An interactive algorithm for large scale multiple objective programming problems with fuzzy parameters through TOPSIS approach

Abstract

In this paper, we extend TOPSIS (Technique for Order Preference by Similarity Ideal Solution) for solving Large Scale Multiple Objective Programming problems involving fuzzy parameters. These fuzzy parameters are characterized as fuzzy numbers. For such problems, the α-Pareto optimality is introduced by extending the ordinary Pareto optimality on the basis of the α-Level sets of fuzzy numbers. An interactive fuzzy decision making algorithm for generating α-Pareto optimal solution through TOPSIS approach is provided, where a decision maker (DM) is asked to specify the degree α and the relative importance of objectives. Finally, a numerical example is given to clarify the main results developed in the paper

Evaluation of Sustainable Development Indicators With Fuzzy TOPSIS Based on Subjective and Objective Weights

“…This new version offers a fuzzy relative closeness for each alternative which the closeness is badly imprecise and overstressed because of the reason of fuzzy arithmetic operations. Besides, Abo-Sinha and Abou-El-Enien [9] used TOPSIS by expanding this method for solving large-scale multiple objective programming problems involving fuzzy parameters. Chen [10] proposed the rate of each alternative as well as the weight of each criterion using linguistic terms; can be expressed in triangular fuzzy numbers.…”

Hybrid models in decision making under uncertainty: The case of training provider evaluation

“…It was developed by Hwang and Yoon [24] to illustrate the ranking of a set of alternatives through their distances from the most optimistic (positive ideal) to pessimistic (negative or anti-ideal) points. On the hybrid modelling forefront, TOPSIS has been integrated with grey relation [9,53], analytic network process for vendor selection problem [44], and used to solve large scale multiobjective programming problems that involve fuzzy parameters [1]. In addition, Chen [8] and Jahanshahloo et al [26] had extended TOPSIS for group-decision making under fuzzy environment.…”

“…Hence, π(d j ) = π (1, 2) and supposing w 1 = 0.4, w 2 = 0.6 and P(d 1 Table 6. The algorithm of Fuzzy PROMETHEE is programmed via MATLAB 2006b.…”

Application of axiomatic design and TOPSIS methodologies under fuzzy environment for proposing competitive strategies on Turkish container ports in maritime transportation network

“…Fuzzy TOPSIS is an effective and also simple method to measure the distance between two triangular fuzzy numbers, when the assessment of alternatives with respect to criteria and the importance weight are suitable to use the linguistic variables instead of numerical values in decision-making process. Up to now, fuzzy TOPSIS method is used to solve decision making and performance evaluation problem under different domains recently (Abo-Sinna, Amer, & Ibrahim, 2008Abo-Sinna & Abou-El-Enien, 2006Benítez, Martín, & Román, 2007;Chen, Lin, & Huang, 2006;Kahraman, Buyukozkan, et al, 2007;Kahraman, Cevik, Ates, & Gulbay, 2007;Kuo, Tzeng, & Huang, 2007;Lin & Chang, 2008 Onut & Soner, in press;Wang & Chang, 2007;Wang & Elhag, 2006;Wang & Lee, 2007;Wang, Luo, & Hua, 2007;Yang, Chen, & Hung, 2007). …”