The priority problem of incomplete preference relations is investigated. Using the transformation relation between multiplicative preference relation and fuzzy preference relation, we develop a least-square model to obtain the collective priority vector of the incomplete preference relations presented by multiple decision makers, with the existence condition of the solution being developed. Mea...

We extend some results obtained in 1998 and 1999 by studying the periodicity of the solutions of the fuzzy difference equations xn+1 = max{A/xn,A/xn−1, . . . ,A/xn−k}, xn+1 = max{A0/xn,A1/xn−1}, where k is a positive integer, A, Ai, i= 0,1, are positive fuzzy numbers, and the initial values xi, i=−k,−k + 1, . . . ,0 (resp., i=−1,0) of the first (resp., second) equation are positive fuzzy numbers.

Difference equations have already been successfully applied in a number of sciences (for a detailed study of the theory of difference equations and their applications, see [1, 2, 7, 8, 11]. The problem of identifying, modeling, and solving a nonlinear difference equation concerning a real-world phenomenon from experimental input-output data, which is uncertain, incomplete, imprecise, or vague, ...

We prove strong completeness of the -version and the 3-version of a Gödel modal logic based on Kripke models where propositions at each world and the accessibility relation are both in…nitely valued in the standard Gödel algebra [0,1]. Some asymmetries are revealed: validity in the …rst logic is reducible to the class of frames having twovalued accessibility relation and this logic does not enj...

In this paper variation of constants formula for the inhomogeneous fuzzy matrix difference system X(n + 1) = A(n)X(n) + F (n) is constructed by considering corresponding matrix difference inclusion Xβ(n+ 1) ∈ AβXβ(n) +Fβ(n), xβ(0) ∈ X0 β after presenting a procedure for solving the fuzzy difference equation by an example. Mathematics Subject Classification: 26E50, 34A12, 34A30

Multi-fuzzy set theory is an extension of fuzzy set theory, L-fuzzy set theory and Atanassov intuitionistic fuzzy set theory. In this paper we study the relation between Atanassov intuitionistic fuzzy and the proposed extension called Multi-fuzzy. Also we present the notion of Multi-fuzzy mappings and Atanassov Intuitionistic Fuzzy Sets Generating Maps. Mathematics Subject Classification: MSC: ...

Zoning the pollution of a river may be the first or even the most important step in water quality management. In order to resolve its pollution, fuzzy clustering analysis may be used whenever a composite classification of water quality incorporates mutiple parameters&#10 &#10In such cases, the technique may be used as a complement or an alternative to comprehensive assessment. In fuzzy cluster...

Zoning the pollution of a river may be the first or even the most important step in water quality management. In order to resolve its pollution, fuzzy clustering analysis may be used whenever a composite classification of water quality incorporates mutiple parameters In such cases, the technique may be used as a complement or an alternative to comprehensive assessment. In fuzzy clustering ...

first we show that the cosets of a fuzzy ideal μ in a bck-algebrax form another bck-algebra  x/μ (called the fuzzy quotient bck-algebra of x by μ). also we show thatx/μ is a fuzzy partition of x and we prove several some isomorphism theorems. moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition p of a commutative bck-algebra iscompatible, then p is a fuzzy quo...

The purpose of this paper is to define the fuzzy quotient group by using some special fuzzy relation which is defined in this study and to prove some basic properties. c ©2003 Yang’s Scientific Research Institute, LLC. All rights reserved.