Gilles CHAMPENOIS Collège Saint-André, Saint-Maur, France [email protected] ABSTRACT. Grainy numbers are defined as tuples of bits. They form a lattice where the meet and the join operations are an addition and a multiplication. They may be substituted for the real numbers in the definition of fuzzy sets. The aim is to propose an alternative negation for the complement that we’ll call ...

The fuzzy VIKOR method has been developed to solve fuzzy multicriteria problem with conflicting and noncommensurable (different units) criteria. This method solves problem in a fuzzy environment where both criteria and weights could be fuzzy sets. The triangular fuzzy numbers are used to handle imprecise numerical quantities. Fuzzy VIKOR is based on the aggregating fuzzy merit that represents d...

A fuzzy graph can be obtained from two given fuzzy graphs using union and join. In this paper, we find the degree of an edge in fuzzy graphs formed by these operations in terms of the degree of edges in the given fuzzy graphs in some particular cases. 1. Introduction Fuzzy graph theory was introduced by Azriel Rosenfeld in 1975 [4]. Though it is very young, it has been growing fast and has nume...

This paper considers various aspects of generalizing mathematical morphology towards a fuzzy discipline. Since mathematical morphology and fuzzy theory are both based on a set theory, there are many approaches for defining dilation and erosion operations of a fuzzy morphology. Among those approaches are: the alpha-Morphology; the triangular norm based approach of Bloch; the logical approach of ...

This paper proposes to study the lattice properties of two closed binary operations in the set of discrete fuzzy numbers. Using these operations to represent the meet and the join, we prove that the set of discrete fuzzy numbers whose support is a set of consecutive natural numbers is a distributive lattice. Finally, we demonstrate that the subsets of discrete fuzzy numbers, which have the same...

Ant colony optimisation, a constructive metaheuristic inspired by the foraging behaviour of ants, has been applied to a wide range of problems since its inception. Many of these are production scheduling problems such as the job shop, in which a collection of operations (grouped into jobs) must be scheduled for processing on different machines. In typical ACO applications, solutions are generat...

In many applications we have a set of objects together with their properties. Since the available information is often incomplete and/or imprecise, the true knowledge about subsets of objects can be determined approximately only. In this paper we present a fuzzy generalisation of two relation–based operations suitable for fuzzy set approximations. Main properties of these operations are present...