Int J Adv Manuf Technol DOI 10.1007/s00170-014-6233-5

ORIGINAL ARTICLE

Fuzzy PROMETHEE GDSS for technical requirements ranking in HOQ Seyyed Mahdi Hosseini Motlagh & Majid Behzadian & Joshua Ignatius & Mark Goh & Mohammad Mehdi Sepehri & Tan Kim Hua

Received: 5 January 2012 / Accepted: 4 August 2014 # Springer-Verlag London 2014

Abstract This paper provides a fuzzy Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) in a Group Decision Support System (GDSS) approach to ranking the technical requirements for the house of quality (HOQ) process in multi-criteria product design. The problem under study involves incorporating the design alternatives of a group of designers located in different geographies who often provide vague and imprecise linguistic design information to the HOQ process. As such, the proposed fuzzy PROMETHEE GDSS allows the quality function deployment (QFD) team of designers to minimize any deviation arising from the individual designer preferences and to capture the ambiguity of the imprecise design information when S. M. Hosseini Motlagh School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran M. Behzadian School of Industrial Engineering, Shomal University, Tehran, Iran J. Ignatius (*) School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia e-mail: [email protected] M. Goh Decision Sciences Department, School of Business, National University of Singapore, Singapore, Singapore M. Goh School of Business IT and Logistics, RMIT University, Melbourne, Victoria 3000, Australia M. M. Sepehri Department of Industrial Engineering, Tarbiat Modares University, Tehran, Iran T. K. Hua Nottingham Business School,, University of Nottingham, Nottingham, UK

expressing the importance of customer needs and to delineate the linkage between customer needs and the technical requirements. The approach advances the HOQ group decisionmaking context in two important aspects. First, it treats each criterion and decision maker (DM) as unique in terms of the preference function and threshold levels. Second, it facilitates a rapid communication among DMs for the HOQ process. A case of a design team for an ergonomic chair manufacturer serves to validate this approach. Keywords Fuzzy . GDSS . PROMETHEE . Quality function deployment . House of quality

1 Introduction Today, firms need to develop products and services that meet customer needs (CNs) and hence customer satisfaction. Often, quality function deployment (QFD), developed in the 1960s [1], is used as a strategic tool to ensure that the voice of the customer is heard throughout the phases of product design and manufacturing, in translating the CNs into the product-based technical requirements (TRs) by integrating the diverse ideas across the marketing, design, engineering, manufacturing, and other key functions of a firm [16]. QFD uses four sets of matrices: (i) product planning (also known as the house of quality (HOQ)), (ii) part development, (iii) process planning, and iv) production planning [15]. The HOQ, as shown in Fig. 1, contains valuable information about the CNs and their relative importance, the relationships between the CNs and TRs, the correlation among the TRs, and the relative importance of the TRs. This paper focuses on the HOQ matrix, which describes the translation of the CNs into a list of TRs, which can sometimes entail complicated decision making.

Int J Adv Manuf Technol Fig. 1 Representation of HOQ chart and its steps Step 6

Step 4 Step 1: Identify CNs Step 2: Find relative importance of CNs.

Step 5

Step 6: Prepare correlation matrix.

Strong

●

9

Medium

◘

3

Weak

○

1

Step 3

Step 5: Prepare relationship matrix.

Step 2

Step 4: Determine TRs

Step 1

Step 3: Customer competitive assessment.

Step 7: Rank TRs and define target Step 7

Although QFD has been successfully applied across many industries, several drawbacks have been reported in its implementation process. According to an in-depth review of the QFD publications, the implementation problems can be categorized as follows: (1) the lack of time to go through all the processes [22, 11, 10]; (2) the large size of the matrices [42, 13]; (3) the inability to discriminate among diverse and conflicting CNs (Benner et al. [5]; [43]); (4) the difficulty in reaching an agreement arising from the conflicting TRs [21, 9]; (5) the inaccuracy in ranking CNs and TRs with the conventional scaling [26, 27]; (6) the inability to respond to the dynamic changes in CNs [45, 2, 38]; (7) poor understanding of CNs across various segments [46, 23, 29]; (8) the focus on the relationship between TRs and cost intead of extending it to other factors affecting the supply chain [18, 40, 28, 32]; (9) the vagueness and ambiguity in the ranks, relationship matrix, and correlation matrix are ignored [30, 31, 12]; and (10) the ineffective knowledge management during the product development process [47]. Hence, this research attempts to improve and illustrate the applicability of the QFD technique. This paper focuses on the HOQ matrix, which describes the transition of CNs into a list of TRs. It aims to highlight the problem of ranking TRs among a group of experts in the HOQ process that are virtually located. In such environment, rapid communication and resolving trade-offs among stakeholders are essential in achieving product development excellence. Hence, successful QFD implementation requires an effective decision-making method to guide a common consensus among the stakeholders. We note the absence of the Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) Group Decision Support System (GDSS) method [7] in the literature coverage and seek to introduce its usefulness in ranking a set of TRs for product planning. Incorporating the fuzzy set theory approach into PROMETHEE GDSS enables the group to properly account for the ambiguity and uncertainty in group decision making.

