In this paper we extend the notion of  degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and  introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. It would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. We give the main properties of the operations defined and prove som...

In this paper, let $L$ be a completeresiduated lattice, and let {bf Set} denote the category of setsand mappings, $LF$-{bf Pos} denote the category of $LF$-posets and$LF$-monotone mappings, and $LF$-{bf CSLat}$(sqcup)$, $LF$-{bfCSLat}$(sqcap)$ denote the category of $LF$-completelattices and $LF$-join-preserving mappings and the category of$LF$-complete lattices and $LF$-meet-preserving mapping...

In this paper we introduce an algebraic fuzzy equation of degree n with fuzzy coefficients and crisp variable, and we present an iterative method to find the real roots of such equations, numerically. We present an algorithm to generate a sequence that can be converged to the root of an algebraic fuzzy equation. 2007 Elsevier Inc. All rights reserved. MSC: 12E12; 39B22; 65H05

Some relevant algebraic structures involved by the so–called Intuitionistic Fuzzy Sets (IFS) are discussed, with a wide description of their relevant properties especially from the point of view of the algebraic semantic of a logical system. Algebraic comparison with analogous structures involving usual Fuzzy Sets are discussed.

The paper presents a short review of some main properties of the most general fuzzy systems used in a large class of practical applications. The fuzzy systems, implemented using different rule bases, fuzzy values, membership functions, fuzzyfication and defuzzification methods, may be classified based on these fuzzy methods used in their development. This paper proposes a unitary theory for des...

A Q -fuzzy set is a mapping from [0,1] X Q × → where X is the universe of discourse and Q is a non-empty set. Some works has been emanated for this Q -fuzzy set. In all the above work the set 'Q' is treated as a non-empty set without any algebraic structure. This article presents an algebraic structure for Q -fuzzy set over a semiring named as 1 Q -fuzzy set and provide some properties and resu...

In this paper, we investigate more relations between the symmetric residuated lattices $L$ with their corresponding intuitionistic fuzzy residuated lattice $tilde{L}$. It is shown that some algebraic structures of $L$ such as Heyting algebra, Glivenko residuated lattice and strict residuated lattice are preserved for $tilde{L}$. Examples are given for those structures that do not remain the sam...

Neuro-Fuzzy Modeling has been applied in a wide variety of fields such as Decision Making, Engineering and Management Sciences etc. In particular, applications of this Modeling technique in Decision Making by involving complex Systems of Linear Algebraic Equations have remarkable significance. In this Paper, we present Polak-Ribiere Conjugate Gradient based Neural Network with Fuzzy rules to so...