Multidimensional solution of fuzzy linear programming
S. A. Edalatpanah
Abstract
There are several approaches to address fuzzy linear programming problems (FLPP). However, due to using standard interval arithmetic (SIA), these methods have some limitations and are not complete solutions. This article establishes a new approach to fuzzy linear programming via the theory of horizontal membership functions and the multidimensional relative-distance-measure fuzzy interval arithmetic. Furthermore, we propose a multidimensional solution based on the primal Simplex approach that satisfies any equivalent form of FLPP. The new solutions of FLPP are also compared with the results of existing methods. Some numerical examples have been illustrated to show the efficiency of the proposed method.
Topics & Concepts
Linear programmingFuzzy logicSimplex algorithmMathematicsMeasure (data warehouse)Fuzzy numberMathematical optimizationInterval arithmeticSimplexInterval (graph theory)Linear-fractional programmingFuzzy setComputer scienceAlgorithmArtificial intelligenceData miningMathematical analysisCombinatoricsBounded functionGeometryFuzzy Systems and OptimizationOptimization and Mathematical ProgrammingMulti-Criteria Decision Making