The rest of the paper is organized as follows. Sect. 2 presents the literature review on QFD and PROMETHEE. Sect. 3 details the fuzzy PROMETHEE GDSS approach. Sect. 4 validates the methodology through a case of an ergonomic chair design. Sect. 5 concludes the paper with suggestions for future research.

2 Literature review In the literature, only a few applications of PROMETHEE were applied to group decision making [3] let alone QFD. This is pale in comparison to the more popular analytic hierarchy process approach in QFD [37] although PROMETHEE has the advantage of allowing the decision makers to specify their preference functions. Raju et al. [39] apply the PROMETHEE GDSS method to rank the alternative strategies for the planning scenario of an irrigation system. Haralambopoulos and Polatidis [20] employ the PROMETHEE method to evaluate and rank renewable energy projects according to a multi-criteria group decision-making action plan. Likewise, to select the best location for an electricity power plant in the EU, Leyya-Lopez and Fernandez-Gonzalez [34] conduct a comparative study of PROMETHEE for group decision making with an extension of the ELECTRE III multi-criteria outranking methodology. Morais and de Almeida [36] later propose a procedure with four stakeholders to develop a leakage management strategy. Although the PROMETHEE GDSS method has been designed for use in a colocated group environment, it is equally applicable to a virtual setting using tele or video conferencing systems [7]. The literature contains even fewer studies on group decision-making techniques for ranking the TRs that incorporate the subjectivity of the decision makers in the modeling framework. Since decision maker subjectivity often affects the ranking of the TRs, allowing the decision makers to express values in linguistic terms and accounting for the fuzziness of their value judgment are imperative to group decision making.

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Hence, fuzzy set theory is often relied upon to deal with the vague and imprecise linguistic terms in the HOQ process. In terms of the TR analysis, Kim et al. [30] combine fuzzy regression and fuzzy optimization theory to deal with the QFD team’s performance trade-offs. Buyukozkan and Feyzioglu [9] introduce a new group decision-making approach that accounts for multiple preference formats, which combines different expressions into a uniform group decision using fuzzy set theory. Subsequently, Liu and Wu [35] present a hybrid version of the group decision-making problem for the customer requirement management of the QFD process. Recently, Buyukozkan et al. [10] propose a fuzzy preference relation technique for aggregating opinions across a crossfunctional team. Nonetheless, current studies do not clarify the challenges arising from evaluating TRs in QFD group decision making, especially the means to resolve poor communication among group members. In many studies, the decision-making process is assumed to be on an ad hoc once-off “face-to-face” basis. However, getting expert opinions resolved in a colocated setting is extremely difficult, and this often would delay the QFD process. Therefore, the main contribution of this paper is to resolve the problems associated with poor communication among team members, who are virtually colocated. These team members may exhibit different weights and tolerances in evaluating the TRs of a QFD project. For this purpose, this study proposes a PROMETHEE GDSS method for rapidly aggregating individual preferences expressed by the team members. Incorporating the fuzzy set theory into PROMETHEE GDSS enables to better capture the ambiguity and uncertainty in group decision making. The PROMETHEE method combined with fuzzy set theory has been applied to environment management, hydrology and water management, energy management, and logistics and transportation. For instance, Le Teno and Mareschal [33] develop a version of PROMETHEE with interval criteria and fuzzy set theory to evaluate the environmental quality of building products through life cycle assessment (LCA). Geldermann et al. [19] also combine PROMETHEE with fuzzy set theory to rank sinter plants through LCA based on 12 impact factors. In logistics and transportation, Radojevic and Petrovic (1997), recognizing that PROMETHEE handles human judgment in a simplistic manner, introduce fuzzy if-then rules that linked the criterion value difference and its preference function. Likewise, Fernandez-Castro and Jimenez [17] apply fuzzy PROMETHEE to rank and select distribution centers in Belgium. Other applications of fuzzy PROMETHEE are hospital Web site evaluation [6], eco-technology model evaluation [14], material handling equipment selection [43], training provider evaluation [25], and optimal choice of investments [44].

