, 1.0000)
C13	(0.1556, 0.4267, 0.4622, 0.8000)	(0.3111, 0.5333, 0.5689, 0.9000)	(0.3111, 0.4622, 0.4800, 0.8000)	(0.3889, 0.6400, 0.6756, 0.9000)
C14	(0.1000, 0.2660, 0.3432, 0.6000)	(0.2500, 0.4480, 0.5616, 0.9000)	(0.2500, 0.4480, 0.5616, 0.9000)	(0.3500, 0.5740, 0.6552, 1.0000)
C15	(0.3200, 0.4680, 0.5400, 0.8000)	(0.3200, 0.5040, 0.6200, 0.8000)	(0.4000, 0.6480, 0.7600, 0.9000)	(0.5600, 0.7560, 0.8800, 1.0000)

Table 9. Partial matrices of dominance: Exploration of fuzzy distance measure formula.

Criteria	Dominance between the alternatives (with respect to individual criterion)
	[S1, S2]	[S1, S3]	[S1, S4]	[S2, S1]	[S2, S3]	[S2, S4]	[S3, S1]	[S3, S2]	[S3, S4]	[S4, S1]	[S4, S2]	[S4, S3]
C1	−0.2532	−0.2914	−0.4582	0.2532	−0.0484	−0.2061	0.2914	0.0484	−0.1774	0.4582	0.3700	0.1774
C2	−0.1734	−0.3058	−0.3466	0.1734	−0.1454	−0.1846	0.3058	0.1454	−0.0540	0.3466	0.3641	0.0540
C3	−0.1162	−0.2423	−0.2573	0.1162	−0.2329	−0.2447	0.2423	0.2329	−0.0181	0.2573	0.4677	0.0181
C4	0.0803	−0.0513	−0.1713	−0.0803	−0.1229	−0.2435	0.0513	0.1229	−0.1336	0.1713	0.4693	0.1336
C5	−0.0809	−0.0891	−0.1443	0.0809	−0.0235	−0.1031	0.0891	0.0235	−0.0854	0.1443	0.2061	0.0854
C6	0.1515	0.0479	−0.1367	−0.1515	−0.1076	−0.2607	−0.0479	0.1076	−0.1697	0.1367	0.5051	0.1697
C7	0.1931	−0.0764	−0.1778	−0.1931	−0.2532	−0.3576	0.0764	0.2532	−0.1080	0.1778	0.6477	0.1080
C8	−0.2031	−0.3478	−0.3343	0.2031	−0.1570	−0.1419	0.3478	0.1570	0.0198	0.3343	0.2523	−0.0198
C9	0.0000	−0.2923	−0.2239	0.0000	−0.2923	−0.2239	0.2923	0.2923	0.0927	0.2239	0.4270	−0.0927
C10	0.1684	−0.1907	−0.2060	−0.1684	−0.2958	−0.3107	0.1907	0.2958	−0.0199	0.2060	0.5877	0.0199
C11	0.1449	−0.1321	−0.1736	−0.1449	−0.2677	−0.3122	0.1321	0.2677	−0.0543	0.1736	0.5974	0.0543
C12	0.0000	−0.1675	−0.1593	0.0000	−0.1675	−0.1593	0.1675	0.1675	0.0244	0.1593	0.2801	−0.0244
C13	−0.1193	−0.0803	−0.1971	0.1193	0.0758	−0.0849	0.0803	−0.0758	−0.1465	0.1971	0.1558	0.1465
C14	−0.2198	−0.2198	−0.3220	0.2198	0.0000	−0.1056	0.2198	0.0000	−0.1056	0.3220	0.1927	0.1056
C15	−0.0439	−0.1559	−0.2721	0.0439	−0.1191	−0.2391	0.1559	0.1191	−0.1242	0.2721	0.4307	0.1242
Total	−0.2532	−0.2914	−0.4582	0.2532	−0.0484	−0.2061	0.2914	0.0484	−0.1774	0.4582	0.3700	0.1774

Table 10. Final matrices of dominance.

