<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

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

Department of Mathematics, Faculty of Science, Turkish Naval Academy

Department of Mathematical Engineering, Faculty of Chemistry-Metallurgy

Cybernetics and Information Technologies

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Multi-objective Solid Transportation Problem (MSTP) is known as a special class of vector-minimization (or maximization) problems and has three parameters:...

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

Published Online: Dec 09, 2021

Page range: 158 - 167

Received: Sep 23, 2021

Accepted: Nov 12, 2021

DOI: https://doi.org/10.2478/cait-2021-0049

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

© 2021 Nurdan Kara et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Published Online: Dec 09, 2021

Page range: 158 - 167

Received: Sep 23, 2021

Accepted: Nov 12, 2021

DOI: https://doi.org/10.2478/cait-2021-0049

KeywordsMulti-objective optimization, solid transportation problem, hyperbolic membership function, fuzzy mathematical programming

© 2021 Nurdan Kara et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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