It is firstly proved that the multi-input-single-output (MISO) fuzzy systems based on interval-valued $R$- and $S$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  A formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

in this paper, we consider the production possibility set with n production units such that the following four principles that governs: inclusion observations, conceivability, immensity and convexity. our goal is to estimate the output of a same and new production unit with existing production possibility and amount of input is specified. so, initially we find the interval changes of each input...

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...

Interval-valued intuitionistic fuzzy sets (IVIFSs) are widely used to handle uncertainty and imprecision in decision making. However, in more complicated environment, it is difficult to express the uncertain information by an IVIFS with considering the decision-making preference. Hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (G-GIVIFSS) which conta...

If all we know about normalized fuzzy sets is which set is a subset of which, will we be able to detect crisp sets? It is known that we can do it if we allow all possible fuzzy sets, including non-normalized ones. In this paper, we show that a similar detection is possible if we only allow normalized fuzzy sets. We also show that we can detect type-1 fuzzy sets based on the subsethood ordering ...

The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered. In fact, this is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set. By using this new idea, the notion of interval valued (∈,∈ ∨q)-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras, is defined, and related properties are investiga...

The relationship between the intuitionistic fuzzy sets and the algebraic hyperstructures is described in this paper. The concept of the quasi-coincidence of an intuitionistic fuzzy interval valued with an interval-valued intuitionistic fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of an intuitionistic fuzzy point in intuitionistic fuzzy sets. By using thi...