The paper is devoted to a general aggregation operator acting on L-fuzzy real numbers. It is defined as a t-norm based extension of an ordinary aggregation operator. The aim of our research is to analyze properties of the general aggregation operator depending on properties of the ordinary aggregation operator and the t-norm. By using the general aggregation operator we consider the properties ...

The extension principle defines the arithmetic operations on fuzzy numbers. In the extension principle one can use any t-norm for modeling the conjunction operator. It is therefore important to know, which t-norms are consistent with a particular type of fuzzy number. We call a t-norm consistent, if the arithmetic operation is closed. In this paper we investigate the addition of sigmoid and two...

Using Generalized Modus Ponens reasoning, we examine the values of the inferred conclusion by using Fodor's implication in order to interpret a fuzzy if-then rule with a single input single output and the tnorm ( ) ( )( ) ( xy y x max y , x t ) λ λ − − + + = 1 1 , 1 − ≥ λ , for composition operation. This t-norm is important to use because for 1 − = λ and 0 = λ it gives the commonly used t-norm...

The objective of this work is to present a triangular interval type-2 (TIT2) intuitionistic fuzzy sets and their corresponding aggregation operators, namely, TIT2 intuitionistic fuzzy weighted averaging, TIT2 intuitionistic fuzzy ordered weighted averaging and TIT2 intuitionistic fuzzy hybrid averaging based on Frank norm operation laws. Furthermore, based on these operators, an approach to mul...

A t-tautology (triangular tautology) is a propositional formula which is a tautology in all fuzzy logics deened by continuous triangular norms. In this paper we show that the problem of recognizing t-tautologies is coNP complete, and thus decidable.

In this note, we introduce the concept of a fuzzy filter of a BLalgebra,with respect to a t-norm briefly, T-fuzzy filters, and give some relatedresults. In particular, we prove Representation Theorem in BL-algebras. Thenwe generalize the notion of a fuzzy congruence (in a BL-algebra) was definedby Lianzhen et al. to a new fuzzy congruence, specially with respect to a tnorm.We prove that there i...

In this paper, the fuzzy dual matrix system as AX + B = CX + D in which A, B, C, D, X are LR fuzzy matrices is studied. At first we solve 1-cut system in order to find the core of LR fuzzy solution; then to obtain the spreads of the LR fuzzy solution, we discuss in several cases. The spreads are obtained by using multiplication, quasi norm and minimization problem with a special objective funct...

In this note, we study an approximation property of regular fuzzy neural network(RFNN). It is shown that any fuzzy-valued measurable function can be approximated by the four-layer RFNN in the sense of fuzzy integral norm for the finite sub-additive fuzzy measure on R.

Welcome to the Journal of Intelligent and Fuzzy Systems’s special issue for “FUZZYSS’2011: 2nd International Fuzzy Systems Symposium”. Since its introduction by Prof. Dr. Lotfi A. Zadeh fuzzy logic, fuzzy sets and systems have been applied to various problems in many diverse areas. As everything try to evolve towards better states, the fuzzy theory and its applications are also evolving to mode...

In this paper, we introduce the notion of fuzzy associative I-ideals in an IS-algebra with respect to a t-conorm and investigate some of its properties. We discuss the properties of homomorphic image and inverse image of S-fuzzy associative I-ideals in an IS-algebras. Relationship between T -fuzzy associative I-ideals and S-fuzzy fuzzy associative Iideals of an IS-algebra is introduced. Connect...