given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

The present contribution is devoted to the theory of fuzzy sets, especially Atanassov Intuitionistic Fuzzy sets (IF sets) and their use in practice. We define correlation between IF coefficient, we bring a new perspective solving problem data file reduction case where input come from sets. specific applications two best-known methods, Principal Component Analysis Factor Analysis, used solve red...

a dominating set $d subseteq v$ of a graph $g = (v,e)$ is said to be a connected cototal dominating set if $langle d rangle$ is connected and $langle v-d rangle neq phi$, contains no isolated vertices. a connected cototal dominating set is said to be minimal if no proper subset of $d$ is connected cototal dominating set. the connected cototal domination number $gamma_{ccl}(g)$ of $g$ is the min...

Modern society is increasingly dependent on, and fearful of, the availability of electronic information. There are numerous examples of situations where sensitive data must be – sometimes reluctantly – shared between two or more entities without mutual trust. As often happens, the research community has foreseen the need for mechanisms to enable limited (privacy-preserving) sharing of sensitive...

P. Grzegorzewski [3] has worked the probability version of the inclusion-exclusion principle and made a generalization for IF-events. He had applied two versions of the generalized formula, corresponding to different t-conorms and so defined the union of IF-events. This paper contains the generalization of the Grzegorzewski theorem. We prove it for mappings from the set of IF sets to the unit i...