Hesitant fuzzy Hamacher aggregation operators for multicriteria decision making

Tan, Chunqiao; Yi, Wentao; Chen, Xiaohong

doi:10.1016/j.asoc.2014.10.007

Cited by 98 publications

(61 citation statements)

References 38 publications

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“…Except the above, previous studies [16,19,22,26,30,39,48] of Hamacher aggregation operators in the context of fuzzy MADM have shown the influence of the parameter r in Hamacher t-norm and t-conorm on decision results by a sensitivity analysis of r only. However, two key points have been omitted in these studies: (1) what is the meaning of the parameter r; and (2) how is this parameter determined in MADM.…”

Section: Introductionmentioning

confidence: 92%

“…More importantly, it plays a key role in fuzzy decision making to combine multiple pieces of uncertain information represented by the extensions of fuzzy set [46] such as Atanassov"s intuitionistic fuzzy (AIF) set [3], interval-valued intuitionistic fuzzy (IVIF) set [4], hesitant fuzzy (HF) set [32], and dual hesitant fuzzy (DHF) set [49]. To address such combination, various aggregation functions or operators have been designed and applied in multiple attribute decision making (MADM) [5,7,13,16,19,20,22,30,34,35,37,38,43,48].…”

Section: Introductionmentioning

confidence: 99%

“…Liao and Xu [20] constructed a series of new HF hybrid arithmetic aggregation operators satisfying idempotency and keeping the advantages of HF hybrid averaging and geometric operators developed by Xia and Xu [37]. In particular, Hamacher t-norm and t-conorm were used to develop a family of HF aggregation operators [30,48]. With regard to the aggregation for DHF information, several aggregation operators and A C C E P T E D M A N U S C R I P T 3 power aggregation operators were constructed based on Archimedean t-norm and t-conorm [34,35].…”

Section: Introductionmentioning

confidence: 99%

“…Existing studies concerning fuzzy Hamacher aggregation operators [16,19,22,30,38,39,48] reveal that they are generally divided into arithmetic and geometric aggregation operators. It can be found from numerical examples or real cases in existing studies that there are two important rules which govern the two types of aggregation operators in the context of fuzzy MADM: (1) the scores of the decision alternatives under consideration decrease and increase with the increase of the parameter r in the Hamacher t-norm and t-conorm when the arithmetic and geometric aggregation operators are applied, respectively; and (2) the scores of the decision alternatives generated by the arithmetic aggregation operator are always larger than those generated by the geometric aggregation operator, regardless of what the parameter r is equal to.…”

Section: Introductionmentioning

confidence: 99%

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

Tang

et al. 2017

Information Sciences

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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.

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Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Tang

et al. 2017

Information Sciences

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“…Within the extended field of Hesitancy in Fuzzy Sets, application papers that contribute to multicriteria decision making include [7], [10], [11], [12], [13], [14], [15] and [16]. Multiexpert multicriteria decision making under this requirement has been explored by Xia et al [17] or Tan et al [18] among others. Rodríguez et al [9], Section 7, emphasize that "a new trend is the application of the theoretical models to real problems".…”

Section: Introductionmentioning

confidence: 99%

Hesitant Fuzzy Worth: An innovative ranking methodology for hesitant fuzzy subsets

Alcantud

Calle

Torrecillas

2016

Applied Soft Computing

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We introduce a novel methodology for ranking hesitant fuzzy sets. It builds on a recent, theoretically sound contribution in Social Choice. In order to justify the applicability of such analysis, we develop two real implementations: (i) new metarankings of world academic institutions that build on real data from three reputed agencies, and (ii) a new procedure for improving teaching performance assessments which we illustrate with real data collected by ourselves. These applications provide new grounds for the theoretical model by hesitant fuzzy sets.

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Development of Archimedean t‐norm and t‐conorm‐based interval‐valued dual hesitant fuzzy aggregation operators with their application in multicriteria decision making

Sarkar¹,

Biswas

2020

Engineering Reports

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In this article, Archimedean t‐norm and t‐conorm (At‐N&t‐CN)‐based aggregation operators are developed for aggregating the interval‐valued dual hesitant fuzzy (IVDHF) elements (IVDHFEs), which can cover a wide variety of existing aggregation operators. After introducing the concept of IVDHF set, several related terms, viz., score function, accuracy function, and degree of hesitancy are defined. Using At‐N&t‐CN, different operations for IVDHFEs are presented. Conversion processes from the developed operators to other forms of operators in several variants of fuzzy environments are discussed. An approach to solve multicriteria decision making problem in IVDHF context is presented using the developed concepts. To demonstrate proficiency of the developed method, an illustrative example is presented. Furthermore, several numerical examples, studied previously, are also solved, and achieved solutions are compared with the existing ones to establish the robustness of the proposed operator.

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Hesitant fuzzy Hamacher aggregation operators for multicriteria decision making

Cited by 98 publications

References 38 publications

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

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

Hesitant Fuzzy Worth: An innovative ranking methodology for hesitant fuzzy subsets

Development of Archimedean t‐norm and t‐conorm‐based interval‐valued dual hesitant fuzzy aggregation operators with their application in multicriteria decision making

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