Journal of Mathematical Extension
Volume:10 Issue: 2, Spring 2016

Ranking fuzzy numbers is a very important decision-making procedure in decision analysis and applications. The last few decades have seen a large number of methods investigated for ranking fuzzy numbers, yet some of these approaches are non-intuitive and inconsistent. The most commonly used approaches for ranking fuzzy numbers are ranking indices based on centroid of fuzzy numbers. Despite their merits, there are some weakness associated with these indices. This paper review several recent fuzzy numbers ranking methods based on centroid points, then proposes a new centroid index ranking method that is capable of effectively ranking various types of fuzzy numbers. The presented method is compared with the given attitude by the way of centroid point. The contents herein present several comparative examples demonstrating the usage and advantages of the proposed centroid index ranking method for fuzzy numbers. Meanwhile, it can overcome the drawback of other methods.

The main aim of this paper is to define and investigate the fuzzy quotient spaces and t-best approximation in fuzzy quotient space and prove some theorems on quotient spaces. Finally, we present an application.

In this paper, using a generalized translation operator, we obtain an analog of Younis [8, Theorem 2.5] in for the generalized Fourier-Bessel transform for functions satisfying the Fourier-Bessel Dini Lipschitz condition in the space L 2 α,n.

In this paper we study the notions of relative information function and relative conditional information function on a relative probability measure space. We present some examples and prove some theorems about them. Also the concept of relative information function for a relative measure preserving transformation is introduced and some of its properties, are proved. Finally, it is proved that the relative information function of relative measure preserving transformations is invariant under isomorphism.

In this paper we study some comparative growth properties of composite entire functions in terms of their maximum terms on the basis of their relative L ∗ order ( relative L ∗ lower order ) with respect to another entire function.

Let R be a prime ring with characteristic different from two, I be a nonzero ideal of R, and F be a generalized derivation associated with a nonzero derivation d of R. In the present paper we investigate the commutativity of R satisfying the relation F([x, y]k) n = ([x, y]k) l for all x, y ∈ I, where l, n, k are fixed positive integers. Moreover, let R be a semiprime ring, A = O(R) be an orthogonal completion of R, and B = B(C) be the Boolean ring of C. Suppose F([x, y]k) n = ([x, y]k) l for all x, y ∈ R, then there exists a central idempotent element e of B such that d vanishes identically on eA and the ring (1 − e)A is commutative.

In this paper, the entropy of fuzzy countable partitions is proposed. In addition, the notion of fuzzy conditional entropy, fuzzy relative entropy and entropy on a fuzzy dynamical system based on fuzzy countable partitions are introduced and some properties of these entropies are analyzed. Using the concept of fuzzy generator, it is proved that the entropy of a dynamical system is done through a fuzzy generator. Furthermore, one of the proven results in this paper is isomorphism invariant property of entropy with fuzzy countable partitions on a fuzzy dynamical system.

In this paper, a new method is presented for solving nonlinear fuzzy optimization problems (NFOP) where all coefficients of the problem are triangular fuzzy numbers. First, we convert NFOP problem to an interval nonlinear programming problem (INP) by α-cuts and in general case, we determine INP based on α. Then by solving INP model, the optimal solution of the main problem is obtained. To illustrate the proposed method numerical examples are solved and the obtained results are discussed.