In this paper, we present a general framework for the study of interval type-2 rough fuzzy sets by using both constructive and axiomatic approaches. First, several concepts and properties of interval type-2 fuzzy sets are introduced. Then, a pair of lower and upper interval type-2 rough fuzzy approximation operators with respect to a crisp binary relation is proposed. Classical representations ...

We define interval valued (∈,∈∨q)-fuzzy k-ideals, interval valued (∈,∈∨q)-fuzzy k-quasi-ideals, interval valued (∈,∈∨q)-fuzzy k-bi-ideals and characterize k-regular and k-intra regular hemirings by the properties of interval valued (∈,∈∨q)-fuzzy k-ideals, interval valued (∈,∈∨q)-fuzzy k-quasi-ideals and interval valued (∈,∈∨q)-fuzzy k-bi-ideals. 2010 mathematics subject classification: 16Y60 • ...

This article concerns a connection of fuzzy logic and lattice theory. Namely, the fuzzy sets form a Heyting lattice with union and intersection of fuzzy sets as meet and join operations. The lattice of fuzzy sets is defined as the product of interval posets. As the final result, we have characterized the composition of fuzzy relations in terms of lattice theory and proved its associativity.

In this paper, we introduce a method to obtain the nearest trapezoidal approximation of fuzzy numbers so that preserving conditions expect interval and include the core of a fuzzy number.

The basic paradigm of simulation is the probabilistic approach to describing real world uncertainty. However, in many cases we do not have an information that would be precise enough to build the corresponding probabilistic model or there are some human factors that prevent doing so. In such situations the mathematical tools of fuzzy set theory may be successfully used. It seems that the simple...