Alternatives	S1	S2	S3	S4
S1	0.0000	−0.4717	−2.5948	−3.5804
S2	0.4717	0.0000	−2.1576	−3.1778
S3	2.5948	2.1576	0.0000	−1.0598
S4	3.5804	5.9537	1.0598	0.0000

Table 11. Global dominance value and corresponding ranking order.

Exploration of trapezoidal fuzzy numbers set theory (Fuzzy representation 1)				Exploration of triangular fuzzy numbers set theory (Fuzzy representation 2)
Alternatives	δ	ξ	Ranking order	δ	ξ	Ranking order
S1	−6.6469	0.0000	4	−6.5600	0.0000	4
S2	−4.8637	0.1034	3	−4.8026	0.1022	3
S3	3.6926	0.5997	2	3.5528	0.5878	2
S4	10.5939	1.0000	1	10.6440	1.0000	1

Table 12. Partial matrices of dominance: Exploration of fuzzy subtraction rule.

Criteria	[S1, S2]	[S1, S3]	[S1, S4]	[S2, S1]	[S2, S3]	[S2, S4]
C1	(−0.650, −0.288, −0.240, 0.170)	(−0.740, −0.304, −0.272, 0.170)	(−0.830, −0.496, −0.464, −0.040)	(−0.170, 0.240, 0.288, 0.650)	(−0.530, −0.048, 0.000, 0.440)	(−0.620, −0.240, −0.192, 0.230)
C2	(−0.730, −0.190, −0.078, 0.320)	(−0.830, −0.374, −0.267, 0.250)	(−0.930, −0.410, −0.284, 0.250)	(−0.320, 0.078, 0.190, 0.730)	(−0.620, −0.253, −0.120, 0.450)	(−0.720, −0.290, −0.137, 0.450)
C3	(−0.544, −0.132, −0.015, 0.689)	(−0.844, −0.369, −0.223, 0.522)	(−0.844, −0.386, −0.255, 0.522)	(−0.689, 0.015, 0.132, 0.544)	(−0.789, −0.289, −0.156, 0.322)	(−0.789, −0.306, −0.188, 0.322)
C4	(−0.520, 0.050, 0.135, 0.610)	(−0.610, −0.106, −0.032, 0.610)	(−0.700, −0.278, −0.138, 0.460)	(−0.610, −0.135, −0.050, 0.520)	(−0.610, −0.182, −0.141, 0.520)	(−0.700, −0.354, −0.248, 0.370)
C5	(−0.733, −0.130, 0.069, 0.578)	(−0.733, −0.172, 0.050, 0.578)	(−0.844, −0.258, −0.048, 0.578)	(−0.578, −0.069, 0.130, 0.733)	(−0.578, −0.133, 0.071, 0.578)	(−0.689, −0.219, −0.027, 0.578)
C6	(−0.340, 0.038, 0.094, 0.710)	(−0.520, −0.007, 0.051, 0.610)	(−0.700, −0.220, −0.136, 0.560)	(−0.710, −0.094, −0.038, 0.340)	(−0.620, −0.079, −0.010, 0.340)	(−0.800, −0.292, −0.197, 0.290)
C7	(−0.260, 0.144, 0.192, 0.670)	(−0.530, −0.112, −0.080, 0.460)	(−0.620, −0.224, −0.160, 0.320)	(−0.670, −0.192, −0.144, 0.260)	(−0.670, −0.288, −0.240, 0.190)	(−0.760, −0.400, −0.320, 0.050)
