Different methods are provided to deal with imprecise judgments of decision makers for the analytical hierarchy process. Most previous methods, which allow consideration of imprecise judgments as fuzzy numbers, provide the local and global weights of elements as fuzzy numbers too. Local and global fuzzy numbers need additional aggregation, computation and ranking procedures.The global weights may overlap each other and make the ranking of alternatives difficult. As a result, since there are different methods of fuzzy computation and fuzzy ranking, in some problems, we cannot have a unique ranking of fuzzy numbers. In order to overcome this deficiency, one method for solving fuzzy analytical hierarchy process problems and obtaining the crisp priority vector is called extent Analysis. As mentioned, the main challenges of solving such problems are the fuzzy computations and ranking of fuzzy numbers, because different computation and ranking of fuzzy numbers may result in the different ranking of alternatives. Since the extent Analysis method derives the crisp priority vector from fuzzy comparison matrices, it eliminates the need for additional computation and ranking of fuzzy numbers.This method is used in much research, but, in this paper, it is indicated that the priority vector of this method is not appropriate. To overcome this defect, in this paper, a new meta-heuristic based algorithm is proposed to derive the crisp priority vector from fuzzy comparison matrices. Furthermore, in order to illustrate the proposed method of this paper, it is compared with four methods available in the literature. The computational results indicate that the proposed method is appropriate for deriving the crisp priority vector from fuzzy comparison matrices.

In this paper, we introduce a new class of implicit functions and also common property (E.A) in Modified intuitionistic fuzzy metric spaces and utilize the same to prove some common fixed point theorems in Modified intuitionistic fuzzy metric spaces besides discussing related results and illustrative examples. We are not aware of any paper dealing with such implicit functions in Modified intuitionistic fuzzy metric spaces.

We are concerned with the development of a k-step method for the numerical solution of fuzzy initial value problems. Convergence and stability of the method are also proved in detail. Moreover, a specific method of order 4 is found. The numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.