Many authors have developed lots of entropies and similarity measures for interval-valued intuitionistic fuzzy sets(IvIFSs). In this paper, we first review some famous entropies for IvIFSs. Then, a new entropy for IvIFSs based on intuitionism and fuzziness is proposed and proved to satisfy the axiomatic requirements given by Liu and Zhang. Furthermore, a new class of similarity measure for IvIF...

Entropy provides a valuable tool for quantifying the regularity of physiological time series and provides important insights for understanding the underlying mechanisms of the cardiovascular system. Before any entropy calculation, certain common parameters need to be initialized: embedding dimension m, tolerance threshold r and time series length N. However, no specific guideline exists on how ...

Simultaneously analyzing multivariate time series provides an insight into underlying interaction mechanisms of cardiovascular system and has recently become an increasing focus of interest. In this study, we proposed a new multivariate entropy measure, named multivariate fuzzy measure entropy (mvFME), for the analysis of multivariate cardiovascular time series. The performances of mvFME, and i...

In this paper the notion of fuzzy topological r-entropy as an extension of the notion of topological r-entropy is studied. It is proved that fuzzy topological r-entropy is an invariant object under uniformly fuzzy equivalent relation and fuzzy topological equivalent relation.

Most information discovery processes need to understand the reasons of the success of the inference methods or the usability of the new information, which can sometimes be somehow explained with a few useful measures on the premises or on the chosen relations, logics and implications. This chapter presents a state of art on the latest concepts of measure, from the additive measures, to monotone...

In this paper, a novel modified evolutionary fuzzy clustering has been proposed. This technique exploits parameters such as Minkowski distance, Xie Beni index, and classification entropy. These parameters turn to account to polish the performance measure by incorporating shape of the cluster, class compactness and partitioning quality respectively in standard Fuzzy C-Means clustering. Moreover,...

Fuzziness (entropy) is a commonly used measure of uncertainty for type-1 fuzzy sets. For interval type-2 fuzzy sets (IT2 FSs), centroid, cardinality, fuzziness, variance and skewness are all measures of uncertainties. The centroid of an IT2 FS has been defined by Karnik and Mendel. In this paper, the other four concepts are defined. All definitions use a Representation Theorem for IT2 FSs. Form...

Relations and relation matrices are important concepts in set theory and intelligent computation. Some general uncertainty measures for fuzzy relations are proposed by generalizing Shannon’s information entropy. Then, the proposed measures are used to calculate the diversity quantity of multiple classifier systems and the granularity of granulated problem spaces, respectively. As a diversity me...

Abstract In this paper, definitions of knowledge granulation and rough entropy are proposed based on dominance relations in incomplete fuzzy system (fuzzy information system), and important properties are obtained. It can be found that using the definitions can measure uncertainty of an attribute set in the incomplete fuzzy information systems. A matrix algorithm for attributes reduction is acq...