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, the notions of $(t,s)$-composition matrix and$(t,s)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(t,s)$ is a dual pair of triangular module. theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. furthermore, theirproperties and characterizations are presented. then a new methodbased on $tilde{...

The aim of this paper is to define the productoperation on a family of interval valued events and the notion ofjoint interval valued observable. We show the connection betweenproduct operations for interval valued events and intuitionisticfuzzy events, too. We display the relation between joint intervalvalued observable and joint intuitionistic fuzzy observable. We...

In this paper, we first use a fuzzy preference relation with a membership function representing preference degree forcomparing two interval-valued fuzzy numbers and then utilize a relative preference relation improved from the fuzzypreference relation to rank a set of interval-valued fuzzy numbers. Since the fuzzy preference relation is a total orderingrelation that satisfies reciprocal and tra...

In this paper, we introduce  the notions of   interval-valued and $(in,ivq)$-interval-valued fuzzy ($p$-,$q$- and $a$-) ideals    of   BCI algebras   and investigate some of their properties.   We then derive characterization theorems for these generalized interval-valued fuzzy ideals  and discuss their relationship.

In this paper, we introduce a new sort of interval valued $left(in ,in vee q_{widetilde{k}}^{widetilde{delta }}right) $-fuzzy bi-ideal in ordered semigroups which is the generalization of interval valued $left( in ,in vee q_{%widetilde{k}}right) $-fuzzy bi-ideal and interval valued $left( in ,in vee qright) $-fuzzy bi-ideal of ordered semigroups. We give examples in which we show that these str...

in this paper, we introduce  the notions of   interval-valued and $(in,ivq)$-interval-valued fuzzy ($p$-,$q$- and $a$-) ideals    of   bci algebras   and investigate some of their properties.   we then derive characterization theorems for these generalized interval-valued fuzzy ideals  and discuss their relationship.