C8	(−0.800, −0.250, −0.111, 0.400)	(−0.900, −0.448, −0.275, 0.250)	(−0.900, −0.412, −0.258, 0.250)	(−0.400, 0.111, 0.250, 0.800)	(−0.800, −0.267, −0.095, 0.550)	(−0.800, −0.231, −0.078, 0.550)
C9	(−0.511, −0.051, 0.051, 0.511)	(−0.844, −0.358, −0.236, 0.278)	(−0.844, −0.256, −0.102, 0.356)	(−0.511, −0.051, 0.051, 0.511)	(−0.844, −0.358, −0.236, 0.278)	(−0.844, −0.256, −0.102, 0.356)
C10	(−0.444, 0.053, 0.160, 0.744)	(−0.744, −0.249, −0.178, 0.511)	(−0.744, −0.267, −0.213, 0.511)	(−0.744, −0.160, −0.053, 0.444)	(−0.744, −0.373, −0.267, 0.211)	(−0.744, −0.391, −0.302, 0.211)
C11	(−0.320, 0.034, 0.187, 0.660)	(−0.620, −0.254, −0.077, 0.450)	(−0.720, −0.293, −0.094, 0.450)	(−0.660, −0.187, −0.034, 0.320)	(−0.760, −0.360, −0.192, 0.250)	(−0.860, −0.398, −0.210, 0.250)
C12	(−0.575, −0.045, 0.045, 0.575)	(−0.825, −0.155, −0.039, 0.400)	(−0.825, −0.111, −0.018, 0.400)	(−0.575, −0.045, 0.045, 0.575)	(−0.825, −0.155, −0.039, 0.400)	(−0.825, −0.111, −0.018, 0.400)
C13	(−0.744, −0.142, −0.071, 0.489)	(−0.644, −0.053, 0.000, 0.489)	(−0.744, −0.249, −0.178, 0.411)	(−0.489, 0.071, 0.142, 0.744)	(−0.489, 0.053, 0.107, 0.589)	(−0.589, −0.142, −0.071, 0.511)
C14	(−0.800, −0.296, −0.105, 0.350)	(−0.800, −0.296, −0.105, 0.350)	(−0.900, −0.389, −0.231, 0.250)	(−0.350, 0.105, 0.296, 0.800)	(−0.650, −0.114, 0.114, 0.650)	(−0.750, −0.207, −0.012, 0.550)
C15	(−0.480, −0.152, 0.036, 0.480)	(−0.580, −0.292, −0.108, 0.400)	(−0.680, −0.412, −0.216, 0.240)	(−0.480, −0.036, 0.152, 0.480)	(−0.580, −0.256, −0.028, 0.400)	(−0.680, −0.376, −0.136, 0.240)
	[S3, S1]	[S3, S2]	[S3, S4]	[S4, S1]	[S4, S2]	[S4, S3]
C1	(−0.170, 0.272, 0.304, 0.740)	(−0.440, 0.000, 0.048, 0.530)	(−0.620, −0.208, −0.176, 0.320)	(0.040, 0.464, 0.496, 0.830)	(−0.230, 0.192, 0.240, 0.620)	(−0.320, 0.176, 0.208, 0.620)
C2	(−0.250, 0.267, 0.374, 0.830)	(−0.450, 0.120, 0.253, 0.620)	(−0.650, −0.101, 0.047, 0.550)	(−0.250, 0.284, 0.410, 0.930)	(−0.450, 0.137, 0.290, 0.720)	(−0.550, −0.047, 0.101, 0.650)
C3	(−0.522, 0.223, 0.369, 0.844)	(−0.322, 0.156, 0.289, 0.789)	(−0.622, −0.098, 0.049, 0.622)	(−0.522, 0.255, 0.386, 0.844)	(−0.322, 0.188, 0.306, 0.789)	(−0.622, −0.049, 0.098, 0.622)
