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-  2018 

A modeling approach for fuzzy programming with echelon form membership functions

DOI: 10.13543/j.bhxbzr.2018.01.013

Keywords: echelon form membership function,fuzzy right-hand side,absolute value representation,
echelon form membership function
,fuzzy right-hand side,absolute value representation

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Abstract:

In order to solve fuzzy mathematical programming with soft constraints,the initial models must first be converted into crisp models.Membership functions are employed to describe the fuzzy right-hand side parameters needed to achieve this conversion.In some cases,echelon form membership functions (EFMFs) are required to depict the actual fuzzy situation.However,due to their discrete properties,fuzzy programming problems with such membership functions cannot be modeled by traditional methods.Motivated by these challenges,this paper introduces a novel absolute value representation modeling approach to formulate fuzzy programming using EFMFs.This approach can translate a discrete model to a continuous one which can then be easily solved.Finally,by means of a numerical example,the effectiveness of our new approach is demonstrated.
Abstract:In order to solve fuzzy mathematical programming with soft constraints,the initial models must first be converted into crisp models.Membership functions are employed to describe the fuzzy right-hand side parameters needed to achieve this conversion.In some cases,echelon form membership functions (EFMFs) are required to depict the actual fuzzy situation.However,due to their discrete properties,fuzzy programming problems with such membership functions cannot be modeled by traditional methods.Motivated by these challenges,this paper introduces a novel absolute value representation modeling approach to formulate fuzzy programming using EFMFs.This approach can translate a discrete model to a continuous one which can then be easily solved.Finally,by means of a numerical example,the effectiveness of our new approach is demonstrated.

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