This survey paper deals with upper and lower bounds on the number of k-matchings in regular graphs on N vertices. For the upper bounds we recall the upper matching conjecture which is known to hold for perfect matchings. For the lower bounds we first survey the known results for bipartite graphs, and their continuous versions as the van der Waerden and Tverberg permanent conjectures and its var...

‎A new method for the defuzzification of fuzzy numbers is developed in this paper. It is well-known, defuzzification methods allow us to find aggregative crisp numbers or crisp set for fuzzy numbers. But different fuzzy numbers are often converted into one crisp number. In this case the loss of essential information is possible. It may result in inadequate final conclusions, for example, expert...

Li and Pedrycz [Y. M. Li, W. Pedrycz, Fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids, Fuzzy Sets and Systems 156 (2005) 68–92] have proved fundamental results that provide different equivalentways to represent fuzzy languageswithmembership values in a lattice-orderedmonoid, and generalize the well-known results of the classical theory of fo...

For example, the pentagon is strongly regular with parameters (v, k, λ, μ) = (5, 2, 0, 1). One easily verifies that a graph G is strongly regular with parameters (v, k, λ, μ) if and only if its complement G is strongly regular with parameters (v, v−k− 1, v− 2k+μ− 2, v−2k+λ). The line graph of the complete graph of order m, known as the triangular graph T (m), is strongly regular with parameters...

For every positive integer m, we construct a symmetric (v, k, λ)-design with parameters v = h((2h−1) 2m−1) h−1 , k = h(2h − 1)2m−1, and λ = h(h − 1)(2h − 1)2m−2, where h = ±3 · 2 and |2h − 1| is a prime power. For m ≥ 2 and d ≥ 1, these parameter values were previously undecided. The tools used in the construction are balanced generalized weighing matrices and regular Hadamard matrices of order...

fuzzy bi-ideals play an important role in the study of ordered semigroupstructures. the purpose of this paper is to initiate and study theintiuitionistic fuzzy bi-ideals in ordered semigroups and investigate thebasic theorem of intuitionistic fuzzy bi-ideals. to provide thecharacterizations of regular ordered semigroups in terms of intuitionisticfuzzy bi-ideals and to discuss the relationships ...

‎this paper deals with one problem that needs to be addressed in the emerging field known under the name computing with perceptions‎. ‎it is the problem of describing‎, ‎approximately‎, ‎a given fuzzy set in natural‎ ‎language‎. ‎this problem has lately been referred to as the problem of retranslation‎. ‎an approaches to ‎dealing with the retranslation problem is discussed in the paper‎, ‎that ...

Let X be a Banach space and T ? B(X). Cohen determined class of regular infinite matrices A = (ank) for which Ln := ?? k=1 ankTk converges strongly to an element invariant under T. In the present paper we study A-mean A-uniform ergodic type results when is matrix satisfying Cohen?s uniformity condition lim j k=j |an,k+1 ank| 0, uniformly in n.

Algebraic structures especially an ordered semigroups play a prominent role in mathematics with wide ranging applications in many disciplines such as control engineering, computer arithmetics, coding theory, sequential machines and formal languages. A theory of fuzzy sets in terms of fuzzy points on ordered semigroups can be developed. In this paper, we generalize the concept of (α, β)-fuzzy le...