C4	(−0.610, 0.032, 0.106, 0.610)	(−0.520, 0.141, 0.182, 0.610)	(−0.700, −0.186, −0.092, 0.460)	(−0.460, 0.138, 0.278, 0.700)	(−0.370, 0.248, 0.354, 0.700)	(−0.460, 0.092, 0.186, 0.700)
C5	(−0.578, −0.050, 0.172, 0.733)	(−0.578, −0.071, 0.133, 0.578)	(−0.689, −0.199, 0.016, 0.578)	(−0.578, 0.048, 0.258, 0.844)	(−0.578, 0.027, 0.219, 0.689)	(−0.578, −0.016, 0.199, 0.689)
C6	(−0.610, −0.051, 0.007, 0.520)	(−0.340, 0.010, 0.079, 0.620)	(−0.700, −0.249, −0.151, 0.470)	(−0.560, 0.136, 0.220, 0.700)	(−0.290, 0.197, 0.292, 0.800)	(−0.470, 0.151, 0.249, 0.700)
C7	(−0.460, 0.080, 0.112, 0.530)	(−0.190, 0.240, 0.288, 0.670)	(−0.550, −0.128, −0.064, 0.320)	(−0.320, 0.160, 0.224, 0.620)	(−0.050, 0.320, 0.400, 0.760)	(−0.320, 0.064, 0.128, 0.550)
C8	(−0.250, 0.275, 0.448, 0.900)	(−0.550, 0.095, 0.267, 0.800)	(−0.650, −0.067, 0.120, 0.650)	(−0.250, 0.258, 0.412, 0.900)	(−0.550, 0.078, 0.231, 0.800)	(−0.650, −0.120, 0.067, 0.650)
C9	(−0.278, 0.236, 0.358, 0.844)	(−0.278, 0.236, 0.358, 0.844)	(−0.611, 0.031, 0.205, 0.689)	(−0.356, 0.102, 0.256, 0.844)	(−0.356, 0.102, 0.256, 0.844)	(−0.689, −0.205, −0.031, 0.611)
C10	(−0.511, 0.178, 0.249, 0.744)	(−0.211, 0.267, 0.373, 0.744)	(−0.511, −0.053, 0.000, 0.511)	(−0.511, 0.213, 0.267, 0.744)	(−0.211, 0.302, 0.391, 0.744)	(−0.511, 0.000, 0.053, 0.511)
C11	(−0.450, 0.077, 0.254, 0.620)	(−0.250, 0.192, 0.360, 0.760)	(−0.650, −0.134, 0.078, 0.550)	(−0.450, 0.094, 0.293, 0.720)	(−0.250, 0.210, 0.398, 0.860)	(−0.550, −0.078, 0.134, 0.650)
C12	(−0.400, 0.039, 0.155, 0.825)	(−0.400, 0.039, 0.155, 0.825)	(−0.650, −0.027, 0.092, 0.650)	(−0.400, 0.018, 0.111, 0.825)	(−0.400, 0.018, 0.111, 0.825)	(−0.650, −0.092, 0.027, 0.650)
C13	(−0.489, 0.000, 0.053, 0.644)	(−0.589, −0.107, −0.053, 0.489)	(−0.589, −0.213, −0.160, 0.411)	(−0.411, 0.178, 0.249, 0.744)	(−0.511, 0.071, 0.142, 0.589)	(−0.411, 0.160, 0.213, 0.589)
C14	(−0.350, 0.105, 0.296, 0.800)	(−0.650, −0.114, 0.114, 0.650)	(−0.750, −0.207, −0.012, 0.550)	(−0.250, 0.231, 0.389, 0.900)	(−0.550, 0.012, 0.207, 0.750)	(−0.550, 0.012, 0.207, 0.750)
C15	(−0.400, 0.108, 0.292, 0.580)	(−0.400, 0.028, 0.256, 0.580)	(−0.600, −0.232, 0.004, 0.340)	(−0.240, 0.216, 0.412, 0.680)	(−0.240, 0.136, 0.376, 0.680)	(−0.340, −0.004, 0.232, 0.600)

