ABSTRACT

Soft set is a generic mathematical tool for dealing with uncertainty. That is why, the soft set theory has drawn attention from many researchers particularly for dealing with uncertainty in decision-making problems. However, the fact that the membership degrees of the elements belonging to the universe set in the theory are expressed only with 0 or 1 makes it difficult to express the uncertainty in the most accurate way. In this study, in order to solve this problem, the concepts of relational membership function and inverse relational membership function were defined and some related properties were studied. In addition, using these new concepts in soft set theory, some new technical formulations have been given and algorithms for decision-making under uncertainty are proposed. Finally, these algorithms were analysed comparatively and the differences from previously proposed algorithms was clearly stated.

摘要

软集是处理不确定性的通用数学工具。这就是为什么软集理论引起了许多研究人员的关注，特别是在处理决策问题的不确定性方面。但是，由于理论中属于宇宙的元素的隶属度只用0或1来表示，因此很难以最准确的方式表达不确定性。本研究为解决这一问题，定义了关系隶属函数和逆关系隶属函数的概念，并研究了一些相关性质。此外，利用软集理论中的这些新概念，给出了一些新的技术公式，并提出了不确定性下的决策算法。最后，