Optimal Pricing With Weighted Factors in a Product Transportation System Based on the Min-Plus Fuzzy Relation Inequality

• Published in: IEEE transactions on fuzzy systems Vol. 31; no. 5; pp. 1 - 12
• Main Author: Yang, Xiaopeng
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Constraint modelling; Fuzzy relation inequality; fuzzy relation programming; Indexes; Inequalities; Linear programming; Manufacturing; Mathematical models; min-plus composition; Optimization; Optimization models; Pricing; product transportation system; solution set; Transportation; Transportation systems
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2022.3201982

In this work, we introduce the fuzzy relation inequalities with min-plus composition for describing the pricing problem in a product transportation system. Some basic properties of the min-plus inequalities system are investigated. We define the concept of feasible index chain and further investigate the corresponding quasi-maximal solution. Moreover, it is found that the solution set of a min-plus system could be generated by a unique minimum solution and a finite number of quasi-maximal solutions. As a consequence, one is able to find the complete solution set of a min-plus system. Besides, motivated by the optimal managerial objective, we establish an optimization model with the min-plus inequalities constraints. A so-called FIS-based algorithm is developed for searching an optimal solution of our studied optimization model. We have provided a simple numerical example for checking the effectiveness of our proposed FIS-based algorithm. The obtained optimal solution would be helpful for the system manager, as an optimal pricing scheme.