Optimal Pricing With Weighted Factors in a Product Transportation System Based on the Min-Plus Fuzzy Relation Inequality
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 investigat...
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| Published in | IEEE transactions on fuzzy systems Vol. 31; no. 5; pp. 1 - 12 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.05.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1063-6706 1941-0034 |
| DOI | 10.1109/TFUZZ.2022.3201982 |
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| Abstract | 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. |
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| AbstractList | 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. 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 a 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 feasible index set (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. |
| Author | Yang, Xiaopeng |
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| SubjectTerms | 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 |
| Title | Optimal Pricing With Weighted Factors in a Product Transportation System Based on the Min-Plus Fuzzy Relation Inequality |
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