Pythagorean Membership Grades in Multicriteria Decision Making
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- 21 August 2013
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Fuzzy Systems
- Vol. 22 (4), 958-965
- https://doi.org/10.1109/tfuzz.2013.2278989
Abstract
We first look at some nonstandard fuzzy sets, intuitionistic, and interval-valued fuzzy sets. We note both these allow a degree of commitment of less then one in assigning membership. We look at the formulation of the negation for these sets and show its expression in terms of the standard complement with respect to the degree of commitment. We then consider the complement operation. We describe its properties and look at alternative definitions of complement operations. We then focus on the Pythagorean complement. Using this complement, we introduce a class of nonstandard Pythagorean fuzzy subsets whose membership grades are pairs, (a, b) satisfying the requirement a 2 + b 2 ≤ 1. We introduce a variety of aggregation operations for these Pythagorean fuzzy subsets. We then look at multicriteria decision making in the case where the criteria satisfaction are expressed using Pythagorean membership grades. The issue of having to choose a best alternative in multicriteria decision making leads us to consider the problem of comparing Pythagorean membership grades.Keywords
Funding Information
- Multidisciplinary University Research Initiative (W911NF-09-1-0392)
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