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...

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...

Interval-valued fuzzy set theory is an extension of fuzzy set theory in which the real, but unknown, membership degree is approximated by a closed interval of possible membership degrees. Since implications on the unit interval play an important role in fuzzy set theory, several authors have extended this notion to interval-valued fuzzy set theory. This chapter gives an overview of the results ...

It is proved that the single input and single output (SISO) fuzzy systems based upon genuine many-valued implications are universal approximators. It is shown theoretically that fuzzy control systems based upon genuine many-valued implications are equivalent to those based upon t-norm implications, the general approach to construct fuzzy systems is given. It is also shown that defuzzi8er based ...

We present a new approach for handling fuzzy triadic data in the setting of Formal Concept Analysis. The starting point is a fuzzyvalued triadic context (K1,K2,K3, Y ), where K1,K2 and K3 are sets and Y is a ternary fuzzy relation between these sets. First, we generalise the methods of Triadic Concept Analysis to our setting and show how they fit other approaches to Fuzzy Triadic Concept Analys...

The main goal of this paper is to apply the method of extension of fuzzy connectives proposed in our previous work for fuzzy implications valued on a bounded lattice. Also we discuss about which properties of implications are preserved by this method and we prove some results involving extension and automorphisms. Finally, we investigate the behavior of the extensions of two special classes of ...

Based on the fully implicational idea, we investigate the interval-valued fuzzy reasoning with multiantecedent rules. First, we construct a class of interval-valued fuzzy implications by means of a type of implications and a parameter on the unit interval, then use them to establish three kinds of fully implicational reasoning methods for the interval-valued fuzzy reasoning with multi-anteceden...

Fuzzy representations of a real-valued random variable have been introduced with the aim of capturing relevant information on the distribution of the variable, through the corresponding fuzzy-valued mean value. In particular, characterizing fuzzy representations of a random variable allow us to capture the whole information on its distribution. One of the implications from this fact is that tes...

In this paper, we take a GL-quantale as the truth value table to study a new rough set model—L-valued fuzzy rough sets. The three key components of this model are: an L-fuzzy set A as the universal set, an L-valued relation of A and an L-fuzzy set of A (a fuzzy subset of fuzzy sets). Then L-valued fuzzy rough sets are completely characterized via both constructive and axiomatic approaches.