Analysis of fuzzy Hamacher aggregation functions for uncertain multiple attribute decision making

Abstract

As generalizations of algebraic and Einstein t-norms and t-conorms, Hamacher t-norm and t-conorm have been widely applied in fuzzy multiple attribute decision making (MADM) to combine assessments on each attribute, which are generally expressed by Atanassov"s intuitionistic fuzzy (AIF) numbers, interval-valued intuitionistic fuzzy (IVIF) numbers, hesitant fuzzy (HF) elements, and dual hesitant fuzzy (DHF) elements. Due to the fact that AIF numbers and HF elements are special cases of IVIF numbers and DHF elements, respectively, two propositions can be established from analyzing numerical examples and real cases concerning MADM with IVIF and DHF assessments in the literature: (1) the monotonicity of alternative scores derived from Hamacher arithmetic and geometric aggregation operators with respect to the parameter r in Hamacher t-norm and t-conorm; and (2) the relationship between alternative scores generated by Hamacher arithmetic and geometric aggregation operators, given the same r. Here, we provide the theoretical proof of these two propositions in the context of MADM with IVIF and DHF assessments.With the theoretical support of these propositions, the meaning of r in MADM is explained, and a new method is proposed to compare alternatives in MADM with consideration of all possible values of r. Two numerical examples are solved by the proposed method and the other two existing methods to demonstrate the applicability and validity of the proposed method and highlight its advantages.

Multi-Attribute Group Decision Making Based on Hesitant Fuzzy Sets, Topsis Method and Fuzzy Preference Relations

“…Therefore, from the perspective of decision making, we still cannot be sure that 1 3 E E  , so we can only say that E 1 has an advantage over E 3 . Many other aggregation operators Wei, 2012;Tang et al, 2017) have been used to integrate hesitant fuzzy information, and the score function is used to deal with the order relations of HFSs. However, by using aggregation operators and the score function, situation similar to the above examples cannot be avoided.…”

“…Zhang, Wang, Tian, & Li (2014) developed a series of induced generalized aggregation operators for hesitant fuzzy or interval-valued hesitant fuzzy information. Tang, Fu, Xu, & Yang (2017) analyzed fuzzy Hamacher aggregation functions for uncertain multi-attribute decision making. Yu, Wu, and Zhou (2011) proposed a new hesitant fuzzy aggregation operator based on the Choquet integral which included the importance of the elements, their ordered posi-tions and a fuzzy measure.…”

A Hesitant Fuzzy Multiple Attribute Decision Making Method Based on Complementary Judgment Matrix

“…Rank and select alternatives is the purpose of solving multiple attribute decision making problem. At present, The common methods including aggregation operators [26,27,28,29], TOPSIS [30,31,32,33] , VIKOR [34,35] , grey relational analysis [36,37] The remaining sections of this paper are set up as follows: section 2 reviews and fixes basic concepts; section 3 constructs a new fuzzy complementary judgment matrix and proves it has additive consistency and then it's generalization is generalized; section 4, a new approach to multiple attribute decision making under hesitant fuzzy environment is developed; section 5 provides a numerical example to demonstrate the feasibility and validity of the proposed method and in section 6 conclusions are gives.…”

Fuzzy Attribute Expansion Method for Multiple Attribute Decision-Making with Partial Attribute Values and Weights Unknown and Its Applications

“…Wan [14] proposed a new risk attitudinal method for IFS and applied it to the MADM of the teacher selection problem. Furthermore, with the initiation of interval-valued intuitionistic fuzzy set (IVIFS) by Atanassov [18], MADM based on IVIFS becomes a hot topic for researchers [19][20][21][22][23][24][25][26][27]. The applications of type-2 fuzzy sets [28][29][30], hesitant fuzzy sets [31,32], and dual hesitant fuzzy linguistic term sets [33] were also reported recently.…”