Table 13. Final matrices of dominance.

Alternatives	S1	S2	S3	S4
S1	(0.000, 0.000, 0.000, 0.000)	(−8.453, −1.356, 0.350, 7.956)	(−10.766, −3.549, −1.790, 6.328)	(−11.827, −4.659, −2.796, 5.518)
S2	(−7.956, −0.350, 1.356, 8.453)	(0.000, 0.000, 0.000, 0.000)	(−10.109, −3.102, −1.231, 6.168)	(−11.171, −4.213, −2.237, 5.358)
S3	(−6.328, 1.790, 3.549, 10.766)	(−6.168, 1.231, 3.102, 10.109)	(0.000, 0.000, 0.000, 0.000)	(−9.542, −2.072, −0.045, 7.671)
S4	(−5.518, 2.796, 4.659, 11.827)	(−5.358, 2.237, 4.213, 11.171)	(−7.671, 0.045, 2.072, 9.542)	(0.000, 0.000, 0.000, 0.000)

Table 14. Global dominance measure, corresponding crisp score, normalised crisp score and supplier ranking order.

Exploration of trapezoidal fuzzy numbers set theory (Fuzzy representation 1)
Alternatives	δ (in terms of fuzzy number)	Defuzzified	ξ	Ranking order
S1	(−31.046, −9.564, −4.236, 19.802)	6.193	0.737	2
S2	(−29.236, −7.665, −2.112, 19.978)	4.907	0.262	3
S3	(−22.038, 0.949, 6.606, 28.547)	3.800	0.000	4
S4	(−18.547, 5.078, 10.944, 32.540)	8.022	1.000	1
Exploration of combination of triangular as well as trapezoidal fuzzy numbers set theory (Fuzzy representation 2)
S1	(−33.550, −8.725, −4.985, 21.734)	6.686	0.742	2
S2	(−31.749, −6.702, −2.834, 22.459)	4.786	0.257	3
S3	(−24.111, 2.219, 5.095, 30.253)	3.681	0.000	4
S4	(−20.343, 6.732, 9.200, 35.3070)	7.977	1.000	1

Table 15. Separation measure of each alternative with respect to ideal and anti-ideal solution : Computation of closeness coefficient and corresponding ranking order (Exploration of Fuzzy-TOPSIS).

Exploration of trapezoidal fuzzy numbers set theory (Fuzzy representation 1)					Exploration of combination of triangular as well as trapezoidal fuzzy numbers set theory (Fuzzy representation 2)
Alternatives			CCi	Ranking order			CCi	Ranking order
S1	9.0046	7.2958	0.447584	4	10.0122	6.5591	0.3958	4
S2	8.5537	7.5023	0.467258	3	9.5497	6.8111	0.4163	3
S3	6.7471	9.5371	0.585666	2	7.6839	8.6723	0.5302	2
S4	5.9008	10.5174	0.640594	1	6.7967	9.765	0.5896	1

Table 16. Ranking order of alternative suppliers based on S_i, R_i and Q_i (Exploration of Fuzzy-VIKOR).

Exploration of trapezoidal fuzzy numbers set theory (Fuzzy representation 1)
Alternatives	Si	Ranking order	Ri	Ranking order		Qi	Ranking order
S1	6.420	4	0.697	4	(0.880,0.961,1.042,1.119)	1.070	4
S2	5.930	3	0.624	3	(0.571,0.705,0.773,0.998)	0.842	3
S3	3.877	2	0.514	1	(0.108,0.134,0.159,0.176)	0.380	2
S4	2.843	1	0.524	2	(0.000,0.033,0.073,0.000)	0.348	1
Exploration of combination of triangular as well as trapezoidal fuzzy numbers set theory (Fuzzy representation 2)
S1	6.759	4	0.711	4	(0.735,0.938,1.147,1.480)	1.123	4
S2	6.244	3	0.646	3	(0.545,0.740,0.759,0.920)	0.837	3
S3	4.250	2	0.563	2	(0.117,0.195,0.215,0.221)	0.404	2
S4	3.194	1	0.555	1	(0.000,0.000,0.000,0.000)	0.333	1

Notes:

S_i= individual utility; R_i= regret measure;  = overall ranking index; Q_i= defuzzified ; method of defuzzification: as given in (Rezvani 2013; Rouhparvar and Panahi 2015)

Table 17. Pertinent attributes relevant to g-resilient supplier selection.

Performance dimensions/main-criteria, PDj	Sub-criteria
Green performance, PD1	Use of environment-friendly technology, C11
	Use of environment-friendly materials, C12
	Green market share, C13
	Partnership with green organisations, C14
	Management commitment, C15
	Adherence to environmental policies, C16
	Green R & D projects, C17
	Staff Training, C18
	Lean process planning, C19
	Design for environment, C1,10
	Environmental certification, C1,11
	Pollution control initiatives, C1,12
Resilience performance, PD2	Investment in capacity buffers, C21
	Responsiveness, C22
	Capacity for holding strategic inventory stocks for crises, C23

Table 18. Weight of g-resilient performance dimensions expressed in linguistic terms as given by the DMs: Corresponding aggregated fuzzy weight.

