On generalization of rough multiset via multiset ideals

Article type: Research Article

Authors: Hosny, Mona^{; *} | Raafat, Mahmoud

Affiliations: Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt

Correspondence: [*] Corresponding author. Mona Hosny, Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt. Tel.: +1113193986; E-mail: [email protected].

Abstract: The main aim of rough multiset is reducing the boundary region and increasing the accuracy measure by increasing the lower approximation and decreasing the upper approximation. So in this paper, a new approach of rough multiset via multiset ideals is proposed to reduce the boundary region and increase the accuracy measure. The concepts of lower and upper multiset approximations via multiset ideals are introduced. In addition, some properties and results of these multiset approximations are studied. The relationships between the current multiset approximations are presented. Moreover, comparisons between the present method and the previous one are presented and shown to be more general. Furthermore, the multiset topology induced by the current method is finer than the multiset topology induced by the previous methods. The importance of the current paper is not only that it is reducing the boundary region and increasing the accuracy of sets which is the main aim of rough multiset, but also it is introducing an applied example in medical by applying the current method to illustrate the concepts in a friendly way.

Keywords: Multiset, rough multiset, lower multiset approximation, upper multiset approximation

DOI: 10.3233/JIFS-17102

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 2, pp. 1249-1261, 2017