دانلود رایگان ترجمه مقاله AHP فازی برای تعیین وزن نسبی معیارهای ارزیابی (نشریه الزویر 2010)

AHP فازی برای تعیین وزن نسبی معیارهای ارزیابی و TOPSIS فازی برای رتبه بندی جایگزین ها

Fuzzy AHP to determine the relative weights of evaluation criteria and Fuzzy TOPSIS to rank the alternatives

Abstract

The aim of this study is to propose a Fuzzy multi-criteria decision-making approach (FMCDM) to evaluate the alternative options in respect to the user’s preference orders. Two FMCDM methods are proposed for solving the MCDM problem: Fuzzy Analytic Hierarchy Process (FAHP) is applied to determine the relative weights of the evaluation criteria and the extension of the Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) is applied to rank the alternatives. Empirical results show that the proposed methods are viable approaches in solving the problem. When the performance ratings are vague and imprecise, this Fuzzy MCDM is a preferred solution.

1 Introduction

MCDM refers to finding the best opinion from all of the feasible alternatives in the presence of multiple, usually conflicting, decision criteria. Priority-based, outranking, distance-based and mixed methods could be considered as the primary classes of the current methods [1]. Multiple objective decision-making (MODM) consists of a set of conflicting goals that cannot simultaneously be achieved. It concentrates invariably on the continuous decision spaces, and can be solved by mathematical programming techniques. MODM deals generally with (i) preferences relating to the decision maker’s objectives and (ii) the relationships between objectives and attributes. An alternative could be described either in terms of its attributes or in terms of the attainment of the decision maker’s objectives [11].

MADM deals with the problem of choosing an option from a set of alternatives, which are characterized in terms of their attributes. MADM is a qualitative approach due to the existence of the criteria subjectivity. It requires information on the preferences among the instances of an attribute, and the preferences across the existing attributes. The decision maker may express or define a ranking for the attributes in terms of importance/weights. The aim of the MADM is to obtain the optimum alternative that has the highest degree of satisfaction for all of the relevant attributes [11].

One of the most outstanding MCDM approaches is the Analytic Hierarchy Process (AHP) [2,39], which has its roots in obtaining the relative weights among the factors and the total values of each alternative based on these weights. In comparison with other MCDM methods, the AHP method has widely been used in multi-criteria decision-making and has been applied successfully in many practical decision-making problems [40]. In spite of AHP method popularity, this method is often criticized because of its inability in handling the uncertain and imprecise decision-making problems [3]. TOPSIS, another MCDM method, is based on choosing the best alternative, which has the shortest distance from the positive-ideal alternative and the longest distance from the negative-ideal alternative. More detailed information about the TOPSIS method can be found in Hwang and Yoon [4].

In the primitive forms of the AHP and TOPSIS methods, experts’ comparisons about the criteria, sub-criteria, and alternatives are represented in the form of exact numbers. However, in many practical cases, the experts’ preferences are uncertain and they are reluctant or unable to make numerical comparisons. Fuzzy decision-making is a powerful tool for decision-making in fuzzy environment. Classical decision-making methods work only with exact and ordinary data, so there is no place for fuzzy and vague data. Human has a good ability for qualitative data processing, which helps him/her to make decisions in fuzzy environments.

The main objective of this paper is to propose new AHP and TOPSIS methods’ frameworks for dealing with the evaluations’ uncertainty and imprecision in which the expert’s comparisons are represented as fuzzy numbers. In this paper, we will use Fuzzy Analytic Hierarchy Process (FAHP) method for determining the final weights of alternatives, also by using a group of experts’ comparisons. However, for evaluating the alternatives of multicriteria problems, different attribute weights have an important role in the decision-making process.

Stam and Silva [41] use multiplicative priority rating methods for the AHP. Saaty [2] showed that eigenvector of one pairwise comparison matrix represents the local priority weights of the compared elements (criteria, sub-criteria, and alternatives). Abosinna and Amer [42] extend TOPSIS approach to solve multiobjective large-scale nonlinear programming (MOLSNLP) problems. Aguaron et al. [5] focused on evaluating the consistency of the experts’ judgments in AHP decision support system (DSS). Holloway and White [43], with uncertainty, used the question– response process as a sequential decision-making method and developed a dynamic programming for it. One of the most diffused approaches in MCDM is the simple additive weight method (SAW), in which all the criteria is weighted by a suitable real number, representing the importance of them. In spite of its simplicity, the SAW method has some problems: no interaction among the attributes is admitted, so the preferential independence axiom is required. Moreover, some difficulties exist about the weights assignment. So later, some new methods such as AHP are suggested [2], and other tools such as Fuzzy logic, and the theory of aggregation operators [6] have been used to improve multiobjective decision-making methods.

For evaluating airlines’ service quality, Tsaur et al. [7] use AHP method to calculate the criteria weights and use TOPSIS method to determine the alternatives’ ranking. Feng and Wang [19] uses TOPSIS method for evaluating the performance of different airlines. TOPSIS and Fuzzy TOPSIS methods have been applied in different applications, and are commonly used in solving multiple attribute decision problems (MADM) [8,9].

Isiklar and Buyukozkan [10] use a multi-criteria decisionmaking approach to evaluate mobile phone alternatives. In this paper, we try to solve their problem but in a fuzzy environment. Yang and Hung [11] focuses on the evaluation of alternative layout designs. We use their problem but we solve it with FAHP and FTOPSIS procedures. Our proposed methodology consists of two steps: in the first step, Fuzzy Analytic Hierarchy Process (FAHP) is applied to determine the relative weights of the evaluation criteria. In the second step, fuzzy TOPSIS method (FTOPSIS) is applied to rank the alternatives.

The rest of this paper is organized as follows: The evaluation framework is presented in Section 2. The next section illustrates the methods used to compute the criteria weights and to select the best alternative. Section 4 illustrates these methods in detail for the special defined problem of this paper. Computational results are represented in Section 5 and Section 6 includes the conclusions and future researches.