Abstract
A Pythagorean fuzzy set is the superset of fuzzy and intuitionistic fuzzy sets, respectively. Yager proposed the concept of Pythagorean fuzzy sets in which he relaxed the condition that sum of square of both membership degree and nonmembership degree of an element of a set must not be greater than 1. This paper introduces two new techniques to solve L R -type fully Pythagorean fuzzy linear programming problems with mixed constraints having unrestricted L R -type Pythagorean fuzzy numbers as variables and parameters by introducing unknown variables and using a ranking function. Furthermore, we show the equivalence of both the proposed methods and compare the solutions obtained by the two techniques. Besides this, we solve an already existing practical model using proposed techniques and compare the result.
Highlights
Zadeh [1, 2] introduced the concepts of fuzzy sets and fuzzy numbers
Zimmermann [4] studied the fuzzy programming technique to solve the multiobjective linear programming problem under a fuzzy environment. e fuzzy optimization technique is based on the maximization of the marginal satisfaction of each element into the fuzzy decision set
Angelov [17] first considered the intuitionistic fuzzy optimization techniques based on intuitionistic fuzzy decision set in decision-making problems
Summary
We review elementary concepts that are useful for this article. Definition 1 (see [34]). Let A1 (a1; η1, θ1; η1′, θ1′)LR be an LR-type PFN in which a1 + θ1′ < 0 and η a1a2 − mina1a2 − η1a2 + θ2a1 − η1θ2, a1a2 + θ2a1 + θ1a2 + θ1θ2, θ maxa1a2 + θ1a2 − η2a1 − η2θ1, a1a2 − η2a1 − η1a2 + η1η2 − a1a2,. Let A (a; η, θ; η′, θ′)LR be an LR-type PFN; ranking of A, denoted R(A), can be defined as. J 1 where Aij, Xj, Bi, and Cj are LR-type PFNs
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