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Properties and Applications of Pythagorean Fuzzy Sets

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Imprecision and Uncertainty in Information Representation and Processing

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 332))

Abstract

We introduce the concept of Pythagorean fuzzy subsets and discuss its relationship with intuitionistic fuzzy subsets. We focus on the negation and its relationship to the Pythagorean theorem. We describe some of the basic set operations on Pythagorean fuzzy subsets. We look at the relationship between Pythagorean membership grades and complex numbers. We consider the problem of multi-criteria decision making with satisfactions expressed as Pythagorean membership grades. We look at the use of the geometric mean and ordered weighted geometric (OWG) operator for aggregating criteria satisfaction. We provide a method for comparing alternatives whose degrees of satisfaction to the decision criteria are expressed as Pythagorean membership grades.

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Author information

Authors and Affiliations

  1. Machine Intelligence Institute, Iona College, New Rochelle, NY, 10801, USA

    Ronald R. Yager

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  1. Ronald R. Yager
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Correspondence to Ronald R. Yager .

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Editors and Affiliations

  1. School of Computing and Communications, Lancaster University Bailrigg, Lancaster, United Kingdom

    Plamen Angelov

  2. Intelligent Systems Laboratory, Prof. Assen Zlatarov University, Bourgas, Bulgaria

    Sotir Sotirov

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Yager, R.R. (2016). Properties and Applications of Pythagorean Fuzzy Sets. In: Angelov, P., Sotirov, S. (eds) Imprecision and Uncertainty in Information Representation and Processing. Studies in Fuzziness and Soft Computing, vol 332. Springer, Cham. https://doi.org/10.1007/978-3-319-26302-1_9

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  • DOI: https://doi.org/10.1007/978-3-319-26302-1_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26301-4

  • Online ISBN: 978-3-319-26302-1

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