In this paper, the fuzzy scalar median (FSM) is proposed, defined by using ordering of fuzzy numbers based on fuzzy minimum and maximum operations defined by using the extension principle. Alternatively, the FSM is defined from the minimization of a fuzzy distance measure, and the equivalence of the two definitions is proven. Then, the fuzzy vector median (FVM) is proposed as an extension of ve...

In this paper, we introduce a modification of the Fuzzy ARTMAP (FAM) neural network, namely, the Fuzzy ARTMAP with adaptively weighted distances (FAMawd) neural network. In FAMawd we substitute the regular L1-norm with a weighted L1-norm to measure the distances between categories and input patterns. The distance-related weights are a function of a category’s shape and allow for bias in the dir...

An axiomatic definition of divergence measure for intuitionistic fuzzy sets (IFSs, for short) is presented in this work, as a particular case of dissimilarity between IFSs. As the concept of divergence measure is more restrictive, it has particular properties which are studied. Furthermore, the relationships among IF-divergences, dissimilarities and distances are studied. We also provide some m...

Composition operators Cφ induced by a selfmap φ of some set S are operators acting on a space consisting of functions on S by composition to the right with φ, that is Cφf = f ◦ φ. In this paper, we consider the Hilbert Hardy spaceH2 on the open unit disk and find exact formulas for distances ‖Cφ−Cψ‖ between composition operators. The selfmaps φ and ψ involved in those formulas are constant, inn...

A concept related to the spectrum of a graph is that of energy. The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of the adjacency matrix of G . The Laplacian energy of a graph G is equal to the sum of distances of the Laplacian eigenvalues of G and the average degree d(G) of G. In this paper we introduce the concept of Laplacian energy of fuzzy graphs. ...

Unraveling functional and ancestral relationships between proteins as well as structure prediction procedures require powerful protein alignment methods. This paper describes the use of fuzzy alignments when matching protein structures. The method use mean-field annealing optimization of fuzzy alignment variables, based on a cost expressed in terms of distances between aligned atoms and of gaps...

A fuzzy clustering based modification of Gaussian mixture models (GMMs) for speaker recognition is proposed. In this modification, fuzzy mixture weights are introduced by redefining the distances used in the fuzzy c-means (FCM) functionals. Their reestimation formulas are proved by minimising the FCM functionals. The experimental results show that the fuzzy GMMs can be used in speaker recogniti...