3 Fuzzy PROMETHEE GDSS To rank the alternatives from a group of DMs, the fuzzy PROMETHEE GDSS goes through the following procedure. Steps 0.1 and 0.2 are the data preprocessing needed for the fuzzy numbers prior to conducting the PROMETHEE GDSS computation. Step 0.1: Generate alternatives and criteria The process begins with generating alternatives and criteria by the facilitator who poses decision problems to the DMs. For this purpose, the facilitator meets the DMs together or individually so that each DM proposes possible alternatives and criteria including their extended description. All the proposed alternatives are collected and displayed by the facilitator, who then provides a frame of the evaluation table. Step 0.2: Fuzzy data elicitation and preparation The DMs express their ratings linguistically, i.e., “very strong” and “weak.” The linguistic variables are modeled as a series of triangular fuzzy numbers instead of crisp numbers. A triangular e takes the form (L, M, U) with fuzzy number A eðxÞ (Fig. 2). membership function μA 8 0; x < L; > > > x−L > < ; L ≤ x ≤ M; eðxÞ ¼ M−L ð1Þ μA x−H > > ; M ≤ x≤ H; > > : H−M 0; x>H The triangular fuzzy number is presented in the LR form of Geldermann et al. [31]: ðL; M ; U Þ ¼ ðM ; M −L; U −M ÞLR

ð2Þ

The term LR is used to denote the left and right spreads of the triangle. Table 1 contains the basic fuzzy operations in the LR mode. The evaluation of alternatives and criteria is expressed using this fuzzy form. For instance, very strong is expressed as (8,9,9)=(9,1,0)LR

Fig. 2 Graphical representation of a triangular fuzzy number

Int J Adv Manuf Technol Table 1 Basic fuzzy LR operations Addition

(m,α,β)LR ⊕(n,γ,δ)LR =(m+n,α+γ,β+δ)LR

Opposite −(m,α,β)LR =(−m,β,α)LR Subtraction (m,α,β)LR −(n,γ,δ)LR =(m−n,α+δ,β+γ)LR Multiplication by (m,α,β)LR ⊗(n,0,0)LR =(mn,αn,βn)LR scalar Multiplication by fuzzy For m>0,n>0 (m,α,β)LR ⊗(n,γ,δ)LR =(mn,mγ+nα,mδ+nβ)LR For m<0,n>0 (m,α,β)LR ⊗(n,γ,δ)LR =(mn,nα−mδ,nβ−mγ)LR For m<0,n<0 (m,α,β)LR ⊗(n,γ,δ)LR =(mn,−nβ−mδ,nα−mγ)LR

Step 1: Evaluate alternatives pairwise for each criterion and DM The difference score between two alternatives for criterion j is derived as follows:     e dj ¼ Cj e a −C j e b

ð3Þ

where Cj ðe aÞ represents the membership function for criterion j on triangular fuzzy number e a in the LR mode. For instance, if C j ðe aÞ ¼ very strongð9; 1; 0Þ   and Cj e b ¼ very weak ð1; 0; 1Þ , t h e n e dj ¼ ð9−1; 1 þ 1; 0 þ 0Þ ¼ ð8; 2; 0Þ . Step 2: Set the preference function and threshold selection for each criterion and DM Brans et al. [8] present the shape of the six possible choices of the preference functions to assist the DMs with this selection. For example, a DM who selects a type 3 function (Fig. 3) is required to specify a threshold value of p (strict preference). This preference threshold can be interpreted as the smallest tolerance that the DM can bear to reflect its sufficiency condition to be considered as maximizing full preference. The type 3 function can be expressed as follows: 8 0 < e   > d P e dj ¼ > p : 1

where e d ¼ ðM ; M −L; U −M ÞLR . Assume that e d j ¼ ð6; 3; 2Þ and the DMs agree   on a threshold value of p = 8. Then, P e dj ¼   6 3 2 p ; p ; p ¼ ð0:75; 0:375; 0:25Þ . Step 3: Weigh the preferences for each DM The weights of the criteria are incorporated into the rating of alternatives with ∑wj =1. The weighted preference indicator for fuzzy PROMETHEE can be expressed as follows:   X   π e dj ¼ dj w jP e

