Solving nonlinear multi-objective optimization problems with fuzzy relation inequality constraints regarding Archimedean triangular norm compositions

We propose an approach to solve a nonlinear multi-objective problem subject to fuzzy relation inequalities with max-Archimedean-t-norm composition by a genetic algorithm. The additive generator of Archimedean t-norms is utilized to reform the existent genetic algorithm to solve the constrained nonli...

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Bibliographic Details
Published inFuzzy optimization and decision making Vol. 11; no. 3; pp. 299 - 335
Main Authors Khorram, E., Ezzati, R., Valizadeh, Z.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.09.2012
Springer Science + Business Media B.V
Springer Nature B.V
Subjects
Artificial Intelligence
Calculus of Variations and Optimal Control; Optimization
Decision making
Fuzzy
Fuzzy logic
Fuzzy set theory
Fuzzy sets
Generators
Genetic algorithms
Inequalities
Integer programming
Linear programming
Mathematical Logic and Foundations
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Methods
Nonlinearity
Norms
Operations Research/Decision Theory
Optimization
Pareto optimum
Probability Theory and Stochastic Processes
Studies
Efficient solutions
Multi-objective optimization
Archimedean t-norm
Fuzzy relation inequality
Genetic algorithms
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Summary:We propose an approach to solve a nonlinear multi-objective problem subject to fuzzy relation inequalities with max-Archimedean-t-norm composition by a genetic algorithm. The additive generator of Archimedean t-norms is utilized to reform the existent genetic algorithm to solve the constrained nonlinear multi-objective optimization problems. We consider thoroughly the feasible set of the fuzzy relation inequality systems in three possible cases, namely “≤”, “≥” and the combination of them. In general, their feasible sets are nonconvex which are completely determined by one vector as their maximum solution and a finite number of minimal solutions. The maximum and minimal solutions are formulated by using the additive generator. Additionally, we present some conditions for each case under which the problem can be reduced. Finally, each reduced problem is solved by the genetic algorithm and the efficiency of the proposed method is shown by some numerical examples.
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ISSN:1568-4539
1573-2908
DOI:10.1007/s10700-012-9129-6