New Generalized Definitions of Rough Membership Relations and Functions from Topological Point of View

In this paper, we shall integrate some ideas in terms of concepts in topology. In fact, we introduce two different views to define generalized membership relations and functions as mathematical tools to classify the sets and help for measuring exactness and roughness of sets. Moreover, we define several types of fuzzy sets. Comparisons between the induced operations were discussed. Finally, many results, examples and counter examples to indicate connections are investigated

Some Results on Multigranulation Neutrosophic Rough Sets on a Single Domain

As a generalization of single value neutrosophic rough sets, the concept of multi-granulation neutrosophic rough sets was proposed by Bo et al., and some basic properties of the pessimistic (optimistic) multigranulation neutrosophic rough approximation operators were studied

Rough Standard Neutrosophic Sets: An Application on Standard Neutrosophic Information Systems

A rough fuzzy set is the result of the approximation of a fuzzy set with respect to a crisp approximation space. It is a mathematical tool for the knowledge discovery in the fuzzy information systems. In this paper, we introduce the concepts of rough standard neutrosophic sets and standard neutrosophic information system, and give some results of the knowledge discovery on standard neutrosophic information system based on rough standard neutrosophic sets

Fifty years of similarity relations: a survey of foundations and applications

On the occasion of the 50th anniversary of the publication of Zadeh's significant paper Similarity Relations and Fuzzy Orderings, an account of the development of similarity relations during this time will be given. Moreover, the main topics related to these fuzzy relations will be reviewed.Peer ReviewedPostprint (author's final draft

Fuzzy Approximating Spaces

Relationships between fuzzy relations and fuzzy topologies are deeply researched. The concept of fuzzy approximating spaces is introduced and decision conditions that a fuzzy topological space is a fuzzy approximating space are obtained

Rough sets, their extensions and applications

Rough set theory provides a useful mathematical foundation for developing automated computational systems that can help understand and make use of imperfect knowledge. Despite its recency, the theory and its extensions have been widely applied to many problems, including decision analysis, data-mining, intelligent control and pattern recognition. This paper presents an outline of the basic concepts of rough sets and their major extensions, covering variable precision, tolerance and fuzzy rough sets. It also shows the diversity of successful applications these theories have entailed, ranging from financial and business, through biological and medicine, to physical, art, and meteorological