New exponential operational laws and their aggregation operators for interval-valued Pythagorean fuzzy multicriteria decision-making

In this paper, we examine the multicriteria decision-making (MCDM) difficulties for Pythagorean fuzzy hypersoft sets (PFHSSs). The PFHSSs are a suitable extension of the Pythagorean fuzzy soft sets (PFSSs) which deliberates the parametrization of multi-subattributes of considered parameters. It is a most substantial notion for describing fuzzy information in the decision-making (DM) procedure to accommodate more vagueness comparative to existing PFSSs and intuitionistic fuzzy hypersoft sets (IFHSSs). The core objective of this study is to plan some innovative operational laws considering the interaction for Pythagorean fuzzy hypersoft numbers (PFHSNs). Also, based on settled interaction operational laws, two aggregation operators (AOs) i.e., Pythagorean fuzzy hypersoft interaction weighted average (PFHSIWA) and Pythagorean fuzzy hypersoft interaction weighted geometric (PFHSIWG) operators for PFHSSs operators have been presented with their fundamental properties. Furthermore, an MCDM technique has been established using planned interaction AOs. To ensure the strength and practicality of the developed MCDM method, a mathematical illustration has been presented. The usefulness, influence, and versatility of the developed method have been demonstrated via comparative analysis with the help of some conventional studies.

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Multicriteria Decision-Making Approach with Hesitant Interval-Valued Intuitionistic Fuzzy Sets

The Scientific World JOURNAL ◽

10.1155/2014/868515 ◽

2014 ◽

Vol 2014 ◽

pp. 1-22 ◽

Cited By ~ 12

Author(s):

Juan-juan Peng ◽

Jian-qiang Wang ◽

Jing Wang ◽

Xiao-hong Chen

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Multicriteria Decision Making ◽

Intuitionistic Fuzzy Sets ◽

Aggregation Operators ◽

Decision Makers ◽

Multicriteria Decision ◽

Intuitionistic Fuzzy ◽

Definition Of ◽

Interval Valued

The definition of hesitant interval-valued intuitionistic fuzzy sets (HIVIFSs) is developed based on interval-valued intuitionistic fuzzy sets (IVIFSs) and hesitant fuzzy sets (HFSs). Then, some operations on HIVIFSs are introduced in detail, and their properties are further discussed. In addition, some hesitant interval-valued intuitionistic fuzzy number aggregation operators based ont-conorms andt-norms are proposed, which can be used to aggregate decision-makers' information in multicriteria decision-making (MCDM) problems. Some valuable proposals of these operators are studied. In particular, based on algebraic and Einsteint-conorms andt-norms, some hesitant interval-valued intuitionistic fuzzy algebraic aggregation operators and Einstein aggregation operators can be obtained, respectively. Furthermore, an approach of MCDM problems based on the proposed aggregation operators is given using hesitant interval-valued intuitionistic fuzzy information. Finally, an illustrative example is provided to demonstrate the applicability and effectiveness of the developed approach, and the study is supported by a sensitivity analysis and a comparison analysis.

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Multicriteria Decision-Making Approach for Aggregation Operators of Pythagorean Fuzzy Hypersoft Sets

Computational Intelligence and Neuroscience ◽

10.1155/2021/2036506 ◽

2021 ◽

Vol 2021 ◽

pp. 1-19

Author(s):

Imran Siddique ◽

Rana Muhammad Zulqarnain ◽

Rifaqat Ali ◽

Fahd Jarad ◽

Aiyared Iampan

Keyword(s):

