The aim of this paper is to study the properties of t-cut set, strong t-cut set, t-quasi-cut set, strong t-quasi-cut set and ∈ ∨q-cut set of a fuzzy set μ. For any intuitionistic fuzzy A =< μA, νA > and α, β ∈ [0, 1], we define and study the properties of upper (α, β) cut setA(α,β), strong upper (α, β) cut setA(α, β) ̇ , lower (α, β) cut set A, strong lower (α, β) cut set A (α, β) ̇ , upper (α, β...

Investigation of reliability characteristics under fuzzy environments is proposed in this paper. Fuzzy Weibull distribution and lifetimes of components are using it described. Formulas of a fuzzy reliability function, fuzzy hazard function and their α-cut set are presented. Furthermore, the fuzzy functions of series systems and parallel systems are discussed, respectively. Finally, some num...

The support of a set A is the crisp subset of A with nonzero membership grades. Similarly, the core of a set A is the crisp subset of A with membership grade equal to one. So, supp(A) = {x|μA(x) > 0} and core(A) = {x|μA(x) = 1}. (1.1.4) The α-cut Aα of a set A is the crisp subset of A with membership grades of at least α. So, Aα = α-cut(A) = {x|μA(x) ≥ α}. (1.1.5) Note that core(A) = 1-cut(A). ...

The article provides an α-cut-based method that solves linear fractional programming problems with fuzzy variables and unrestricted parameters. parameters are considered as asymmetric triangular numbers, which is a generalization of the symmetric case. problem solved by using α-cut numbers wherein α- r-cut applied to objective function constraints, respectively. This reduces into equivalent bio...

investigation of reliability characteristics under fuzzy environments is proposed in this paper. fuzzy weibull distribution and lifetimes of components are using it described. formulas of a fuzzy reliability function, fuzzy hazard function and their α-cut set are presented. furthermore, the fuzzy functions of series systems and parallel systems are discussed, respectively. finally, some numeric...

The (α, β) cut of an Intuitionistic Fuzzy Set (IFS) was studied by P. K. Sharma [4]. In this paper we introduce a new type of cut strong (α, β) cut of IFS and study their properties. Also three decomposition theorems are discussed.

In this paper, a new Fuzzy Morphology (FM) based on the GeneralizedDempster-Shafer Theory (GDST) is proposed. At first, in order to clarify the similarity ofdefinitions between Mathematical Morphology (MM) and Dempster-Shafer Theory (DST),dilation and erosion morphological operations are studied from a different viewpoint. Then,based on this similarity, a FM based on the GDST is proposed. Unlik...

In 2014, some scholars showed that every 2-connected claw-free graph G with independence number α(G)≤3 is Hamiltonian one exception of family graphs. If a nontrivial path contains only internal vertices degree two and end not two, then we call it branch. A set S branches called branch cut if delete all edges leading to more components than G. We use bond denote minimal cut. branch-bond has an o...

We have started a search for High Redshift Radio Galaxies (HZRGs) in an area covering 7 sr by selecting a sample of Ultra Steep Spectrum (USS) sources with a low flux density cut-off S1400 > 10 mJy and a steep spectral index cut-off of α < −1.3 (S ∝ ν) from the WENSS, NVSS and TEXAS surveys. Our first results for 27 sources show that we are almost twice as effective in finding HZRGs than than s...