based on the point of view of geometrical representation of an intuitionistic fuzzy set, we take into account all three parameters describing intuitionistic fuzzy set, propose a kind of new method to calculate correlation and correlation coefficient of intuitionistic fuzzy sets which is similar to the cosine of the intersectional angle in finite sets and probability space, respectively. further...

The zero forcing number Z(G) is used to study the minimum rank/maximum nullity of the family of symmetric matrices described by a simple, undirected graph G. The positive semidefinite zero forcing number is a variant of the (standard) zero forcing number, which uses the same definition except with a different color-change rule. The positive semidefinite maximum nullity and zero forcing number f...

In this paper, we introduce the concept of fuzzy congruences on n-ary semigroups and describe quotient n-ary semigroups by fuzzy congruences. Some isomorphism theorems about n-ary semigroups are established. Moreover, we discuss a special kind of n-ary semigroups. We also establish relationships between normal fuzzy ideals and fuzzy congruences. In particular, we prove that there exists a prese...

Zero forcing is a deterministic iterative graph coloring process in which vertices are colored either blue or white, and every round, any that have single white neighbor force these to become blue. Here we study probabilistic zero forcing, where non-zero probability of each We explore the propagation time for on Erd?s–Réyni random G ( n , p ) when start with vertex show = log ? o 1 then high it...

With every σ-ideal I on a Polish space we associate the σ-ideal generated by closed sets in I. We study the forcing notions of Borel sets modulo the respective σ-ideals and find connections between their forcing properties. To this end, we associate to a σ-ideal on a Polish space an ideal on a countable set and show how forcing properties of the forcing depend on combinatorial properties of the...

This paper begins the study of reconfiguration zero forcing sets, and more specifically, graph. Given a base graph G, its graph, Z(G), is whose vertices are minimum sets G with an edge between B B′ Z(G) if only can be obtained from by changing single vertex G. It shown that forest connected, but many graphs disconnected. We characterize complete graphs, show star cannot computing takes 2Θ(n) op...