ð5Þ

Consider the simple case of a pair of alternatives   (1, 2) of two criteria. Hence, π e d j ¼ πð1; 2Þ and   suppose w1 =0.3, w2 =0.7 and P e d 1 ¼ ð1; 0; 2Þ   and P e d 2 ¼ ð3; 2; 2Þ , then π(1,2) = 0.3(1,0,2) ⊕ 0.7(3,2,2) = (0.51,1.4,2) Step 4: Calculate the outranking flows for each DM There are two types of flows, positive (ϕ+) and negative (ϕ−). For an alternative to be preferred over another, φ+(a) > φ+(b) and φ−(a) <φ−(b) where ϕ+ sums all outgoing paths from node a in the form π(a,x), with a as the origin node in an outranking graph while x represents the rest of the destination nodes. For instance, π(a,x) for x=b,c where π(a,b)=(0.7,0.4,0.2) and π(a,c)=(0.6,0.3,0.2). Then, ϕ+(a)=1/2[(0.7,0.4,0.2)⊕(0.6,0.3,0.2)]= 1/2(1.3,0.7,0.4)=(0.65,0.35,0.2). The computation for ϕ− is similar to ϕ+, but the origin node is now the destination node. For instance, let π(x,a) for x=b,c, where π(b,a)=(0.55,0.4,0.25) and π(c,a)=(0.35,0.25, 0.2).

if L ≤ 0 if 0 ≤ L and U ≤ p if U ≤ p

ð4Þ

ϕ− ðaÞ ¼ 1=2½ð0:55; 0:4; 0:25Þ⊕ð0:35; 0:25; 0:2ފ ¼ 1=2ð0:9; 0:65; 0:45Þ ¼ ð0:45; 0:325; 0:225Þ: Step 5: Calculate the net flow for each DM For a net comparison, the positive flow for alternative a is as follows:

Fig. 3 Type 3 preference function for PROMETHEE

ϕnet ðaÞ ¼ ϕþ ðaÞ−ϕ− ðaÞ

ð6Þ

Int J Adv Manuf Technol

In our two-criteria example, the net flow is calculated as ϕnet ðaÞ ¼ ð0:65; 0:35; 0:2Þ−ð0:45; 0:325; 0:225Þ ¼ ð0:2; 0:575; 0:525Þ:

ðM ; M −L; U −M ÞLR ¼ ½3M −ðM −LÞ þ ðU −M ފ=3

Step 6: Calculate the net flows for all DMs The net flow vectors of all the DMs are then put into a global decision matrix. Steps 1–5 are repeated for the group net flow. However, instead of using e d j to represent the fuzzy difference between the two alternatives for criterion j, e d k is used to represent the fuzzy difference between two alternatives for each of the k DMs. The equations below are a generalization of steps 1–5 in a group decision-making context. Thus, the fuzzy PROMETHEE GDSS can be summarized as follows:   h    i Pi e a; e b ¼ F i ϕi e a −ϕi e b i ¼ 1tok

ð7Þ

where Pi(a,b) denotes the preference of alternative a with respect to alternative b for k DMs. m   X   πgdss e Pi e a; e b ¼ a; e b wi

ð8Þ

i¼1

  where πgdss e a; e b is defined as the fuzzy   weighted sum Pi e a; e b for all DMs. The PROMETHEE GDSS partial and complete rankings are obtained as shown.     1 X πgdss e a ¼ a; ex and ϕþ gdss e m−1 x∈A     1 X ϕ− gdss e πgdss ex; e a ¼ a m−1 x∈A

      ϕgdss e a ¼ ϕgdss þ e a −ϕgdss − e a

Step7: Defuzzification In order to provide a ranking of alternatives, the LR triangular fuzzy number is defuzzified as follows [41]:

ð9Þ

ð11Þ F o r ex a m p l e , th e d e f u z z i f i e d va l ue o f (0.5, 0.6, 0.9) = 3(0.5) −(0.6) + (0.9)/ 3 is 0.6. The defuzzified value is then used to rank the alternatives, where a higher alternative is given greater preference. The algorithm for the fuzzy PROMETHEE GDSS is programmed via MATLAB 2008.