Performance dimensions	Linguistic weights as given by the DMs					Aggregated fuzzy weight: Exploration of trapezoidal fuzzy numbers set theory (Fuzzy representation 1)	Aggregated fuzzy weight: Exploration of combination of triangular as well as trapezoidal fuzzy numbers set theory (Fuzzy representation 2)
	DM1	DM2	DM3	DM4	DM5
PD1	VH	H	VH	H	MH	(0.600, 0.800, 0.860, 1.000)	(0.625, 0.825, 0.825, 1.000)
PD2	VH	VH	VH	H	H	(0.700, 0.860, 0.920, 1.000)	(0.625, 0.825, 0.825, 1.000)

Table 19. Computed fuzzy rating of g-resilient performance dimensions.

Performance dimensions	Computed fuzzy rating of alternative suppliers with respect to g-resilient performance dimensions
	S1	S2	S3	S4
PD1	(0.1588, 0.4455, 0.5277, 1.1066)	(0.1877, 0.4575, 0.5435, 1.0395)	(0.3149, 0.6495, 0.7520, 1.3250)	(0.3570, 0.7076, 0.8247, 1.4237)
PD2	(0.1931, 0.4333, 0.5413, 1.0600)	(0.2931, 0.5550, 0.7057, 1.2550)	(0.3207, 0.5860, 0.7307, 1.2600)	(0.4345, 0.7388, 0.8930, 1.4050)

Table 20. Computed fuzzy g-resilient index of alternative suppliers and corresponding ranking order.

Exploration of trapezoidal fuzzy numbers set theory (Fuzzy representation 1)
Alternatives	GRIi	Defuzzified value	Ranking order
S1	(0.1152, 0.4096, 0.5734, 1.6666)	0.654	4
S2	(0.1589, 0.4738, 0.6727, 1.7650)	0.718	3
S3	(0.2067, 0.5750, 0.7945, 1.9885)	0.811	2
S4	(0.2592, 0.6750, 0.9222, 2.1759)	0.909	1
Exploration of combination of triangular as well as trapezoidal fuzzy numbers set theory(Fuzzy representation 2)
S1	(0.1100, 0.4392, 0.5347, 1.7333)	0.653	4
S2	(0.1503, 0.5078, 0.6271, 1.8356)	0.715	3
S3	(0.1986, 0.6168, 0.7410, 2.0680)	0.808	2
S4	(0.2473, 0.7237, 0.8599, 2.2629)	0.906	1

Table 21. Determination of FPII; performance ranking order of criteria (for individual suppliers).

