In this paper we prove the existence of fixed point theorems for $\mathcal{Z}$-contractive map, Geraghty type contractive map and interpolative Hardy-Rogers type contractive mapping in the setting of $S^{JS}$metric spaces with two metrics. Examples are constructed to highlight the significance of newly obtained results. تفاصيل المقالة

In this paper we extend fuzzy analytic hierarchy process into neutrosophic cubic environment. The neutrosophic cubic analytic hierarchy process can be used to manage more complex problems when the decision makers has a number of uncertainty, assigning preferences values to the considered object. We also define the concept of triangular neutrosophic cubic numbers and their operations laws. The advantages of the proposed methodology and the application of neutrosophic cubic analytic hierarchy process in decision making are shown by testing the numerical example in practical life. تفاصيل المقالة

Hyper Wiener index of fuzzy graphs and edge deleted fuzzy subgraphs areproposed in this article. A relationship between Connectivity index andHyper Wiener index of fuzzy graphs is obtained. تفاصيل المقالة

‎When it comes to solving dynamic‎ ‎programming challenges‎, ‎it is essential to have a well-structured ‎‎‎‎decision theory‎. ‎As a result‎, ‎the decision-makers must operate in a‎ ‎dynamically complicated environment where appropriate and rapid‎ ‎reaction in a cooperative way is the fundamental key to effectively‎ ‎completing the task‎. ‎We express a theory of decision modeling and‎ ‎axiomatizing a decision-making process‎. ‎The payoffs and‎ ‎probabilities are represented with simplified neutrosophic sets‎. ‎We‎ ‎therefore‎, ‎provide the theory of choice with the implementation of‎ ‎simplified neutrosophic sets‎. ‎By exploiting the idea of pure‎ ‎strategy‎, ‎we introduce two steps‎: ‎in the first step‎, ‎for each‎ ‎attractive point‎, ‎some particular event is selected that can bring‎ ‎about a relatively neutrosophic upper payoff with a relatively‎ ‎neutrosophic upper probability or a relatively neutrosophic lower‎ ‎payoff with a relatively neutrosophic upper probability‎. ‎A‎ ‎decision-maker selects the most favored attractive point in the‎ ‎second stage‎, ‎based on the focus on all attractive points‎. ‎Neutrosophic focus theory has been introduced to improve overall‎ ‎performance with more flexibility in complex decision-making‎. ‎The‎ ‎approach suggested in this work has been implemented in a real-life‎ ‎example to determine its effectiveness‎. ‎The proposed method is shown to‎ ‎be the most useful for ranking scenarios and addressing dynamic‎ ‎programming problems in decision-making‎. تفاصيل المقالة

In this paper, based on embedding approach three numericalmethods namely Richardson, Gauss-Seidel, and successive over relaxation (SOR)have been developed to solve bipolar neutrosophic system of linear equations.To check the accuracy of these newly developed schemes an example with exactand iterative solution is given. تفاصيل المقالة