Fuzzy Compromise Approach for Solving Stochastic Multi-objective q-Rung Orthopair Fuzzy Linear Programming Problem

Sultan S. Alodhaibi; Hissah Ibrahim Almuzini; Hamiden Abd El-Wahed Khalifa

doi:10.31181/sor202770

Authors

Sultan S. Alodhaibi Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia Author https://orcid.org/0000-0002-0064-1110
Hissah Ibrahim Almuzini Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia Author https://orcid.org/0009-0000-1873-8714
Hamiden Abd El-Wahed Khalifa Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia Author https://orcid.org/0000-0002-8269-8822

DOI:

https://doi.org/10.31181/sor202770

Keywords:

MOLP, q-ROFNs, Score function, Probabilistic constraints, Probability distributions, Optimal compromise solution

Abstract

The model considered in this study is a multi-objective linear programming (MOLP) model under uncertainty, in which the coefficients of the objective functions are represented by q-rung orthopair fuzzy numbers (q-ROFNs), while the right-hand side constraint parameters are treated as probabilistic quantities. The random variables are assumed to follow known probability distributions and are characterized by specified means and variances. By employing an appropriate score function and considering several probability distributions, namely Gamma, log-normal, and exponential distributions, the initial probabilistic q-rung orthopair fuzzy (q-ROF) MOLP problem is transformed into an equivalent deterministic MOLP model. The Zimmermann methodology with linear membership degrees (MDs) is then applied to represent the preferences of the decision-maker and obtain a satisfactory compromise solution. A numerical example is provided to demonstrate the applicability and efficiency of the proposed methodology. The study concludes with final observations and suggestions for future research.

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