LR型全区间直觉模糊线性规划问题的词典排序解法
Developing solution algorithm for LR-type fully interval-valued intuitionistic fuzzy linear programming problems using lexicographic-ranking method
摘要：
本文引入了LR型区间直觉模糊数的概念。通过展示LR型IVIFNs的图形表示和建立这些模糊数之间的算术运算，也丰富了该理论。字典序准则的全序性质已被用于LR型IVIFNs的排序。此外，一个线性规划问题，具有等式以及不等式型约束的LR型IVIFNs和无限制的决策变量的所有参数已制定。一个算法来找到一个唯一的最优解的问题，使用字典排序方法已经开发出来。该方法将给定的线性规划问题转化为等价的混合0 - 1字典式非线性规划问题。各种定理已被证明，以显示所提出的问题和它的不同结构的等价性。模型的建立、算法和讨论结果不仅开拓了一种新的思路，而且推广了已有的各种著名的相关工作。一个数值问题也被举例说明，以显示在该方法中所涉及的步骤。最后，以一个生产计划的实际应用为例，进行了框架设计、求解和分析，以确定本研究的适用性。
英文摘要：
In this article, a new concept of LR-type interval-valued intuitionistic fuzzy numbers (LR-type IVIFN) has been introduced. The theory has also been enriched by demonstrating diagrammatic representations of LR-type IVIFNs and establishing arithmetic operations among these fuzzy numbers. The total order properties of lexicographic criteria have been used for ranking LR-type IVIFNs. Further, a linear programming problem having both equality as well as inequality type constraints with all the parameters as LR-type IVIFNs and unrestricted decision variables has been formulated. An algorithm to find a unique optimal solution to the problem using the lexicographic ranking method has been developed. In the proposed methodology, the given linear programming problem is converted to an equivalent mixed 0-1 lexicographic non-linear programming problem. Various theorems have been proved to show the equivalence of the proposed problem and its different constructions. The model formulation, algorithm and discussed results have not only developed a new idea but also generalized various well-known related works existing in the literature. A numerical problem has also been exemplified to show the steps involved in the approach. Finally, a practical application in production planning is framed, solved and analyzed to establish the applicability of the study.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
