On the solution of linear programming problems with rough interval coefficients in a fuzzy environment
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This paper focuses on solving fuzzy variables linear programming problems with rough intervals coefficients (FVRILP). First, FVRILP problems can be decomposed into three linear programming problems with rough intervals coefficients (RILP) using a crisp linear technique. Then, interval method is utilized to convert each RILP problem into two linear programming problems with interval coefficients (ICLP). Second, the ensuing final, crisp linear programming problems are constructed for each ICLP problem and finally, they are solved to obtain a fuzzy rough solution for FVRILP problems in general. A numerical example is given to illustrate the applicability of the proposed method.
Abstract
This paper focuses on solving fuzzy variables linear programming problems with rough intervals coefficients (FVRILP). First, FVRILP problems can be decomposed into three linear programming problems with rough intervals coefficients (RILP) using a crisp linear technique. Then, interval method is utilized to convert each RILP problem into two linear programming problems with interval coefficients (ICLP). Second, the ensuing final, crisp linear programming problems are constructed for each ICLP problem and finally, they are solved to obtain a fuzzy rough solution for FVRILP problems in general. A numerical example is given to illustrate the applicability of the proposed method.
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