Criteria	S1			S2
	Fuzzy Performance Importance Index (FPII)	Defuzzified FPII (using ‘incentre of centroids’ method)	Ranking order	Fuzzy Performance Importance Index (FPII)	Defuzzified FPII (using ‘incentre of centroids’ method)	Ranking order
C11	(0.0300, 0.0440, 0.0480, 0.0500)	0.3407	15	(0.1200, 0.1080, 0.1160, 0.0800)	0.3541	10
C12	(0.0300, 0.0560, 0.0336, 0.0000)	0.3467	14	(0.1200, 0.0756, 0.0464, 0.0000)	0.3633	5
C13	(0.0500, 0.0896, 0.0912, 0.0800)	0.3485	13	(0.1000, 0.1176, 0.1104, 0.0600)	0.3572	8
C14	(0.2000, 0.1488, 0.1496, 0.0900)	0.3796	2	(0.2000, 0.1248, 0.1188, 0.0800)	0.3748	3
C15	(0.0600, 0.0600, 0.0224, 0.0000)	0.3551	8	(0.1200, 0.0648, 0.0232, 0.0000)	0.3642	4
C16	(0.2000, 0.1568, 0.1344, 0.0900)	0.3840	1	(0.1000, 0.1288, 0.1152, 0.0600)	0.3606	7
C17	(0.1200, 0.1280, 0.1320, 0.0900)	0.3583	7	(0.0600, 0.0840, 0.0920, 0.0600)	0.3451	15
C18	(0.1000, 0.0756, 0.0460, 0.0000)	0.3606	5	(0.2000, 0.1152, 0.0660, 0.0000)	0.3818	2
C19	(0.0600, 0.0644, 0.0384, 0.0000)	0.3529	9	(0.0600, 0.0644, 0.0384, 0.0000)	0.3529	12
C1,10	(0.0600, 0.0960, 0.1040, 0.0900)	0.3529	10	(0.0600, 0.0680, 0.0840, 0.0600)	0.3458	14
C1,11	(0.1200, 0.0648, 0.0232, 0.0000)	0.3642	3	(0.0600, 0.0504, 0.0184, 0.0000)	0.3532	11
C1,12	(0.0600, 0.0736, 0.0576, 0.0000)	0.3516	11	(0.0600, 0.0736, 0.0576, 0.0000)	0.3516	13
C21	(0.0600, 0.0960, 0.1040, 0.0800)	0.3509	12	(0.1200, 0.1200, 0.1280, 0.0900)	0.3557	9
C22	(0.1000, 0.1140, 0.0968, 0.0000)	0.3640	4	(0.2500, 0.1920, 0.1584, 0.0000)	0.4063	1
C23	(0.0800, 0.0520, 0.0000, 0.0000)	0.3601	6	(0.0800, 0.0560, 0.0000, 0.0000)	0.3611	6
C11	(0.1200, 0.1160, 0.1200, 0.0900)	0.3556	14	(0.2100, 0.1640, 0.1680, 0.1000)	0.3848	7
C12	(0.1500, 0.1064, 0.0624, 0.0000)	0.3738	6	(0.1500, 0.1092, 0.0656, 0.0000)	0.3742	9
C13	(0.2500, 0.1904, 0.1776, 0.0900)	0.4017	3	(0.2500, 0.2016, 0.1824, 0.0900)	0.4057	4
C14	(0.2000, 0.1776, 0.1628, 0.0900)	0.3893	4	(0.3500, 0.2112, 0.2112, 0.1000)	0.4242	2
C15	(0.1200, 0.0672, 0.0248, 0.0000)	0.3646	12	(0.1200, 0.0792, 0.0280, 0.0000)	0.3672	13
C16	(0.2000, 0.1456, 0.1296, 0.0800)	0.3811	5	(0.2500, 0.2184, 0.1968, 0.1000)	0.4111	3
C17	(0.1500, 0.1520, 0.1560, 0.0900)	0.3704	9	(0.2100, 0.1720, 0.1840, 0.1000)	0.3864	6
C18	(0.3500, 0.1512, 0.0880, 0.0000)	0.4048	2	(0.3500, 0.1476, 0.0840, 0.0000)	0.4039	5
C19	(0.1500, 0.1064, 0.0624, 0.0000)	0.3738	6	(0.1200, 0.0868, 0.0544, 0.0000)	0.3653	14
C1,10	(0.1500, 0.1440, 0.1520, 0.0900)	0.3677	10	(0.1500, 0.1520, 0.1560, 0.0900)	0.3704	11
C1,11	(0.1500, 0.0864, 0.0304, 0.0000)	0.3723	8	(0.1500, 0.0888, 0.0320, 0.0000)	0.3727	10
C1,12	(0.1200, 0.0864, 0.0696, 0.0000)	0.3627	13	(0.1200, 0.0832, 0.0648, 0.0000)	0.3625	15
C21	(0.1200, 0.1040, 0.1080, 0.0800)	0.3541	15	(0.1500, 0.1440, 0.1520, 0.0900)	0.3677	12
C22	(0.2500, 0.1920, 0.1584, 0.0000)	0.4063	1	(0.3500, 0.2460, 0.1848, 0.0000)	0.4358	1
C23	(0.1000, 0.0720, 0.0000, 0.0000)	0.3674	11	(0.1400, 0.0840, 0.0000, 0.0000)	0.3744	8

Figure 4. 7-memner scale consisting of trapezoidal fuzzy numbers (also Refer to Table 2). Fuzzy representation 1.

Figure 5. 7-memner scale consisting of a combination of triangular as well as trapezoidal fuzzy numbers (also Refer to Table 2) (Fuzzy representation 2)

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