In this paper, we propose a novel method for ranking a set of fuzzy numbers. In this method a preference index is proposed based on $alpha$-optimistic values of a fuzzy number. We propose a new ranking method by adopting a level of credit in the ordering procedure. Then, we investigate some desirable properties of the proposed ranking method.

Abstract Many chemical indices have been invented in theoretical chemistry, such as Wiener index, Merrifield-Simmons index, Hosoya index, spectral radius and Randić index, etc. The extremal trees and unicyclic graphs for these chemical indices are interested in existing literature. Let G be a molecular graph (called a cacti), which all of blocks of G are either edges or cycles. Denote G (n, r) ...

We define a family of properties on hyperhypersimple sets and show that they yield index sets at each level of the hyperarithmetical hierarchy. An extension yields a nj-complete index set. We also classify the index set of quasimaximal sets, of coinfinite r.e. sets not having an atomless superset, and of r.e. sets major in a fixed nonrecursive r.e. set. 0. Introduction. The present paper deals ...

Fuzzy set theory has been used to model systems that are hard to define precisely. As a methodology, fuzzy set theory incorporates imprecision and subjectivity into the model formulation and solution process. Fuzzy set theory represents an attractive tool to aid research in production management when the dynamics of the production environment limit the specification of model objectives, constra...

The purpose of this note is to describe how central multiplier theorems for compact Lie groups can be reduced to corresponding results on a maximal torus. We shall show that every multiplier theorem for multiple Fourier series gives rise to a corresponding theorem for such groups and, also, for expansions in terms of special functions. We use the notation and terminology of N. J. Weiss [4]. Let...

this new field known as Expert Control. Fuzzy Logic Controllers (FLCs), initiated by Mamdani and Assilian in the work [Mam75], are now considered as one of the most important applications of the Fuzzy Set Theory suggested by Zadeh in 1965 ([Zad65]). FLCs are knowledge based controllers usually derived from a knowledge acquisition process or automatically synthesized from a self-organizing contr...

The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.

 We consider generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be convex. Considering a lower level constraint qualification, we derive a formula for estimating the subdifferential of the value function. Finally, we establish the Fritz-John necessary optimality con...

bi = supply/demand corresponding to a node in Vn C M = cost of an egalitarian peer-to-peer solution M CLB = optimal value of objective function of the optimization problem cij = cost of an edge in Gn cij = cost of an edge in G‘ c i; j; k = cost of a triplet i; j; k representing an egalitarian peer-to-peer maneuver d = distance between two triplets tp and tq E‘ = set of edges in G‘ Ef = set of e...