In many contexts, type-2 fuzzy sets (T2 FS) are obtained from a type-1 set to which we wish add uncertainty. However, in the current representation, there is no restriction on shape of footprint uncertainty and embedded (ESs) that can be considered acceptable. This leads, usually, loss semantic relationship between T2 FS concept it models. As consequence, interpretability some ESs explainabilit...

The concept of quasi-coincidence of an interval-valued fuzzy set is considered. By using this new idea, the notion of interval-valued (α, β)−fuzzy k−ideals of semirings is introduced, which is a generalization of a fuzzy k−ideal. Also some related properties are studied and in particular, the interval-valued (∈,∈ ∨q)−fuzzy k−ideals in a semiring will be investigated. Finally, the concept of imp...

So far, computational complextity of the general formula for the extended t-norm does not allow to construct fuzzy logic systems of type-2 other than interval type. In this paper, we derive new formulae for extended t-norms for arguments with Gaussian and piecewise-Gaussian membership functions basing on our original theorems.

one-third of the people with an age over twenty have some signs of degenerated discs. however, in most of the patients the mere presence of degenerative discs is not a problem leading to pain, neurological compression, or other symptoms. this paper presents an interval type-2 fuzzy hybrid rule-based system to diagnose the abnormal degenerated discs where pain variables are represented by interv...

Since the discovery of fuzzy sets, the arithmetic operations of fuzzy numbers (Zadeh [7, 8]) which may be viewed as a generalization of interval arithmetic (Moore [5]) have emerged as an important area of research within the theory of fuzzy sets (Mizumoto and Tanaka [4], Dubois and Prade [2]). The arithmetic operations of fuzzy numbers have been performed either by extension principle [7, 8] or...

This paper has its motivation in the occurrence of uncertain knowledge in different application areas, and introduces an expressive fuzzy description logic that extends classical description logics to manyvalued logics. We represent, and reason with, uncertain knowledge in the description logic ALCHIN extended by an interval-based, normparameterized Fuzzy Logic. First, the syntax and the semant...

In interval type-2 fuzzy logic controllers (IT2-FLCs), the output processing includes type reduction and defuzzification. Recently, researchers have proposed many efficient type reduction algorithms, but there are no effective schemes to improve the output of defuzzification. This paper presents a geneticalgorithm-based type reduction algorithm, which reduces the type of an interval type-2 fuzz...

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 ...