Generalized Orthopair Fuzzy Sets

We note that orthopair fuzzy subsets are such that that their membership grades are pairs of values, from the unit interval, one indicating the degree of support for membership in the fuzzy set and the other support against membership. We discuss two examples, Atanassov's classic intuitionistic...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems Vol. 25; no. 5; pp. 1222 - 1230
Main Author: Yager, Ronald R.
Format: Journal Article
Language:English
Published: IEEE 01.10.2017
Subjects:
Dual of aggregation
Fuzzy set theory
Fuzzy sets
Indexes
intuitionistic sets
Knowledge representation
Machine intelligence
non-standard fuzzy sets
Pragmatics
Pythagorean fuzzy sets
ISSN:1063-6706, 1941-0034
Online Access:Get full text
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Summary:We note that orthopair fuzzy subsets are such that that their membership grades are pairs of values, from the unit interval, one indicating the degree of support for membership in the fuzzy set and the other support against membership. We discuss two examples, Atanassov's classic intuitionistic sets and a second kind of intuitionistic set called Pythagorean. We note that for classic intuitionistic sets the sum of the support for and against is bounded by one, while for the second kind, Pythagorean, the sum of the squares of the support for and against is bounded by one. Here we introduce a general class of these sets called q-rung orthopair fuzzy sets in which the sum of the qth power of the support for and the qth power of the support against is bonded by one. We note that as q increases the space of acceptable orthopairs increases and thus gives the user more freedom in expressing their belief about membership grade. We investigate various set operations as well as aggregation operations involving these types of sets.
ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2016.2604005