4 Case example We consider the design of high-end ergonomic office chairs, by a manufacturing company identified for its well-known brand of ergonomic office chairs, to illustrate the performance of the proposed methodology. The company usually offers a range of models that are designed based on CNs and ergonomic standards. Recently, the after sales department has registered a considerable number of complaints arising from the innovation in engineering and quality of the products, which saw customer satisfaction rate reduced by 20 %. Hence, the company embarked on a QFD project to improve the development process of an existing product line based on CNs. In the first attempt, a joint task force was formed, which comprises three product designers working in different locations and a facilitator from the marketing department. Since all designers (who are also the DMs in the QFD team) were geographically scattered, it was decided that a virtual team with online video communication be established. The facilitator played a crucial role in ensuring smooth coordination throughout the video conference sessions (i.e., 3 h per session). The stages involved in the ranking of the TRs in a group decision-making context are provided below. 4.1 Stage I: Identify CNs and their relative importance

ð10Þ

where ϕgdss − ðe aÞ and ϕgdss ðe aÞ denote the positive, negative, and the net outranking flow for each alternative, respectively, in fuzzy terms.

The facilitator initiated the study with a thorough evaluation of the needs of the customers across a set of criteria such as sturdy arm rest (CN1), flexibility of swivelling (CN2), smooth and easy seat position adjustment (CN3), height suitability (CN4), lumbar support (CN5), durability and life expectancy (CN6), and aesthetics (CN7). This includes an evaluation of the previous customer complaints related to these criteria. The

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matrix. To measure the relationships between the CNs and TRs, five linguistic terms in the following scale (VW to VS) were introduced.

facilitator also initiated a questionnaire survey and numerous face-to-face interviews with prospective customers. Prospective customers were asked to rate the relative importance of the seven CNs using the following five linguistic terms (VU to VI). Very unimportant Unimportant Medium Important Very important (VU) (U) (M) (I) (VI) [1, 0, 1]

[3, 1, 1]

[5, 2, 2]

[7, 1, 1]

[9, 1, 0]

Very weak (VW)

Weak (U)

Moderate (M)

Strong (S)

Very strong (VS)

[1, 0, 1]

[3, 1, 1]

[5, 1, 1]

[7, 1, 1]

[9, 1, 0]

For example, DM1 perceives that CN1 is very strongly associated with TR1 but very weakly associated with TR8 (see Table 3). Table 3 further provides an overall HOQ matrix, i.e., the relationships between the CNs and TRs for all DMs. The final weights of each DM are obtained as follows:

The linguistic assessments of the CNs and transformed results are shown in Table 2. For example, customer 1 considers CN1 as “important,” which was represented by a triangular fuzzy number [7, 1, 1]LR. The relative importance ratings of each CN is obtained by averaging the fuzzy linguistic terms of 50 customers (see final ratings in Table 2). The fuzzy arithmetic operations can be obtained from Table 1.

e dk ¼

7 X

eclet m ∀k∈k;

ð12Þ

l¼1

where e d k refers to the final fuzzy rating of each DM k based on the relationships between the lCNs and m TRs. For instance, the final fuzzy rating for DM1 for TR1 can be computed as follows:

4.2 Stage II: Generate TRs and the criteria for decision making The QFD team in the first round of online communications identified eight TRs: height and width adjustable arms (TR1), degree of base movement (TR2), pneumatic height adjustment (TR3), the range of seat pan height (TR4), back height adjustment (TR5), back angle adjustment (TR6), the quality of materials (fabric and textile) used (TR7), and the shape of the components (TR8).

