This paper generalizes the concept of rough membership functions in pattern classi$cation tasks to rough–fuzzy membership functions and rough–fuzzy ownership functions. Unlike the rough membership value of a pattern, which is sensitive only towards the rough uncertainty associated with the pattern, the rough–fuzzy membership (or ownership) value of the pattern signi$es the rough uncertainty as ...

in this paper, countable compactness and the lindel¨of propertyare defined for l-fuzzy sets, where l is a complete de morgan algebra. theydon’t rely on the structure of the basis lattice l and no distributivity is requiredin l. a fuzzy compact l-set is countably compact and has the lindel¨ofproperty. an l-set having the lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

Data used in machine learning applications is prone to contain both vague and incomplete information. Many authors have proposed to use fuzzy rough set theory in the development of new techniques tackling these characteristics. Fuzzy sets deal with vague data, while rough sets allow to model incomplete information. As such, the hybrid setting of the two paradigms is an ideal candidate tool to c...

Introducing rough sets in hesitant fuzzy set domain and using it for the various applications would open up new possibilities in rough set theory. For this purpose the notion of hesitant fuzzy relations is introduced. The foundation of equivalence hesitant fuzzy relation is laid. Definition of anti-reflexive kernel, symmetric kernel etc. is proposed and the formulae to evaluate them are derived...

Many of the new fuzzy structures with complete MV-algebras as value sets, such hesitant, intuitionistic, neutrosophic, or soft can be transformed into one type set values in special algebras, called AMV-algebras. The category AMV-algebras is isomorphic to pairs (R,R∗) commutative semirings and corresponding sets are (R,R∗)-fuzzy sets. We use this theory define relations, lower upper approximati...

This keynote talk considers how one might utilize fuzzy sets, near sets, and rough sets, taken separately or taken together in hybridizations in solving a variety of problems commonly faced in science and engineering. These technologies offer set theoretic approaches to solving problems such as classifying sensor output, image retrieval and image correspondence. Fuzzy sets result from the intro...

This paper aims to apply the concept of rough sets Pythagorean fuzzy in UP-algebras. Then we introduce fifteen types UP-algebras and study their generalization. In addition, will also discuss $t$-level subsets relationships between