Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm

Mao, Xia; Zhang, Xu; Zhu, Bin

doi:10.1016/j.knosys.2012.02.004

Cited by 259 publications

(123 citation statements)

References 35 publications

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“…Regarding the first issue, in existing studies many researchers have associated r with the preference or risk attitude of a decision maker (e.g., [30,38]). However, the reason for such an association is not clear.…”

Section: Meaning Of the Parameter R In Hamacher Aggregation Operatorsmentioning

confidence: 99%

“…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%

“…Garg [13] constructed a number of generalized intuitionistic fuzzy interactive geometric interaction operators using Einstein t-norm and t-conorm. Xia et al [38] designed intuitionistic fuzzy weighted averaging and geometric operators based on Archimedean t-norm and t-conorm [11]. Liao and Xu [21] proposed a family of intuitionistic fuzzy hybrid weighted aggregation operators in which the properties of idempotency and boundedness are satisfied.…”

Section: Introductionmentioning

confidence: 99%

“…It is worth mentioning that Hamacher t-norm and t-conorm can reduce to algebraic and Einstein t-norms and t-conorms when the parameter r in Hamacher t-norm and t-conorm is set as 1 and 2, respectively [38]. For this reason, the aggregation operators based on algebraic and Einstein t-norms and t-conorms of the above four kinds of fuzzy assessments are not reviewed individually.…”

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: Meaning Of the Parameter R In Hamacher Aggregation Operatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Tang

et al. 2017

Information Sciences

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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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Group decision making based on generalized intuitionistic fuzzy prioritized geometric operator

2012

Int. J. Intell. Syst.

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Intuitionistic fuzzy set was studied by many authors because it is a powerful technique to depict uncertainty, which is a set containing three functions: the membership function; the nonmembership function; and the hesitancy function. The aggregation of intuitionistic fuzzy values (IFVs) is of paramount importance in decision making. In this paper, we research IFVs aggregation problems, where there exist a prioritization relationship over the aggregated arguments. First, we propose the generalized intuitionistic fuzzy prioritized weighted geometric operator based on Archimedean t-conorm and t-norm. Then, some of its desirable properties and special cases are investigated in detail. Furthermore, a multicriteria group decision-making problems is formulated with IFVs using the proposed operator. Finally, the validity and applicability of the proposed method, as well as analysis of the comparison with different generator functions, are illustrated with a real example about talent introduction. C 2012 Wiley Periodicals, Inc.

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Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm

Cited by 259 publications

References 35 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

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

Group decision making based on generalized intuitionistic fuzzy prioritized geometric operator

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