ð½4:6; 0:9; 0:8Š⊗ ½9; 1; 0ŠÞ⊕ð½7:2; 1; 0:66Š⊗½5; 1; 1ŠÞ⊕ ð½4:4; 0:92; 0:9Š⊗½1; 0; 1ŠÞ ¼ ½110:6; 29:82; 20:06Š

4.4 Stage IV: Rate the TRs for each DM 4.3 Stage III: Build relationship matrix of CNs and TRs of each DM

Aside from establishing the strength of the association between the CNs and TRs or the relative importance from the customers’ perspective, another two criteria are used for assessing the TRs, namely technical difficulty and estimated expenditure. Technical difficulty describes the level of

The QFD team is required to determine the strength of the association between the CNs and the TRs. To begin the process, each member filled in his own HOQ

Table 2 Relative importance rating of CNs Customer 1

CN1 CN2 CN3 CN4 CN5 CN6 CN7 CN8

Customer 2

Customer i

Customer n

Final ratings

Perception

Fuzzy

Perception

Fuzzy

Perception

Fuzzy

Perception

Fuzzy

I VU U U VI I M VI

[7, 1, 1] [1,0,1] [3, 1, 1] [3, 1, 1] [9,1,0] [7, 1, 1] [5, 1, 1] [9,1,0]

I U M M VI I I U

[7, 1, 1] [3, 1, 1] [5, 1, 1] [5, 1, 1] [9,1,0] [7, 1, 1] [7, 1, 1] [3, 1, 1]

… … … … … … … …

… … … … … … … …

VU U U I U VI M VU

[1, 0, 1] [3, 1, 1] [3, 1, 1] [7, 1, 1] [3, 1, 1] [9,1,0] [5, 1, 1] [1,0,1]

VU very unimportant, U unimportant, M medium, I important, VI very important

[4.6, 0.9, 0.8] [1.6, 0.42, 1] [2.8, 0.54, 0.96] [4, 0.88, 0.9] [5.8, 0.94, 0.82] [7.2, 1, 0.66] [4.2, 0.9, 0.88] [4.4, 0.92, 0.9]

[95.5, 32.24, 27.46] [14.4, 5.38, 9] [31, 8.6, 15.26] [81.8, 25.82, 24,62] [14.4, 5.38, 9] [19.6, 6.58, 9.52]

Final rating for DM1

Final rating for DM2

Final rating for DM3

Relative Importance

L

VH

H

VH

D

VD

D

L

L

L

E

VE

E

[87.8, 28.96, 24.16]

VL very low [2, 1.5, 1.5], L low [5, 2, 2], M modest [9, 3, 3], H high[14, 3, 3], VH very high [20, 5, 5]

VE very easy [1, 0, 2], E easy[3, 2, 2], MD moderately difficult [5, 2, 2], D difficult[7, 2, 2], VD very difficult [9, 2, 0]

VS [35.6, 12.68, 8.1]

M

L

M

MD

E

VE

M

M

L

D

D

MD

VH

VH

VH

E

E

MD

M

M

H

VD

D

VD

[64.8, 16.2, 5.94] [64.8, 16.2, 5.94] [72.2, 24.18, 26.14] [49.4, 19.98, 15.64]

[102.2, 31.96, 25.48] [50.4, 14.2. 11.82] [64.8, 16.2, 5.94] [95, 34.18, 25.2]

VW very weak [1, 0,1], W weak [3, 1, 1], M moderate[5, 1, 1], S strong[7, 1, 1], VS very strong[9, 1, 0]

L

VL

M

MD

Final rating for DM3

MD

Final rating for DM3

MD

MD

VL

E

Final rating for DM2 L

D

Final rating for DM1

VS

DM3 VW

VS

VS

W

VW

TR8

[64.8, 16.2, 5.94] [64.8, 16.2, 5.94] [75.8, 24.14, 26.3] [40.2, 13.58, 13.68]

S VS

DM2 W

S

DM1 VW

DM3

VS

VW

W

VW

TR7

VS

Estimated Final rating for DM1 Expenditure Final rating for DM2

Technical Difficulty

[110.6, 29.82, 20.06] [14.4, 5.38, 9] [46.2, 16.36, 17.24] [61, 18.68, 13.06]

[4.4, 0.92, 0.9]

CN7

M

VS

VS

VS

TR6

DM2

DM1

[4.2, 0.9, 0.88]

W

DM3 M

CN6

S VS

VS M

DM2 S

VS

TR5

DM1 M

[7.2, 1, 0.66]

DM3

VS VS

VW

M

DM2

S

[5.8, 0.94, 0.82] DM1

DM3

M

W

TR4

CN5

CN4

VS

DM3 VS

VS

DM2

TR3

VS

CN3

VS

DM1

DM3 VS

TR2

DM2

[1.6, 0.42, 1]

