论文标题
开发用于LR型完全间隔值直觉模糊的线性编程问题的解决方案算法使用词典级别的方法
Developing solution algorithm for LR-type fully interval-valued intuitionistic fuzzy linear programming problems using lexicographic-ranking method
论文作者
论文摘要
在本文中，引入了LR型间隔值的新概念（LR-type IVIFN）。该理论还通过证明LR型IVIFNS的图表表示并在这些模糊数字之间建立算术操作来丰富该理论。词典标准的总顺序特性已用于对LR型IVIFN进行排名。此外，已经制定了具有平等性以及所有参数的不平等类型约束的线性编程问题，例如LR-type IVIFN和不受限制的决策变量。已经开发了一种使用词典排名方法来找到问题的唯一最佳解决方案的算法。在拟议的方法论中，给定的线性编程问题被转换为等效的混合词典非线性编程问题。事实证明，各种定理表明了所提出的问题及其不同的结构的等效性。模型公式，算法和讨论的结果不仅开发了一个新的想法，而且还普遍化了文献中存在的各种知名相关作品。还例证了一个数值问题，以显示该方法所涉及的步骤。最后，对生产计划中的实际应用进行了构架，解决和分析，以确定研究的适用性。
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.
