Multiattribute Decision-Making Methods with Intuitionistic Fuzzy Sets
In management applications, the intuitionistic fuzzy set has already been a popular topic due to its flexibility and expedience for dealing with imprecision and uncertainty, especially the hesitancy degree of decision makers in judgment and decision. In 2
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Multiattribute Decision-Making Methods with Intuitionistic Fuzzy Sets
3.1 Introduction In management applications, the intuitionistic fuzzy set has already been a popular topic due to its flexibility and expedience for dealing with imprecision and uncertainty, especially the hesitancy degree of decision makers in judgment and decision. In 2005, we firstly proposed the formal mathematical expression of multiattribute decision-making with intuitionistic fuzzy sets and established the intuitionistic fuzzy relative closeness degree method [1]. Hereafter, many researches were conducted and some valued results were achieved along this direction. Presently, how to solve complex multiattribute decision-making problems with intuitionistic fuzzy sets has become an important field. In the aforementioned Chap. 2, we mainly discussed the intuitionistic fuzzy aggregation operators and intuitionistic fuzzy generalized hybrid weighted averaging method of multiattribute decision-making with intuitionistic fuzzy sets. This chapter will discuss the linear weighted averaging method of multiattribute decision-making with both weights and attribute ratings expressed by intuitionistic fuzzy sets, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and the optimum seeking method for multiattribute decision-making with intuitionistic fuzzy positive and negative ideal-solutions and weights known [2], the Linear Programming Technique for Multidimensional Analysis of Preference (LINMAP) for multiattribute decision-making with an intuitionistic fuzzy positive ideal-solution and weights unknown [3], and the fraction mathematical programming method and the linear programming method of intuitionistic fuzzy multiattribute decision-making with intuitionistic fuzzy weights unknown [4].
D.-F. Li, Decision and Game Theory in Management with Intuitionistic Fuzzy Sets, Studies in Fuzziness and Soft Computing 308, DOI: 10.1007/978-3-642-40712-3_3, Springer-Verlag Berlin Heidelberg 2014
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3 Multiattribute Decision-Making Methods with Intuitionistic Fuzzy Sets
3.2 The Linear Weighted Averaging Method of Multiattribute Decision-Making with Weights and Ratings Expressed by Intuitionistic Fuzzy Sets In the foregoing Sect. 2.3.1, we gave the formal mathematical expression of multiattribute decision-making with intuitionistic fuzzy sets. Namely, n alternatives xj ðj ¼ 1; 2; . . .; nÞ and m attributes oi ði ¼ 1; 2; . . .; mÞ constitute the sets of the alternatives and attributes, which are denoted by X ¼ fx1 ; x2 ; . . .; xn g and O ¼ fo1 ; o2 ; . . .; om g, respectively. The ratings (or evaluations) of alternatives xj 2 X ðj ¼ 1; 2; . . .; nÞ on attributes oi 2 O ði ¼ 1; 2; . . .; mÞ are expressed with intuitionistic fuzzy sets Fij ¼ lij ; tij , where lij 2 ½0; 1; tij 2 ½0; 1, and 0 lij þ tij 1. Thus, the ratings of any alternative xj 2 X ðj ¼ 1; 2; . . .; nÞ on all m attributes are expressed with the intuitionistic fuzzy vector ð l1j ; t1j ; T l2j ; t2j ; . . .; lmj ; tmj Þ . The intuitionistic fuzzy de
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