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Extending Set Measures to Pythagorean Fuzzy Sets
International Journal of Fuzzy Systems, 2019We introduce the idea of level sets which are crisp sets associated with a fuzzy set. We show how we can represent a fuzzy set using a collection of level sets; this allows us to extend set functions, such as probability and other set measures, to fuzzy subsets. We emphasize that this extension is itself a fuzzy subset.
Ronald Yager, Yager Ronald R
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Distance and similarity measures for Pythagorean fuzzy sets
Granular Computing, 2018The concept of Pythagorean fuzzy sets is very much applicable in decision science because of its unique nature of indeterminacy. The main feature of Pythagorean fuzzy sets is that it is characterized by three parameters, namely, membership degree, non-membership degree, and indeterminate degree, in such a way that the sum of the square of each of the ...
Paul Augustine Ejegwa +1 more
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Incomplete pythagorean fuzzy soft sets
AIP Conference Proceedings, 2020There are several methods to solve decision making problem based on Pythagorean fuzzy soft sets (PFSS). If there is a case in which corresponding to some parameters we do not have any information regarding the universal set, then the existing decision making algorithms in literature fail to serve their purpose.
T. M. Athira +2 more
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Bitopological spaces in the context of pythagorean fuzzy set
Afrika Matematika, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Pythagorean and Complex Fuzzy Set Operations
IEEE Transactions on Fuzzy Systems, 2016Complex fuzzy logic is a new multivalued logic system that has emerged in the last decade. At this time, there are a limited number of known instances of complex fuzzy logic, and only a partial exploration of their properties. There has also been relatively little progress in developing interpretations of complex-valued membership grades. In this paper,
Scott Dick +2 more
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Constrained Pythagorean Fuzzy Sets and Its Similarity Measure
IEEE Transactions on Fuzzy Systems, 2022Pythagorean fuzzy set (PFS) is an extension of the Intuitionistic fuzzy set (IFS). It has a more wider space of membership degrees. Thus, it is more capable of expressing and handling the fuzzy information in engineering practice and scientific research.
Lipeng Pan +3 more
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Comment on Pythagorean and Complex Fuzzy Set Operations
IEEE Transactions on Fuzzy Systems, 2018Dick et al. introduced a relation $\leq ^*$ on $\Pi -i$ numbers and proved that $(\Pi -i, \leq ^*)$ is a bounded distributive complete lattice. In the present paper, we point out that the relation $\leq ^*$ is not a partial order and that $(\Pi -i, \leq ^*)$ is not a lattice. In addition, we study some partial orders on $\Pi -
Lianzhen Liu, Xiangyang Zhang
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RETRACTED: A new fuzzy entropy on Pythagorean fuzzy sets
Journal of Intelligent & Fuzzy Systems, 2019This article has been retracted. A retraction notice can be found at https://doi.org/10.3233/JIFS-219434 .
Thao, Nguyen Xuan +1 more
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Pythagorean fuzzy set: state of the art and future directions
Artificial Intelligence Review, 2017Pythagorean fuzzy set, generalized by Yager, is a new tool to deal with vagueness considering the membership grade $$\mu $$ and non-membership
Xindong Peng, Ganeshsree Selvachandran
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Pythagorean Fuzzy Soft Sets-Based MADM
2021Modern set theory offers intelligent, unbiased, and comprehensive solutions to many problems faced by human beings in day-to-day life. Most of the extensively held problems from daily life involve uncertainties, imprecision, and vagueness. Fuzzy sets, introduced by Zadeh and soft sets, introduced by Molodstov are significant mathematical models to cope
Khalid Naeem, Muhammad Riaz
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