CN2

DM2 VS

DM1 VS

TR1

[2.8, 0.54, 0.96] DM1

[4.6, 0.9, 0.8]

CN1

Table 3 HOQ rating

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Int J Adv Manuf Technol Table 4 Multi-criteria information Criteria

Preference functions

Min/Max p

Relative importance V-shape criterion (type3) Max Technical difficulty V-shape criterion (type3) Min Estimated expenditure V-shape criterion (type3) Min

wj

0.05 0.4 3 0.3 3 0.3

difficulty in the following linguistic terms (VE to VD) and measures how much complexity is associated with carrying out each TR. Very easy (VE)

Easy (E)

Moderately difficult (MD)

Difficult (D)

Very difficult (VD)

[1, 0, 2]

[3, 2, 2]

[5, 2, 2]

[7, 2, 2]

[9, 2, 0]

Finally, estimated expenditure, in the following linguistic terms, indicates the degree of the necessary expenses on labor and material (in $‘000), which were required to meet each TR. Very low (VL)

Low (L)

Modest (M)

High (H)

Very high (VH)

[2, 1.5, 1.5]

[5, 2, 2]

[9, 3, 3]

[14, 3, 3]

[20, 5, 5]

Table 3 shows the HOQ for all the DMs and the criteria. 4.5 Stage V: Set the parameter p Aside from the relationship between the CNs and TRs (i.e., relative Importance), the DMs decided that it would be more useful to consider a multi-criteria approach. Therefore, the second round of virtual communication was organized to decide on the parameter setting for the weights and type of preference function for the additional criteria of technical difficulty and estimated expenditure. A Delphi method was

used to generate consensus on the type of preference function and the weights of criteria among the DMs. All criteria except relative importance are to be minimized. Table 4 contains the parameter setting p for the type 3 preference function and the weights which were set by the DMs through a Delphi approach. 4.6 Stage VI: Conduct the fuzzy PROMETHEE GDSS algorithm With the HOQ matrix and parameter setting finalized, the fuzzy PROMETHEE GDSS algorithm was programmed and computed via MATLAB 2008 in two phases. The first phase considers up to the first five steps of the fuzzy PROMETHEE GDSS. The results of the three DMs are given in Table 5. While the DMs presented slightly different concerns and opinions for assessing and ranking the proposed alternatives, they provided similar rankings for the best alternative (TR7) and the worst alternative (TR2). In the second phase, another round of the Delphi process was initiated for the parameter p, and each DM finally agreed to a value of 0.15 or a 15 % tolerance. The DMs also agreed that all of their preferences were of equal importance in this decision-making process, which is reflected by the weights of 0.333 in Table 5. However, our approach can cater to varying importance across the DMs and threshold values. Subsequently, we compute steps 5 and 6 of the fuzzy PROMETHEE GDSS to arrive at the fuzzy global net flows for the TRs (see Table 6). To provide a ranking of the alternatives, the LR triangular fuzzy numbers were defuzzified according to step 7 of the fuzzy PROMETHEE GDSS. The defuzzified value was then used to rank the alternatives, where a higher alternative was given greater preference. The final results show that alternatives TR7, TR1, and TR3 were preferred, whereas TR2 and TR5 were considered as the

Table 5 Data matrix for group decision making DM1

DM2

DM3

Weight Max/Min Type p

0.333 Max 3 0.15

Rank

0.333 Max 3 0.15

Rank

0.333 Max 3 0.15

Rank

TR1 TR2 TR3 TR4 TR5 TR6 TR7 TR8

[0.267, 0.514, 0.503] [−0.432, 0.376, 0.407] [0.233, 0.332, 0.319] [−0.227, 0.259, 0.263] [−0.235, 0.257, 0.322] [−0.149, 0.235, 0.225] [0.271, 0.303, 0.303] [0.272, 0.351, 0.285]

2 8 4 7 6 5 1 3

[0.153, 0.367, 0.378] [−0.447, 0.438, 0.452] [0.121, 0.385, 0.336] [0.014, 0.346, 0.4] [−0.249, 0.270, 0.276] [0.177, 0.229, 0.192] [0.294, 0.419, 0.431] [−0.064, 0.326, 0.315]

