A Fuzzy approach to multi-objective solid transportation problem with mixed constraints using hyperbolic membership function


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Kara N., Kocken H.

Cybernetics and Information Technologies, vol.21, no.4, pp.158-167, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.2478/cait-2021-0049
  • Journal Name: Cybernetics and Information Technologies
  • Journal Indexes: Emerging Sources Citation Index, Scopus, Aerospace Database, Communication Abstracts, INSPEC, Metadex, Directory of Open Access Journals, Civil Engineering Abstracts
  • Page Numbers: pp.158-167
  • Keywords: Multi-objective optimization, solid transportation problem, hyperbolic membership function, fuzzy mathematical programming

Abstract

© 2021 Nurdan Kara et al., published by Sciendo.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.