# Comparative Analysis of Hybrid Soft Set Methods

DOI: 10.4018/978-1-4666-4936-1.ch013

## Abstract

The whole mathematical scenario has changed with the advent of the Rough Set Theory, a powerful tool to deal with uncertainty and incompleteness of knowledge in information system. With the advancement of research, the Soft Set Theory has emerged as an advanced mathematical tool to deal with data associated with uncertainty. The present chapter endeavors to forge a connection between soft set and rough set and maps a new model rough soft set to address the challenges of vagueness and impreciseness. Although the research contribution of M. Irfan Ali, Dan Meng, et al. and Feng Feng et al. had given distinct definition of rough soft set and soft rough set, the analysis explaining the genesis of these sets is not appropriate. This chapter is a new attempt to construct the relationship between a rough set, soft set, and fuzzy set to form a hybrid soft set giving a concrete comprehensive definition of rough soft set in border perspective.
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## Literary Background

In the present context the theory of fuzzy set is advancing fast in geometrical progression. But difficulty arises to set the membership in each particular case. The nature of the membership function is extremely individual. The fuzzy set operations with membership functions sometimes do not appear natural. To avoid these difficulties, a mathematical tool, called as soft set theory, is developed to deal with uncertainties. In 1999, soft set theory was derived by D.Molodtsov as:

Let be an initial universe and let E be the set of parameters. A pair (F,E) is called a soft set over when F is a mapping from E into the set of subsets of .

Thus a soft set is a parameterized family of subsets of set .

In 2003 an article “soft set theory” was published by P.K.Maji and others [P.K.Majhi,R. Biswas and A.R.Roy,2003] which strengthened the soft set analysis [P.K.Majhi,R. Biswas and A.R.Roy,2002]. Then the researchers made the research on soft set, soft groups, fuzzy soft set, fuzzy soft group and the combination of soft set, fuzzy set and rough set.

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