This paper describes the theory and algorithms of distance transform for fuzzy subsets, called fuzzy distance transform (FDT). The notion of fuzzy distance is formulated by first defining the length of a path on a fuzzy subset and then finding the infimum of the lengths of all paths between two points. The length of a path π in a fuzzy subset of the n-dimensional continuous space n is defined a...

Since its original formulation, the theory of fuzzy sets has spawned a number of extensions where the role of membership values in the real unit interval $[0, 1]$ is handed over to more complex mathematical entities. Amongst the many existing extensions, two similar ones, the fuzzy multisets and the hesitant fuzzy sets, rely on collections of several distinct values to represent fuzzy membershi...

The main aim of this paper intends to discuss the solution of general dual fuzzy linear system (GDFLS) C BX F AX + = + where A , B are real n m× matrix , F and C are fuzzy vectors, and the unknown vector X is a vector consisting of n fuzzy numbers, by a special algorithm based on a class of ABS algorithms called Huang algorithm. In special case, we apply the proposed algorithm for the solution ...

This paper examines the fuzzy system for function approximation in a macroscopic level. The rules of a fuzzy function approximation system are expressed in the form of polynomials such that each rule forms a local approximator. We show that this kind of fuzzy function approximation is equivalent to piecewise polynomial interpolation between turning points when normalized fuzzy function membersh...

Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by n-ary operations is considered. Namely, with the use of fuzzy...

In these notes we review Klimč́ık’s construction of noncommutative gauge theory on the fuzzy supersphere. This theory has an exact SUSY gauge symmetry with a finite number of degrees of freedom and thus in principle it is amenable to the methods of matrix models and Monte Carlo numerical simulations. We also write down in this article a novel fuzzy supersymmetric scalar action on the fuzzy super...