This paper reviews and compares theories of fuzzy sets and rough sets. Two approaches for the formulation of fuzzy sets are reviewed, one is based on many-valued logic and the other is based on modal logic. Two views of rough sets are presented, set-oriented view and operator-oriented view. Rough sets under set-oriented view are closely related to fuzzy sets, which leads to non-truth-functional...

A ternary semigroup is a nonempty set together with a ternary multiplication which is associative. Any semigroup can be reduced to a ternary semigroup but a ternary semigroup does not necessarily reduce to a semigroup. The notion of fuzzy sets was introduced by Zadeh in 1965 and that of rough sets by Pawlak in 1982. Applications of the fuzzy set theory and rough set theory have been found in va...

Article history: Received 4 May 2014 Received in revised form 9 December 2014 Accepted 12 December 2014 Available online 26 December 2014

The objective of this chapter is to provide a semantic framework for fuzzy sets in the theory of rough sets. Rough membership functions are viewed as a special type of fuzzy membership functions interpretable using conditional probabilities. The relationships between fuzzy membership functions and rough membership functions, between core and support of fuzzy set theory and lower and upper appro...

This model for fuzzy rough sets is one of the most important parts in rough set theory. Moreover, it is based on an equivalence relation (indiscernibility relation). However, many systems are not only concerned with fuzzy sets, but also based on a dominance relation because of various factors in practice. To acquire knowledge from the systems, construction of model for fuzzy rough sets based on...

In this presentation we shall raise the following issues connected with the discourse of rough set theory: 1. indistinguishability 2. definition of a rough set 3. language dependency, the problem of referent 4. vagueness 5. abstraction 6. application-friendliness We shall argue that existing practices prevailing in rough set research fall short in addressing most of the issues. After almost fif...

High dimensional microarray datasets are difficult to classify since they have many features with small number ofinstances and imbalanced distribution of classes. This paper proposes a filter-based feature selection method to improvethe classification performance of microarray datasets by selecting the significant features. Combining the concepts ofrough sets, weighted rough set, fuzzy rough se...

The paradox of the heap of grains in respect to roughness, fuzziness, and negligibility p. 19 Rough sets-what are they about? p. 24 Reasoning about data-a rough set perspective p. 25 Information granulation and its centrality in human and machine intelligence p. 35 Classification strategies using certain and possible rules p. 37 Well-behaviored operations for approximate sets p. 45 Searching fo...