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A New Method to Optimize the Satisfaction Level of the Decision Maker in Fuzzy Geometric Programming Problems

Author

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  • Armita Khorsandi

    (Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong, Higher Education Institutes, School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China)

  • Bing-Yuan Cao

    (Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong, Higher Education Institutes, School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
    School of Mathematics and Big Data, Foshan University, Foshan 528000, China
    Guangzhou Vocational College of Science and Technology, Guangzhou 510550, China)

  • Hadi Nasseri

    (Department of Mathematics, University of Mazandaran, 47419-134767 Babolsar, Iran)

Abstract

Geometric programming problems are well-known in mathematical modeling. They are broadly used in diverse practical fields that are contemplated through an appropriate methodology. In this paper, a multi-parametric vector α is proposed for approaching the highest decision maker satisfaction. Hitherto, the simple parameter α , which has a scalar role, has been considered in the problem. The parameter α is a vector whose range is within the region of the satisfaction area. Conventionally, it is assumed that the decision maker is sure about the parameters, but, in reality, it is mostly hesitant about them, so the parameters are presented in fuzzy numbers. In this method, the decision maker can attain different satisfaction levels in each constraint, and even full satisfaction can be reached in some constraints. The goal is to find the highest satisfaction degree to maintain an optimal solution. Moreover, the objective function is turned into a constraint, i.e., one more dimension is added to n -dimensional multi-parametric α . Thus, the fuzzy geometric programming problem under this multi-parametric vector α ∈ ( 0 , 1 ] n + 1 gives a maximum satisfaction level to the decision maker. A numerical example is presented to illustrate the proposed method and the superiority of this multi-parametric α over the simple one.

Suggested Citation

  • Armita Khorsandi & Bing-Yuan Cao & Hadi Nasseri, 2019. "A New Method to Optimize the Satisfaction Level of the Decision Maker in Fuzzy Geometric Programming Problems," Mathematics, MDPI, vol. 7(5), pages 1-18, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:464-:d:233850
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    References listed on IDEAS

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    1. R. E. Bellman & L. A. Zadeh, 1970. "Decision-Making in a Fuzzy Environment," Management Science, INFORMS, vol. 17(4), pages 141-164, December.
    2. Dheeraj Kumar Joshi & Ismat Beg & Sanjay Kumar, 2018. "Hesitant Probabilistic Fuzzy Linguistic Sets with Applications in Multi-Criteria Group Decision Making Problems," Mathematics, MDPI, vol. 6(4), pages 1-20, March.
    3. G. Z. Ruan & S. Y. Wang & Y. Yamamoto & S. S. Zhu, 2004. "Optimality Conditions and Geometric Properties of a Linear Multilevel Programming Problem with Dominated Objective Functions," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 409-429, November.
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    1. Shafiq Ahmad & Firoz Ahmad & Intekhab Alam & Abdelaty Edrees Sayed & Mali Abdollahian, 2022. "Modeling and Optimizing the System Reliability Using Bounded Geometric Programming Approach," Mathematics, MDPI, vol. 10(14), pages 1-19, July.

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