SYSTEMS OF FUZZY NUMBER MAX-PLUS LINEAR EQUATIONS

M. Andy Rudhito, Sri Wahyuni, Ari Suparwanto, Frans Susilo

Abstract


This paper discusses the solution of systems of fuzzy number max-plus linear equations through the greatest fuzzy number subsolution of the system. We show that if entries of each column of the coecient matrix are not equal to infinite, the system has the greatest fuzzy number subsolution. The greatest fuzzy number subsolution of the system could be determined by first finding the greatest interval subsolution of the alpha-cuts of the system and then modifying it if needed, such that each its components is a family of alpha-cut of a fuzzy number. Then, based on the Decomposition Theorem on Fuzzy Set, we can determine the membership function of the elements of greatest subsolution of the system. If the greatest subsolution satisfies the system then it is a solution of the system.

DOI : http://dx.doi.org/10.22342/jims.17.1.10.17-28


Keywords


Max-Plus algebra, system of linear equations, fuzzy number.

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DOI: https://doi.org/10.22342/jims.17.1.10.17-28

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Journal of the Indonesian Mathematical Society
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