This paper looks to introduce the reader to the idea of a fuzzy logic system and how this type of system differs from traditional propositional logic systems by way of summarizing the foundational ideas presented in Hájek’s Metamathematics of Fuzzy Logic. Because a fuzzy system has different laws from a standard propositional one, propositional logic operations such as conjunction and implicati...

This paper proposes a complexity management methodology for fuzzy systems with feedback rule bases. The methodology is based on formal methods for presentation, manipulation and transformation of fuzzy rule bases. First, Boolean matrices are used for formal presentation of rule bases. Then, binary merging operations are used for formal manipulation of rule bases. Finally, repetitive merging ope...

In this paper, by using operations, some characterizations and some properties of fuzzy lower and upper continuous multifunctions and its weaker and stronger forms including fuzzy lower and upper weakly continuous, fuzzy lower and upper θ-continuous, fuzzy lower and upper strongly θ-continuous, fuzzy lower and upper almost strongly θ-continuous, fuzzy lower and upper weakly θ-continuous, fuzzy ...

Fuzzy semantics comprehension and fuzzy inference are two of the central abilities of human brains that play a crucial role in thinking, perception, and problem solving. A formal methodology for rigorously describing and manipulating fuzzy semantics and fuzzy concepts is sought for bridging the gap between humans and cognitive fuzzy systems. A mathematical model of fuzzy concepts is created bas...

An approach based on interval belief degrees and fuzzy evidential reasoning analytical algorithm is developed for multi-criteria decision problems with uncertainties. The criteria weights are represented by interval numbers and criteria values by triangular intuitionistic fuzzy numbers. The proposed approach does not need to utilize the theories such as arithmetic operations for Triangular intu...

Recent literature on fuzzy numbers is rich of several approaches to approximate operations between fuzzy numbers. The desirable feature is to preserve the real shape of the fuzzy numbers resulting from the operations, without loosing in simplicity and applicability and in goodness of the approximations. In some recent papers we introduce a representation of the fuzzy numbers, based on the use o...

This paper first improves Chen and Hsieh’s definition of generalized fuzzy numbers, which makes it the generalization of definition of fuzzy numbers. Secondly, in terms of the generalized fuzzy numbers set, we introduce two different kinds of orders and arithmetic operations and metrics based on the λ-cutting sets or generalized λ-cutting sets, so that the generalized fuzzy numbers are integrat...