Applications of the extent analysis method on fuzzy AHP
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.
About: This article is published in European Journal of Operational Research.The article was published on 1996-12-20. It has received 3724 citations till now. The article focuses on the topics: Fuzzy number & Fuzzy set operations.
Citations
More filters
TL;DR: A fuzzy AHP approach is proposed to determine the level of faulty behavior risk (FBR) in work systems and faulty behavior is prevented before occurrence and work system safety is improved.
412 citations
Cites methods from "Applications of the extent analysis..."
...The steps of Chang’s extent analysis can be given as follows: Step 1: The value of fuzzy synthetic extent with respect to the ith object is defined as Si Xm j¼1 eM jgi Xn i¼1 Xm j¼1 eM jgi " # 1 ; ð6Þ where denotes the extended multiplication of two fuzzy numbers....
[...]
...Chang’s fuzzy AHP method Let X = {o1,o2, . . . ,on} be an object set, and U = {g1,g2, . . . ,gm} be a goal set....
[...]
...According to the method of Chang’s extent analysis, each object is considered one by one, and for each object, the analysis is carried out for each of the possible goals, gi....
[...]
...Chang’s extent analysis method used in this paper has proved to be simpler, less time consuming and having less computational expense compared to other existing fuzzy AHP methods....
[...]
...The definition of the triangular fuzzy number and the steps of Chang’s extent analysis method are given in Appendix....
[...]
TL;DR: In this paper, fuzzy multicriteria decision-making methodologies are suggested for the selection among renewable energy alternatives, which are based on axiomatic design (AD) and analytic hierarchy process (AHP).
404 citations
TL;DR: A new way to check the consistency of an intuitionistic preference relation is proposed and an automatic procedure to repair the inconsistent one is introduced and a novel normalizing rank summation method is developed, on which the priorities of the hierarchy in the IFAHP are derived.
Abstract: The intuitionistic fuzzy set has shown definite advantages in handling vagueness and uncertainty over a fuzzy set. Taking the powerfulness of the analytic hierarchy process (AHP) and the fuzzy AHP (FAHP) into account when tackling comprehensive multi-criteria decision-making problems, in this paper, we extend the classic AHP and the FAHP into the intuitionistic fuzzy AHP (IFAHP) in which the preferences are represented by intuitionistic fuzzy values. The IFAHP can be used to handle more complex problems, where the decision maker has some uncertainty in assigning preference values to the objects considered. The paper proposes a new way to check the consistency of an intuitionistic preference relation and then introduces an automatic procedure to repair the inconsistent one. It is worth pointing out that our proposed method can improve the inconsistent intuitionistic preference relation without the participation of the decision maker, and thus, it can save much time and show some advantages over the AHP and the FAHP. This paper also develops a novel normalizing rank summation method to derive the priority vector of an intuitionistic preference relation, on which the priorities of the hierarchy in the IFAHP are derived. The procedure of the IFAHP is given in detail, and an example concerning global supplier development is used to demonstrate our results.
402 citations
TL;DR: A fuzzy analytic hierarchy process (FAHP) model, which incorporates the benefits, opportunities, costs and risks (BOCR) concept, is constructed to evaluate various aspects of suppliers to propose an analytical approach to select suppliers under a fuzzy environment.
Abstract: Even though the research on supplier selection is abundant, the works usually only consider the critical success factors in the buyer-supplier relationship. However, the negative aspects of the buyer-supplier relationship must also be considered simultaneously. The main objective in this study is to propose an analytical approach to select suppliers under a fuzzy environment. A fuzzy analytic hierarchy process (FAHP) model, which incorporates the benefits, opportunities, costs and risks (BOCR) concept, is constructed to evaluate various aspects of suppliers. Multiple factors that are positively or negatively affecting the success of the relationship are analyzed by taking into account experts' opinion on their importance, and a performance ranking of the suppliers is obtained. TFT-LCD manufacturers in Taiwan, which is the largest TFT-LCD producer country in the world, are facing increasing competition nowadays, and the selection of the most appropriate suppliers for cooperation is essential for firms to achieve competitive advantage. A case study of backlight unit supplier selection for a TFT-LCD manufacturer is presented, and the proposed model is applied to facilitate the decision process. The model is a general form that can be tailored and applied by firms that are making decisions on supplier selection.
401 citations
TL;DR: A modified fuzzy TOPSIS methodology is proposed for the selection of the best energy technology alternative and the weights of the selection criteria are determined by fuzzy pairwise comparison matrices.
Abstract: Research highlights? We proposed a modified fuzzy TOPSIS methodology for energy planning decisions. ? The weights of the selection criteria are determined by fuzzy AHP. ? The method is applied to a multicriteria energy planning problem. Energy planning is a complex issue which takes technical, economic, environmental and social attributes into account. Selection of the best energy technology requires the consideration of conflicting quantitative and qualitative evaluation criteria. When decision-makers' judgments are under uncertainty, it is relatively difficult for them to provide exact numerical values. The fuzzy set theory is a strong tool which can deal with the uncertainty in case of subjective, incomplete, and vague information. It is easier for an energy planning expert to make an evaluation by using linguistic terms. In this paper, a modified fuzzy TOPSIS methodology is proposed for the selection of the best energy technology alternative. TOPSIS is a multicriteria decision making (MCDM) technique which determines the best alternative by calculating the distances from the positive and negative ideal solutions according to the evaluation scores of the experts. In the proposed methodology, the weights of the selection criteria are determined by fuzzy pairwise comparison matrices. The methodology is applied to an energy planning decision-making problem.
395 citations
References
More filters
01 Jan 1985
TL;DR: Analytic Hierarchy Process (AHP) as mentioned in this paper is a systematic procedure for representing the elements of any problem hierarchically, which organizes the basic rationality by breaking down a problem into its smaller constituent parts and then guides decision makers through a series of pairwise comparison judgments to express the relative strength or intensity of impact of the elements in the hierarchy.
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.
16,547 citations
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.
2,631 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....
[...]
537 citations