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Journal ArticleDOI

Applications of the extent analysis method on fuzzy AHP

20 Dec 1996-European Journal of Operational Research (North-Holland)-Vol. 95, Iss: 3, pp 649-655

TL;DR: The use of triangular fuzzy numbers for pairwise comprison scale of fuzzy AHP is introduced, and the use of the extent analysis method for the synthetic extent value S i of the pairwise comparison is used.
Abstract: In this paper, a new approach for handling fuzzy AHP is introduced, with the use of triangular fuzzy numbers for pairwise comprison scale of fuzzy AHP, and the use of the extent analysis method for the synthetic extent value Si of the pairwise comparison. By applying the principle of the comparison of fuzzy numbers, that is, V(M1 ⩾ M2) = 1 iff m1 ⩾ m2, V(M2 ⩾ M1) = hgt(M1 ∩ M2) = μM1 (d), the vectors of weight with respect to each element under a certaine criterion are represented by d(Ai) = min V(Si ⩾ Sk), k = 1, 2,…, n; k ≠ i. This decision process is demonstrated by an example.
Topics: Fuzzy number (60%), Fuzzy set operations (56%), Defuzzification (54%), Fuzzy classification (54%), Fuzzy mathematics (52%)
Citations
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Journal ArticleDOI
Felix T.S. Chan1, Niraj Kumar1Institutions (1)
Abstract: Global supplier development is a multi-criterion decision problem which includes both qualitative and quantitative factors. The global supplier selection problem is more complex than domestic one and it needs more critical analysis. The aim of this paper is to identify and discuss some of the important and critical decision criteria including risk factors for the development of an efficient system for global supplier selection. Fuzzy extended analytic hierarchy process (FEAHP) based methodology will be discussed to tackle the different decision criteria like cost, quality, service performance and supplier's profile including the risk factors involved in the selection of global supplier in the current business scenario. FEAHP is an efficient tool to handle the fuzziness of the data involved in deciding the preferences of different decision variables. The linguistic level of comparisons produced by the customers and experts for each comparison are tapped in the form triangular fuzzy numbers to construct fuzzy pair-wise comparison matrices. The implementation of the system is demonstrated by a problem having four stages of hierarchy which contains different criteria and attributes at wider perspective. The proposed model can provide not only a framework for the organization to select the global supplier but also has the capability to deploy the organization's strategy to its supplier.

1,078 citations


Journal ArticleDOI
Cengiz Kahraman1, Ufuk Cebeci1, Ziya Ulukan2Institutions (2)
Abstract: A supplier selection decision inherently is a multi‐criterion problem. It is a decision of strategic importance to companies. The nature of this decision usually is complex and unstructured. Management science techniques might be helpful tools for these kinds of decision‐making problems. The aim of this paper is to use fuzzy analytic hierarchy process (AHP) to select the best supplier firm providing the most satisfaction for the criteria determined. The purchasing managers of a white good manufacturer established in Turkey were interviewed and the most important criteria taken into account by the managers while they were selecting their supplier firms were determined by a questionnaire. The fuzzy AHP was used to compare these supplier firms.

1,009 citations


Journal ArticleDOI
Cengiz Kahraman1, Ufuk Cebeci1, Da RuanInstitutions (1)
TL;DR: The customers of three Turkish catering firms were interviewed and the most important criteria taken into account by the customers while they were selecting their catering firmsWere determined by a designed questionnaire and the fuzzy analytic hierarchy process was used to compare these catering firms.
Abstract: Catering is the act of providing food and services or it may be defined as preparing or providing food for someone else to serve; or preparing, delivering and serving food at the premises of another person or event. The aim of this paper is to provide an analytical tool to select the best catering firm providing the most customer satisfaction. The customers of three Turkish catering firms were interviewed and the most important criteria taken into account by the customers while they were selecting their catering firms were determined by a designed questionnaire. The fuzzy analytic hierarchy process was used to compare these catering firms. The means of the triangular fuzzy numbers produced by the customers and experts for each comparison were successfully used in the pairwise comparison matrices.

689 citations


Cites methods from "Applications of the extent analysis..."

  • ...Chang (1996) introduces a new approach for handling fuzzy AHP, with the use of triangular fuzzy numbers for pairwise comparison scale of fuzzy AHP, and the use of the extent analysis method for the synthetic extent values of the pairwise comparisons....

    [...]


Journal ArticleDOI
TL;DR: With the proposed model, manufacturers can have a better understanding of the capabilities that a green supplier must possess and can evaluate and select the most suitable green supplier for cooperation.
Abstract: With growing worldwide awareness of environmental protection, green production has become an important issue for almost every manufacturer and will determine the sustainability of a manufacturer in the long term. A performance evaluation system for green suppliers thus is necessary to determine the suitability of suppliers to cooperate with the firm. While the works on the evaluation and/or selection of suppliers are abundant, those that concern environmental issues are rather limited. Therefore, in this study, a model for evaluating green suppliers is proposed. The Delphi method is applied first to differentiate the criteria for evaluating traditional suppliers and green suppliers. A hierarchy is constructed next to help evaluate the importance of the selected criteria and the performance of green suppliers. Since experts may not identify the importance of factors clearly, the results of questionnaires may be biased. To consider the vagueness of experts' opinions, the fuzzy extended analytic hierarchy process is exploited. With the proposed model, manufacturers can have a better understanding of the capabilities that a green supplier must possess and can evaluate and select the most suitable green supplier for cooperation.

