The OSPF cost is proportionally indicated the transmitting packet overhead through a certain interface and inversely proportional to the interface bandwidth. Thus, this cost may minimized by direct packet transmitting to the other side via various probable paths simultaneously. Logically, the minimum weight path is the optimum path. This paper propose a novel Fuzzy Artificial Neural Network to create Smart Routing Protocol Algorithm. Consequently, the Fuzzy Artificial Neural Network Overlap has been reduced from (0.883 ms) to (0.602 ms) at fuzzy membership 1.5 to 4.5 respectively. This indicated the transmission time is two-fold faster than the standard overlapping time (1.3 ms).

     A fuzzy valued diffusion term, which in a fuzzy stochastic differential equation refers to one-dimensional Brownian motion, is defined by the meaning of the stochastic integral of a fuzzy process. In this paper, the existence and uniqueness theorem of fuzzy stochastic ordinary differential equations, based on the mean square convergence of the mathematical induction approximations to the associated stochastic integral equation, are stated and demonstrated.

Simulation  of  the  Linguistic  Fuzzy Trust  Model  (LFTM)  over  oscillating  Wireless  Sensor Networks (WSNs) where the goodness of the servers belonging to them could change along the time is presented in this paper, and the comparison between the outcomes achieved with LFTM model over oscillating WSNs with the outcomes obtained by applying the model over static WSNs where the servers maintaining always the same goodness, in terms of the selection percentage of trustworthy servers (the accuracy of the model) and the average path length are also presented here. Also in this paper the comparison between the LFTM and the Bio-inspired Trust and Reputation Model for Wireless Sensor Network

The aim of this paper is to introduce the concept of N  and Nβ -closed sets in terms of neutrosophic topological spaces. Some of its properties are also discussed.

In this article an attempt has been made to procure the concept of pairwise neutrosophic simply open set, pairwise neutrosophic simply continuous mapping, pairwise neutrosophic simply open mapping, pairwise neutrosophic simply compactness, pairwise neutrosophic simply b-open set, pairwise neutrosophic simply b-continuous mapping, pairwise neutrosophic simply b-open mapping and pairwise neutrosophic simply b-compactness via neutrosophic bi-topological spaces (in short NBTS). Besides, we furnish few illustrative examples on them via NBTS. Further, we investigate some basic properties of them, and formulate several results on NBTSs.

 In this paper, we proved the existence and uniqueness of the solution of nonlinear Volterra fuzzy integral equations of the second kind.
 

In this paper, we introduce the concept of almost Quasi-Frobcnius fuzzy ring as a " " of Quasi-Frobenius ring. We give some properties about this concept with qoutient fuzzy ring. Also, we study the fuzzy external direct sum of fuzzy rings.