10.30495/fomj.2022.1970961.1078

On Characterizing Solutions of Optimization Problems with Roughness in the Objective Functions

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  • S. A. Edalatpanah1,
  • Hamiden Abd El- Wahed Khalifa2,
  • Hashem Saberi Najafi*1,
  1. Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran.
  2. Operations Research Department, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt,

Received: 2022-08-19

Accepted: 2022-10-28

Published in Issue 2022-07-01

Copyright (c) -1 S. A. Edalatpanah, Hamiden Abd El- Wahed Khalifa, Hashem Saberi Najafi (Author)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Edalatpanah, S. A., Abd El- Wahed Khalifa, H., & Saberi Najafi, H. (2022). On Characterizing Solutions of Optimization Problems with Roughness in the Objective Functions. Fuzzy Optimization and Modeling Journal (FOMJ), 3(3), 48-58. https://doi.org/10.30495/fomj.2022.1970961.1078
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Abstract

Rough set theory expresses vagueness, not by means of membership, but employing a boundary region of a set. If the boundary region of a set is empty, it means that the set is crisp. Otherwise, the set is rough. Nonempty boundary region of a set means that our knowledge about the set is not sufficient to define the set precisely. In this paper, a rough programming (RP) problem is introduced where a rough function concept and its convexity and differentiability depending on the boundary region is studied. The RP problem is converted into two subproblems namely, lower and upper approximation problem. The Kuhn-Tucker. Saddle point of rough programming problem (RPP) is discussed. In addition, in the case of differentiability assumption the solution of the RP problem is investigated A numerical example is given to illustrate the methodology.

Keywords

  • Convex Rough Function,
  • Differentiable Rough Function,
  • Kuhn-Tucker’s Optimal,
  • Surely optimal Solution,
  • Possibly Optimal Solution,
  • NearlyOptimal Solution
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