دانلود رایگان مقاله برنامه های کاربردی و فضای تقریبی پوشش تعمیم یافته

Abstract

In this paper, we shall integrate some ideas in terms of concepts in topology. First, we introduce some new concepts of rough membership relations and functions in the generalized covering approximation space. Second, we introduce some topological applications namely ‘‘near concepts’’ in the generalized covering approximation space. Accordingly, several types of fuzzy sets are constructed. The basic notions of near approximations are introduced and suffi- ciently illustrated. Near concepts are provided to be easy tools to classify the sets and to help for measuring exactness and roughness of sets. Many proved results, examples and counter examples are provided. Finally, we give two practical examples to illustrate our approaches.

6. Conclusions and future works

In this work, we introduced one of an important topological application that named ‘‘near concepts’’ in rough context. Accordingly, different types of approximations (resp. rough membership relations and functions) were provided to be easy mathematical tools to classify the sets and help for measuring exactness and roughness of sets. These tools are more accurate than other types that were defined by others authors. Consequently, our approaches are very interesting in decision making. We believe that these structures are useful in the applications and thus these techniques open the way for more topological applications in rough context and help in formalizing many applications from real-life data. In our future works, we will apply the suggested methods in this paper in real life applications and problems.