Decision Making ◽

Weighted Average ◽

Multicriteria Decision Making ◽

Aggregation Operators ◽

Fuzzy Soft Set ◽

Multicriteria Decision ◽

Fundamental Properties ◽

Operational Laws ◽

Shift Invariance ◽

Parameterized Family

The Pythagorean fuzzy hypersoft set (PFHSS) is the most advanced extension of the intuitionistic fuzzy hypersoft set (IFHSS) and a suitable extension of the Pythagorean fuzzy soft set. In it, we discuss the parameterized family that contracts with the multi-subattributes of the parameters. The PFHSS is used to correctly assess insufficiencies, anxiety, and hesitancy in decision-making (DM). It is the most substantial notion for relating fuzzy data in the DM procedure, which can accommodate more uncertainty compared to available techniques considering membership and nonmembership values of each subattribute of given parameters. In this paper, we will present the operational laws for Pythagorean fuzzy hypersoft numbers (PFHSNs) and also some fundamental properties such as idempotency, boundedness, shift-invariance, and homogeneity for Pythagorean fuzzy hypersoft weighted average (PFHSWA) and Pythagorean fuzzy hypersoft weighted geometric (PFHSWG) operators. Furthermore, a novel multicriteria decision-making (MCDM) approach has been established utilizing presented aggregation operators (AOs) to resolve decision-making complications. To validate the useability and pragmatism of the settled technique, a brief comparative analysis has been conducted with some existing approaches.

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Uncertainty evaluations through interval-valued Pythagorean hesitant fuzzy Archimedean aggregation operators in multicriteria decision making

Intelligent Decision Technologies ◽

10.3233/idt-200065 ◽

2021 ◽

pp. 1-29

Author(s):

Arun Sarkar ◽

Nayana Deb ◽

Animesh Biswas

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Multicriteria Decision Making ◽

Uncertain Information ◽

Fuzzy Information ◽

Hesitant Fuzzy Sets ◽

Multicriteria Decision ◽

Fuzzy Environment ◽

Operational Laws ◽

Interval Valued

In many cases, use of Pythagorean hesitant fuzzy sets may not be sufficient to characterize uncertain information associated with decision making problems. From that view point the concept of interval-valued Pythagorean hesitant fuzzy sets are introduced in this paper. Considering the flexibility with the general parameters, Archimedean t-conorms and t-norms are applied to develop several operational laws in interval-valued Pythagorean hesitant fuzzy environment. Some characteristics of the developed operators are presented. The newly developed operators are used to derive a methodology for solving multicriteria decision making problems with interval-valued Pythagorean hesitant fuzzy information. Finally, two illustrative examples are provided to establish the validity of the proposed approach and are compared with the existing technique to exhibit its flexibility and effectiveness.

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Approach to Multi-Attribute Decision-Making Methods for Performance Evaluation Process Using Interval-Valued T-Spherical Fuzzy Hamacher Aggregation Information

Axioms ◽

10.3390/axioms10030145 ◽

2021 ◽

Vol 10 (3) ◽

pp. 145

Author(s):

Yun Jin ◽

Zareena Kousar ◽

Kifayat Ullah ◽

Tahir Mahmood ◽

Nimet Yapici Pehlivan ◽

...

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Evaluation Process ◽

Aggregation Operators ◽

Weighted Averaging ◽

Membership Degree ◽

Operational Laws ◽

Multi Attribute Decision Making ◽

Interval Valued ◽

Do So

Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence degree (AD), non-membership degree (NMD), and refusal degree (RD). MD, AD, NMD, and RD are defined in terms of closed subintervals of that reduce information loss compared to the T-spherical fuzzy set (TSFS), which takes crisp values from intervals; hence, some information may be lost. The purpose of this manuscript is to develop some Hamacher aggregation operators (HAOs) in the environment of IVTSFSs. To do so, some Hamacher operational laws based on Hamacher t-norms (HTNs) and Hamacher t-conorms (HTCNs) are introduced. Using Hamacher operational laws, we develop some aggregation operators (AOs), including an interval-valued T-spherical fuzzy Hamacher (IVTSFH) weighted averaging (IVTSFHWA) operator, an IVTSFH-ordered weighted averaging (IVTSFHOWA) operator, an IVTSFH hybrid averaging (IVTSFHHA) operator, an IVTSFH-weighted geometric (IVTSFHWG) operator, an IVTSFH-ordered weighted geometric (IVTSFHOWG) operator, and an IVTSFH hybrid geometric (IVTSFHHG) operator. The validation of the newly developed HAOs is investigated, and their basic properties are examined. In view of some restrictions, the generalization and proposed HAOs are shown, and a multi-attribute decision-making (MADM) procedure is explored based on the HAOs, which are further exemplified. Finally, a comparative analysis of the proposed work is also discussed with previous literature to show the superiority of our work.

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