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...

The priority method on the intuitionistic fuzzy preference relation (IFPR) is proposed. In order to avoid the operational difficulty in dealing with the intuitionistic sets, the equivalent interval matrices of the IFPR are introduced. Based on the multiplicative consistent definition of the fuzzy interval preference relation (FIPR), the goal programming models for deriving the priority vector o...

Intuitionistic cubic fuzzy sets (ICFSs), as a hybrid set consisting of interval-valued and intuitionistic sets, can deal with the uncertainty information in decision problems more comprehensively. Muirhead mean (MM) operators correlation between attributes realistically. However, there has been no research on MM under so far. In this study, some new are proposed set. It contains (ICFMM) operato...

Clustering plays an important role in data mining, pattern recognition, and machine learning. Singlevalued neutrosophic sets (SVNSs) are useful means to describe and handle indeterminate and inconsistent information that fuzzy sets and intuitionistic fuzzy sets cannot describe and deal with. To cluster the data represented by single-valued neutrosophic information, this article proposes single-...

In this paper, relations among the membership values of gener- alized fuzzy languages such as intuitionistic fuzzy language, interval-valued fuzzy language and vague language are studied. It will aid in studying the properties of one language when the properties of another are known. Further, existence of a minimized nite automaton with vague ( final) states for any vague regular language recog...