In this paper, we discuss various k-g inverses associated with a k-regular Interval-Valued Fuzzy Matrix. We obtain some characterization of the set of all k-g inverses.

This is the announcement, and the long summary, of a series of articles on the algorithmic study of Thurston maps. We describe branched coverings of the sphere in terms of group-theoretical objects called bisets, and develop a theory of decompositions of bisets. We introduce a canonical “Levy” decomposition of an arbitrary Thurston map into homeomorphisms, metrically-expanding maps and maps dou...

An integral component of Fuzzy ARTMAP's training phase is the use of Match Tracking (MT), whose functionality is to search for an appropriate category that will correctly classify a presented training pattern in case this particular pattern was originally misclassified. In this paper we explain the MT's role in detail, why it actually works and finally we put its usefulness to the test by compa...

We establish the existence of a best proximity pair for which the best proximity set is nonempty for a finite family of multimaps whose product is either an Ac -multimap or a multimap T : A → 2 such that both T and S ◦ T are closed and have the KKM property for each Kakutani multimap S : B → 2. As applications, we obtain existence theorems of equilibrium pairs for free n-person games as well as...

Memory plays a major role in Artificial Neural Networks. Without memory, Neural Network can not be learned itself. One of the primary concepts of memory in neural networks is Associative neural memories. A survey has been made on associative neural memories such as Simple associative memories (SAM), Dynamic associative memories (DAM), Bidirectional Associative memories (BAM), Hopfield memories,...

We claim that monomorphisms in Sets and Groups are the usual injective maps and homomorphisms. First, suppose that f : A → B is a set injection and that fg = gh. Then for all c ∈ C, we have f(g(c)) = f(h(c)) implies g(c) = h(c) by injectivitiy. Hence g = h. Conversely, suppose f : A → B is not an injection. Then let f(a) = f(a′) for some a 6= a′ ∈ A. Then let g(c) = a and h(c) = a′ for all c ∈ ...