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Authors' ORCIDs

Sultan S. Alodhaibi: https://orcid.org/0000-0002-0064-1110

Hissah Ibrahim Almuzini: https://orcid.org/0009-0000-1873-8714

Hamiden Abd El-Wahed Khalifa: https://orcid.org/0000-0002-8269-8822

Article Type

Research Article

Abstract

In this paper, a linear programming framework with completely uncertain parameters is investigated by employing trapezoidal spherical fuzzy numbers (TrSFNs). The proposed formulation incorporates a spherical fuzzy (SF) decision environment in which the optimization process simultaneously maximizes the degree of positive membership while minimizing the corresponding neutral and negative membership degrees. By utilizing the concept of the α -cut associated with TrSFNs, the original fully fuzzy linear programming problem is transformed into an interval-valued linear programming model with confidence levels. To rank and compare the resulting interval objective values, an interval ordering approach based on the decision maker's preferences—considering the lower bound, upper bound, midpoint, and dispersion of the intervals—is adopted. A weighting-based mechanism is then employed to derive an α -efficient solution. In addition, the stability set of the first kind associated with the obtained solution is studied to determine its robustness with respect to variations of the parameters. A series of numerical examples are provided to illustrate the practical application of the proposed approach and the effectiveness of the results. A case study is also provided which shows the validity and relevance of the proposed approach. Finally, summary and suggestions for future research are given.

Keywords

Linear programming, Trapezoidal SF numbers, Interval confidence, Multiple criteria programming, Weighting method, Interactive decision making, α -efficient solution, Parametric study

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