Linear Orthopair Fuzzy Sets

Gao, Shan; Zhang, Xianyong

doi:10.1007/s40815-021-01241-4

Cited by 2 publications

(1 citation statement)

References 41 publications

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“…Tey introduced diferent types of operations and aggregation operators via the environment of (m, n)-fuzzy sets. Gao and Zhang [19] provided the concept of linear orthopair fuzzy sets to address some empirical problems of vagueness.…”

Section: Introductionmentioning

confidence: 99%

Applications of nth Power Root Fuzzy Sets in Multicriteria Decision Making

Ibrahim

Al-shami

Mhemdi

2023

Journal of Mathematics

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An nth power root fuzzy set is a useful extension of a fuzzy set for expressing uncertain data. Because of their wider range of showing membership grades, nth power root fuzzy sets can cover more ambiguous situations than intuitionistic fuzzy sets. In this article, we present several novel operations on nth power root fuzzy sets, as well as their various features. Besides, we develop a new weighted aggregated operator, namely, nth power root fuzzy weighted power average (nPR-FWPA) over nth power root fuzzy sets to deal with choice information and show some of their basic properties. In addition, we define a scoring function for nth power root fuzzy sets ranking. Furthermore, we use this operator to determine the optimal location for constructing a home and demonstrate how we may choose the best alternative by comparing aggregate outputs using score values. Finally, we compare the nPR-FWPA operator outcomes to those of other well-known operators.

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Section: Introductionmentioning

confidence: 99%

Applications of nth Power Root Fuzzy Sets in Multicriteria Decision Making

Ibrahim

Al-shami

Mhemdi

2023

Journal of Mathematics

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Generalized Frame for Orthopair Fuzzy Sets: (m,n)-Fuzzy Sets and Their Applications to Multi-Criteria Decision-Making Methods

Al-shami

Mhemdi

2023

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Orthopairs (pairs of disjoint sets) have points in common with many approaches to managing vaguness/uncertainty such as fuzzy sets, rough sets, soft sets, etc. Indeed, they are successfully employed to address partial knowledge, consensus, and borderline cases. One of the generalized versions of orthopairs is intuitionistic fuzzy sets which is a well-known theory for researchers interested in fuzzy set theory. To extend the area of application of fuzzy set theory and address more empirical situations, the limitation that the grades of membership and non-membership must be calibrated with the same power should be canceled. To this end, we dedicate this manuscript to introducing a generalized frame for orthopair fuzzy sets called “(m,n)-Fuzzy sets”, which will be an efficient tool to deal with issues that require different importances for the degrees of membership and non-membership and cannot be addressed by the fuzzification tools existing in the published literature. We first establish its fundamental set of operations and investigate its abstract properties that can then be transmitted to the various models they are in connection with. Then, to rank (m,n)-Fuzzy sets, we define the functions of score and accuracy, and formulate aggregation operators to be used with (m,n)-Fuzzy sets. Ultimately, we develop the successful technique “aggregation operators” to handle multi-criteria decision-making problems in the environment of (m,n)-Fuzzy sets. The proposed technique has been illustrated and analyzed via a numerical example.

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Linear Orthopair Fuzzy Sets

Cited by 2 publications

References 41 publications

Applications of nth Power Root Fuzzy Sets in Multicriteria Decision Making

Applications of nth Power Root Fuzzy Sets in Multicriteria Decision Making

Generalized Frame for Orthopair Fuzzy Sets: (m,n)-Fuzzy Sets and Their Applications to Multi-Criteria Decision-Making Methods

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