The entropy of intuitionistic fuzzy sets is used to indicate the degree of fuzziness of an interval-valued intuitionistic fuzzy set(IvIFS). In this paper, we deal with the entropies of IvIFSs. Firstly, we propose a set of entropies on IvIFSs with a parameter λ ∈ [0,+∞), which generalizes the entropy measure defined by Gao, for IvIFSs, and then we prove that the new entropy is an increasing func...

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...

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...

Under the background of global economic integration, with international competition between enterprises increasing, the risks are more diverse. Financial crisis has led to many companies became the victim of the financial crisis era. Chinese enterprises want to survive and develop healthy in the fierce competition, they must enhance the competitiveness of enterprises, improve themselves from th...

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...