3 8 4 5 7 2 1 6

[0.007, 0.210, 0.221] [−0.375, 0.299, 0.335] [0.042, 0.505, 0.529] [−0.046, 0.253, 0.264] [−0.038, 0.132, 0.124] [0.025, 0.164, 0.145] [0.296, 0.425, 0.435] [0.089, 0.234, 0.170]

5 8 3 7 6 4 1 2

Int J Adv Manuf Technol Table 6 Global ranking of alternatives Alternative

Fuzzy global net flows in LR mode

Defuzzification

Ranking

TR1 TR2 TR3 TR4

[0.147, 0.133, 0.169] [−0.396, 0.201, 0.270] [0.142, 0.205, 0.189] [−0.103, 0.050, 0.045]

0.159 −0.373 0.137 −0.105

2 8 3 6

TR5 TR6 TR7 TR8

[−0.142, 0.177, 0.210] [−0.065, 0.038, 0.015] [0.291, 0.218, 0.185] [0.084, 0.163, 0.225]

−0.131 −0.073 0.280 0.105

7 5 1 4

worst alternatives as a group (Table 6). The results also show the inconsistencies and similarities among the individual and global rankings. While individual and global evaluations agree on the best (TR7) and worst (TR2) alternatives, the results for the six other alternatives were quite different. Also, the result for the global evaluation was similar to DM1, whereas DM2 and DM3 expressed rather different concerns and preferences in the six alternative TRs to global ranking. 4.7 Comparison with fuzzy TOPSIS Table 7 presents ranking results obtained from fuzzy TOPSIS, which can be compared with the results derived earlier with the Fuzzy PROMETHEE GDSS method. The TOPSIS approach considers a preferred alternative to be one that has the closest distance to the positive ideal solution and the farthest distance from the negative ideal solution [24]. A positive ideal solution is composed of the best performance values of each criterion whereas the negative ideal solution consists of the worst performance values. The closeness coefficient determines the ranking order of alternatives by calculating the distances of alternatives to both the positive ideal and negative ideal solutions. The various applications of fuzzy TOPSIS for group decision making are discussed in Behzadian et al. [4]. This paper uses an extended fuzzy TOPSIS method that was originally

Table 7 Ranking of alternatives by fuzzy TOPSIS

Alternative

CCi

Ranking

TR1 TR2 TR3 TR4 TR5 TR6 TR7 TR8

0.685 0.323 0.654 0.419 0.431 0.517 0.761 0.588

2 8 3 7 6 5 1 4

proposed by Chen [13] for comparison purposes. In order to pool the decision makers’ opinions, the aggregated data matrix and weights for criteria are obtained from Tables 3 and 4, respectively. According to the closeness coefficient (CC) of alternatives, the ranking order of eight alternatives is determined as TR7>TR1>TR3>TR8>TR6>TR5>TR4>TR2. In this problem, there is no difference between the final solution produced by the two MCDA methods. It indicates that the ranks obtained from PROMETHEE GDSS are highly reliable for the purposes of ranking TRs. The main advantage of PROMETHEE GDSS was the rapid communication among team members. It allows each member to express their own preferences rapidly, while comparing their individual rankings with the global ranking.

5 Conclusion This article presents a fuzzy PROMETHEE GDSS method to handle the ranking and selection of the TRs in the final stage of the HOQ process for a high-end ergonomic chair manufacturer. The approach allows a facilitator to collect the relevant data from each DM located in different geographical areas and aggregate into a group decision matrix for use by the QFD team of designers. The approach also allows each criterion to have different tolerance levels contributing to the TR, as well as each DM to possess a different threshold level toward the TR. We show that applying the fuzzy PROMETHEE GDSS can prevent the loss of valuable evaluation data and overcome the difficulty of integrating subjective linguistic assessments into the group decision-making process. Future research can explore the assignment of weights for the alternatives and DMs. During the decision-making process, serious conflicts may arise from different concerns and preferences between DMTs. A further geometrical analysis for interactive assistance (GAIA) allowed the DMTs to check the consistency, independency, and similarity of preferences among the DMTs and to ensure the quality of the group decision-making process, based on the quality of information preserved. Acknowledgments Dr. Joshua Ignatius would like to express his gratitude to Universiti Sains Malaysia for partially supporting this research under the research grant no. 1001/pmaths/817060.

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