In this paper two ranking functions are employed to treat the fuzzy multiple objective (FMO) programming model, then using two kinds of membership function, the first one is trapezoidal fuzzy (TF) ordinary membership function, the second one is trapezoidal fuzzy weighted membership function. When the objective function is fuzzy, then should transform and shrinkage the fuzzy model to traditional model, finally solving these models to know which one is better

           This paper introduce two types of edge degrees (line degree and near line degree) and total edge degrees (total line degree and total near line degree) of an edge in a fuzzy semigraph, where a fuzzy semigraph is defined as (V, σ, μ, η) defined on a semigraph G^* in which σ : V → [0, 1], μ : VxV → [0, 1] and η : X → [0, 1] satisfy the conditions that for all the vertices u, v in the vertex set,  μ(u, v) ≤ σ(u) ᴧ σ(v) and  η(e) = μ(u₁, u₂) ᴧ μ(u₂, u₃) ᴧ … ᴧ μ(u_n-1, u_n) ≤ σ(u₁) ᴧ σ(u_n), if e = (u₁, u₂, …, u_n), n ≥ 2 is an edge in the semigraph G

Let  be a commutative ring with identity, and  be a unitary left -module. In this paper we introduce the concept pseudo weakly closed submodule as a generalization of -closed submodules, where a submodule  of an -module  is called a pseudo weakly closed submodule, if for all , there exists a -closed submodule  of  with  is a submodule of  such that . Several basic properties, examples and results of pseudo weakly closed submodules are given. Furthermore the behavior of pseudo weakly closed submodules in class of multiplication modules are studied. On the other hand modules with chain conditions on pseudo weakly closed submodules are established. Also, the relationships of  pseudo weakly closed

An R-module M is called rationally extending if each submodule of M is rational in a direct summand of M. In this paper we study this class of modules which is contained in the class of extending modules, Also we consider the class of strongly quasi-monoform modules, an R-module M is called strongly quasi-monoform if every nonzero proper submodule of M is quasi-invertible relative to some direct summand of M. Conditions are investigated to identify between these classes. Several properties are considered for such modules

    Let R be a commutative ring with unity and let M, N be unitary R-modules. In this research, we give generalizations for the concepts: weakly relative injectivity, relative tightness and weakly injectivity of modules. We call M weakly N-quasi-injective, if for each f  Hom(N,) there exists a submodule X of  such that  f (N)  X ≈ M, where  is the quasi-injective hull of M. And we call M N-quasi-tight, if every quotient N / K of N which embeds in  embeds in M. While we call M weakly quasi-injective if M is weakly N-quasiinjective for every finitely generated R-module N.         Moreover, we generalize some properties of weakly N-injectiv

The fuzzy assignment models (FAMs) have been explored by various literature to access classical values, which are more precise in our real-life accomplishment. The novelty of this paper contributed positively to a unique application of pentagonal fuzzy numbers for the evaluation of FAMs. The new method namely Pascal’s triangle graded mean (PT-GM) has presented a new algorithm in accessing the critical path to solve the assignment problems (AP) based on the fuzzy objective function of minimising total cost. The results obtained have been compared to the existing methods such as, the centroid formula (CF) and centroid formula integration (CFI). It has been demonstrated that operational efficiency of this conducted method is exquisitely deve

Data centric techniques, like data aggregation via modified algorithm based on fuzzy clustering algorithm with voronoi diagram which is called modified Voronoi Fuzzy Clustering Algorithm (VFCA) is presented in this paper. In the modified algorithm, the sensed area divided into number of voronoi cells by applying voronoi diagram, these cells are clustered by a fuzzy C-means method (FCM) to reduce the transmission distance. Then an appropriate cluster head (CH) for each cluster is elected. Three parameters are used for this election process, the energy, distance between CH and its neighbor sensors and packet loss values. Furthermore, data aggregation is employed in each CH to reduce the amount of data transmission which le

To damp the low-frequency oscillations which occurred due to the disturbances in the electrical power system, the generators are equipped with Power System Stabilizer (PSS) that provide supplementary feedback stabilizing signals. The low-frequency oscillations in power system are classified as local mode oscillations, intra-area mode oscillation, and interarea mode oscillations. A suitable PSS model was selected considering the low frequencies oscillation in the inter-area mode based on conventional PSS and Fuzzy Logic Controller. Two types of (FIS) Mamdani and suggeno were considered in this paper. The software of the methods was executed using MATLAB R2015a package.

      In this work we discuss the concept of pure-maximal denoted by (Pr-maximal) submodules as a generalization to the type of R- maximal submodule, where a proper submodule  of an R-module  is called Pr- maximal if  ,for any submodule  of W is a pure submodule of W, We offer some properties of a Pr-maximal submodules, and we give Definition of the concept, near-maximal, a proper submodule  

 of an R-module  is named near (N-maximal) whensoever  is pure submodule of  such that  then K=.Al so we offer the concept Pr-module, An R-module W is named Pr-module, if every proper submodule of  is Pr-maximal. A ring  is named Pr-ring if whole proper ideal of  is a Pr-maximal ideal, we offer the concept pure local (Pr-loc