Interval-valued Pythagorean fuzzy geometric aggregation operators and their application to group decision making problem

Rahman, Khaista; Abdullah, Saleem; Shakeel, Muhammad; Khan, Muhammad Numan; Ullah, Mukhtar

doi:10.1080/23311835.2017.1338638

Cited by 98 publications

(38 citation statements)

References 15 publications

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“…Insert Table 7 here From the above results shown in Table 7, we can know that the ranking order of the four alternatives and optimal alternative are in agreement with the results of [32,37]. For Garg [32] (IPFWA) and Liang et al [17] (IPFWA), the optimal alternative is A 3 , which is different from other methods, it is unreasonable due to its drawback discussed in Definition 12.…”

Section: A Comparison Analysis From Example 6 Examplesupporting

confidence: 72%

“…Insert Table 6 here If the existing methods in Garg [32], Rahman et al [37], Liang et al [17], and the proposed method are applied to solve the MCDM problem in Example 6, then the results can be obtained and are shown in Table 7.…”

Section: A Comparison Analysis From Example 6 Examplementioning

confidence: 99%

“…For Garg [32] (IPFWG) and Rahman et al [37] (IPFWG), the optimal alternative is A 5 , which is different from other methods, it is unreasonable due to its drawback discussed in Definition 13.…”

Section: A Comparison Analysis From Examplementioning

confidence: 99%

“…In order to further verify the practicability of the proposed multi-attribute decision making approach based on the proposed ♠ operator under IVPFS environment, a comparison study with some existing methods [17,32,37] is now conducted.…”

Section: A Comparison Analysismentioning

confidence: 99%

“…Garg [36] introduced a novel interval-valued Pythagorean fuzzy accuracy function for solving MCDM problem. Rahman [37] discussed interval-valued Pythagorean fuzzy geometric aggregation operators and their application to MCGDM problem. Garg [38] proposed a new improved score function of an interval-valued Pythagorean fuzzy set based TOPSIS method.…”

Section: Introductionmentioning

confidence: 99%

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New Operations for Interval-valued Pythagorean Fuzzy Set

Peng¹

2018

Scientia Iranica

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Interval-valued Pythagorean fuzzy set (IVPFS), originally proposed by Peng and Yang, is a novel tool to deal with vagueness and incertitude. As a generalized set, IVPFS has close relationship with interval-valued intuitionistic fuzzy set (IV-IFS). IVPFS can be reduced to IVIFS satisfying the condition µ + + ν + ≤ 1. However, the related operations of IVPFS do not take different conditions into consideration. In this paper, we initiate some new interval-valued Pythagorean fuzzy operators (♢, , ♠, ♣, , →, $) and discuss their properties in relation with some existing operators (∪, ∩, ⊕, ⊗) in detail. It will promote the development of interval-valued Pythagorean fuzzy operators. Later, we propose an algorithm to deal with multi-criteria decision making (MCDM) problem based on proposed ♠ operator. Finally, the effectiveness and feasibility of proposed algorithm is demonstrated by mine emergency decision making example.

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Section: A Comparison Analysis From Example 6 Examplesupporting

confidence: 72%

Section: A Comparison Analysis From Example 6 Examplementioning

confidence: 99%

Section: A Comparison Analysis From Examplementioning

confidence: 99%

Section: A Comparison Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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New Operations for Interval-valued Pythagorean Fuzzy Set

Peng¹

2018

Scientia Iranica

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New q-rung orthopair fuzzy partitioned Bonferroni mean operators and their application in multiple attribute decision making

2018

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The q-rung orthopair fuzzy sets are superior to intuitionistic fuzzy sets or Pythagorean fuzzy sets in expressing fuzzy and uncertain information. In this paper, some partitioned Bonferroni means (BMs) for q-rung orthopair fuzzy values have been developed. First, the q-rung orthopair fuzzy partitioned BM (q-ROFPBM) operator and the q-rung orthopair fuzzy partitioned geometric BM (q-ROFPGBM) operator are developed. Some desirable properties and some special cases of the new aggregation operators have been studied. The q-rung orthopair fuzzy weighted partitioned BM (q-ROFWPBM) operator and the q-rung orthopair fuzzy partitioned geometric weighted BM (q-ROFPGWBM) operator are also developed. Then, a new multiple-attribute decision-making method based on the q-ROFWPBM (q-ROFPGWBM) operator is proposed. Finally, a numerical example of investment company selection problem is given to illustrate feasibility and practical advantages of the new method. K E Y W O R D S aggregation operator, Bonferroni mean, multiple attribute decision making, q-rung orthopair fuzzy sets Int J Intell Syst. 2019;34:439-476.wileyonlinelibrary.com/journal/int

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On some correlation coefficients in Pythagorean fuzzy environment with applications

Singh

Ganie

2020

Int J Intell Syst

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A Pythagorean fuzzy set (PFS) is an extension of an intuitionistic FS that can be extended by relaxing the restriction on the grades of satisfaction and dissatisfaction. PFS is a powerful tool for dealing with uncertainty and vagueness. Correlation analysis of PFSs is a hot research topic in Pythagorean fuzzy (PF) theory and has practical applications in many areas, such as decision‐making, pattern recognition, medical diagnosis, engineering, and so forth. In this communication, we introduce some novel correlation coefficients in the PF‐environment satisfying the condition that the correlation coefficient of two PFSs is one if and only if the two sets are equal. We discuss the properties and applications of the proposed measures in pattern recognition, medical diagnosis, multicriteria decision‐making, and clustering analysis. Furthermore, the superiority of our proposed correlation coefficients over some existing ones is also established. We also extend the correlation coefficients to interval‐valued PFSs.

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Interval-valued Pythagorean fuzzy geometric aggregation operators and their application to group decision making problem

Cited by 98 publications

References 15 publications

New Operations for Interval-valued Pythagorean Fuzzy Set

New Operations for Interval-valued Pythagorean Fuzzy Set

New q-rung orthopair fuzzy partitioned Bonferroni mean operators and their application in multiple attribute decision making

On some correlation coefficients in Pythagorean fuzzy environment with applications

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