On optimistic, pessimistic and mixed approaches under different membership functions for fully intuitionistic fuzzy multiobjective nonlinear programming problems

The concept of measuring the membership degree along with a non-membership degree, gives rise to the intuitionistic fuzzy set theory. The present study formulates a nonlinear programming problem with multiple objectives, including all the parameters and decision variables as intuitionistic fuzzy num...

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Vydáno v:Expert systems with applications Ročník 168; s. 114309
Hlavní autoři: Mahajan, Sumati, Gupta, S.K.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Elsevier Ltd 15.04.2021
Elsevier BV
Témata:
Accuracy function
Algorithms
Equivalence
Fuzzy set theory
Fuzzy sets
Fuzzy systems
Intuitionistic fuzzy variables
Membership functions
Multiobjective programming problem
Nonlinear programming
Optimistic
Pessimistic and mixed approaches
Production planning
Transportation problem
Membership functions
Accuracy function
Intuitionistic fuzzy variables
Optimistic
Pessimistic and mixed approaches
Multiobjective programming problem
ISSN:0957-4174, 1873-6793
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Shrnutí:The concept of measuring the membership degree along with a non-membership degree, gives rise to the intuitionistic fuzzy set theory. The present study formulates a nonlinear programming problem with multiple objectives, including all the parameters and decision variables as intuitionistic fuzzy numbers. The problem is further investigated subject to optimistic, pessimistic and mixed approaches under linear, exponential and hyperbolic membership functions. The article redefines pessimistic and mixed point of view to be in the true spirit compatible with the definition of an intuitionistic fuzzy number. Accuracy function is used to reduce the problem to an equivalent crisp multiobjective nonlinear programming problem and then optimal compromise solution is obtained under different approaches using various membership/non-membership functions. At appropriate places, theorems have also been proved to establish the equivalence between the original formulation and its crisp counterparts under each approach. Further, practical applications in production planning and transportation problem are illustrated to explain the optimistic, pessimistic and mixed approaches using the proposed algorithm and finally a comparison is also drawn. •A fully intuitionistic fuzzy multiobjective nonlinear problem is formulated.•Optimistic, pessimistic and mixed approaches are proposed.•Linear, exponential and hyperbolic memberships are used to illustrate the concept.•Theorems are proved to show equivalence with the original formulation.•Two practical examples are investigated and a comparison is drawn.
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ISSN:0957-4174
1873-6793
DOI:10.1016/j.eswa.2020.114309