3.8 Article

A Fuzzy Approach to Multi-Objective Solid Transportation Problem with Mixed Constraints Using Hyperbolic Membership Function

Journal

CYBERNETICS AND INFORMATION TECHNOLOGIES
Volume 21, Issue 4, Pages 158-167

Publisher

INST INFORMATION & COMMUNICATION TECHNOLOGIES-BULGARIAN ACAD SCIENCES
DOI: 10.2478/cait-2021-0049

Keywords

Multi-objective optimization; solid transportation problem; hyperbolic membership function; fuzzy mathematical programming

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This paper discusses the conflicts between objectives in Multi-objective Solid Transportation Problem (MSTP) and proposes a fuzzy approach to integrate these objectives as much as possible. The hyperbolic membership function is used instead of the commonly used linear membership function, and the mixed constrained form of MSTP is addressed. A numerical example is provided to illustrate the construction of the hyperbolic membership function and its representation of the degree of satisfaction of the objective functions.
Multi-objective Solid Transportation Problem (MSTP) is known as a special class of vector-minimization (or maximization) problems and has three parameters: source, destination, and conveyance. The objectives such as transportation cost, transportation time, transportation safety level, and objectives in terms of environmental and social issues are generally in conflict with each other. In this paper, we present a fuzzy approach to bring these conflicting objectives together as high as possible. Instead of using the linear membership function, which is frequently used in the literature for ease of use, we use the hyperbolic membership function in our approach. Also, while most of the papers in the literature deal with the standard equality constrained form of MSTP, the mixed constrained form is addressed in this paper. Finally, a numerical example from the literature is used to illustrate the construction of the hyperbolic membership function and how well it represents the objective functions' degree of satisfaction.

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