653 citations


Cites background from "Applications of the extent analysis..."

  • ...FEAHP was first introduced by Chang (1992, 1996)....

    [...]

  • ...Otherwise, the degree of possibility V(M1 P M2) is the ordinate of the highest intersection point between l ðM1Þ and l ðM2Þ (Chang, 1996; Lee, 2009; Lee, Kang, & Chang, in press; Zhu, Jing, & Chang, 1999):...

    [...]

  • ...Otherwise, the degree of possibility V(M1 P M2) is the ordinate of the highest intersection point between l ðM1Þ and l ðM2Þ (Chang, 1996; Lee, 2009; Lee, Kang, & Chang, in press; Zhu, Jing, & Chang, 1999): VðM2 P M1Þ ¼ hgtðM1 \M2Þ ¼ lðdÞ ¼ m 1 mþ2 ðm2 mþ2 Þ ðm1 m 1 Þ ð2Þ where M is a convex fuzzy…...

    [...]


Journal ArticleDOI
Hepu Deng1Institutions (1)
TL;DR: The result shows that the approach developed is simple and comprehensible in concept, efficient in computation, and robust and flexible in modeling the human evaluation process, thus making it of general use for solving practical MA problems.
Abstract: The analytic hierarchy process (AHP) is a popular method for solving multicriteria analysis (MA) problems involving qualitative data. However, this method is often criticized due to its use of an unbalanced scale of judgements and its inability to adequately handle the inherent uncertainty and imprecision of the pairwise comparison process. This paper presents a fuzzy approach for tackling qualitative MA problems in a simple and straightforward manner. As a result, effective decisions can be made based on adequate modeling of the uncertainty and imprecision in human behavior. An empirical study of a tender selection problem at Monash municipal government of Victoria in Australia is conducted. The result shows that the approach developed is simple and comprehensible in concept, efficient in computation, and robust in modeling human evaluation processes which make it of general use for solving practical qualitative MA problems.

646 citations


References
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Book ChapterDOI
Thomas L. Saaty1, Kevin P. KearnsInstitutions (1)
01 Jan 1985
Abstract: This chapter provides an overview of Analytic Hierarchy Process (AHP), which is a systematic procedure for representing the elements of any problem hierarchically. It organizes the basic rationality by breaking down a problem into its smaller constituent parts and then guides decision makers through a series of pair-wise comparison judgments to express the relative strength or intensity of impact of the elements in the hierarchy. These judgments are then translated to numbers. The AHP includes procedures and principles used to synthesize the many judgments to derive priorities among criteria and subsequently for alternative solutions. It is useful to note that the numbers thus obtained are ratio scale estimates and correspond to so-called hard numbers. Problem solving is a process of setting priorities in steps. One step decides on the most important elements of a problem, another on how best to repair, replace, test, and evaluate the elements, and another on how to implement the solution and measure performance.

16,510 citations


Journal ArticleDOI
TL;DR: A fuzzy version of Saaty's pairwise comparison method (1980) extended by de Graan and Lootsma (1981), adapted in such a way, that decision-makers are asked to express their opinions in fuzzy numbers with triangular membership functions.
Abstract: We present a fuzzy method for choosing among a number of alternatives under conflicting decision criteria: a fuzzy version of Saaty's pairwise comparison method (1980) extended by de Graan (1980) and Lootsma (1981).Each ratio expressing the relative significance of a pair of factors is displayed in a matrix, from which suitable weights can be extracted. Since these ratios are essentially fuzzy-they express the opinion of a decision-maker on the importance of a pair of factors-we have adapted the above-mentioned method in such a way, that decision-makers are asked to express their opinions in fuzzy numbers with triangular membership functions. We apply the method at two distinct levels: first to find fuzzy weights for the decision criteria, and second, to find fuzzy weights for the alternatives under each of the decision criteria. By a suitable combination of these results, we obtain fuzzy scores for the alternatives, as well as their sensitivities. Using these fuzzy scores, the decision-makers should be able to make a choice for one of the alternatives.

2,390 citations


"Applications of the extent analysis..." refers background or methods in this paper

  • ...The ordering relation between the candidates is exactly the same as in [3]....

    [...]

  • ...Since the publication of Saaty's The Analy t ic Hierarchy Process (for short AHP), Netherlands's scholars van Laarhoven and Pedrycg [3] proposed a method, where the fuzzy comparing judgment is represented by triangular fuzzy numbers....

    [...]


Journal ArticleDOI
V. K. Rohatgi1Institutions (1)

530 citations


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Performance
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No. of citations received by the Paper in previous years
YearCitations
202219
2021358
2020383
2019318
2018286
2017291