We interpret fuzzy linear programming (FLP) problems with fuzzy coefficients and fuzzy inequality relations as multiple fuzzy reasoning schemes (MFR), where the antecedents of the scheme correspond to the constraints of the FLP problem and the fact of the scheme is the objective of the FLP problem. Then the solution process consists of two steps: first, for every decision variable x ∈ IRn, we c...

The psychology of concepts has been undergoing significant changes since the early 1970s, when the classical view of concepts was seriously challenged by convincing experimental evidence that conceptual categories never have sharp boundaries. Some researchers recognized already in the early 1970s that fuzzy set theory and fuzzy logic were potentially suitable for modeling of concepts and obtain...

The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is considered. In fact, this concept is a generalized concept of the quasi-coincidence of a fuzzy point in a fuzzy set. By using this new concept, the authors define the notion of interval valued (∈,∈ ∨q)fuzzy h-ideals of hemirings and study their related properties. In addition, the authors also extend t...

This paper is a reply to the article entitled Elkan’s Theoretical Argument, Reconsidered by Prof. Enric Trillas and Prof. Claudi Alsina. I would like to express my thanks to Dr. Piero Bonissone for inviting me to write this paper and for showing me the article by Trillas and Alsina in advance of its publication. Ever since mathematical studies of fuzziness began with a 1965 paper entitled Fuzzy...

This paper introduces fuzzy belief nets (FBN). The ability to invert arcs between nodes is key to solving belief nets. The inversion is accomplished by defining closeness measures which allow diagnostic reasoning from observed symptoms to cause of failures. The closeness measures are motivated by a Lukasiewicz operator which takes into account the distance from an observed symptom set to the mo...

The paper discusses some core topics which present open problems in the field of mathematical fuzzy logic and in the foundations of fuzzy set theory. It may reasonably be assumed that these problems shall have great influence for the future development of fuzzy logic within the next decade.

A complex fuzzy set is a set whose membership values are vectors in the unit circle in the complex plane. This paper establishes the orthogonality relation of complex fuzzy sets. Two complex fuzzy sets are said to be orthogonal if their membership vectors are perpendicular. We present the basic properties of orthogonality of complex fuzzy sets and various results on orthogonality with respect t...

Based on fuzzy set theory, flexible querying enables users to express preferences inside requirements. Quantifications and preferences on data have led us to define the notion of fuzzy integers ( f). This framework has been extended (to f and f ) in order to dealing with queries based on difference or division operations. In this paper we study how to define fuzzy order relations between such f...

The objective of this paper is to present the strength of fuzzy artmap which is kind of neural networks in the medical field by improving its performance by genetic algorithm. Fuzzy ARTMAP is both much faster and incrementally stable than the other ordinary neural networks models like Multilayer Perceptron. Fuzzy artmap’s parameters have legal range of values that should be determined in the si...