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...

In this paper, we propose a novel balanced scorecard design based on fuzzy analytic network process and then conduct performance evaluation through a case study. After analyzing the related works about balanced scorecard design and the algorithm of fuzzy analytic network process, we illustrate the improved balanced scorecard design. Firstly, the basic concepts for the balanced scorecards are in...

In this paper we propose a new adaptation of the Fuzzy Pattern Matching (FPM) to build a classifier which has a good discrimination ability for classes of non convex shape. We show the limits of the classical FPM. Then we expose some details about the correlated FPM method which we propose. Two other adaptations of the Fuzzy Pattern Matching are described and the results obtained and the result...

In this paper the cone of convex cooperative fuzzy games is studied. As in the classical case of convex crisp games, these games have a large core and the fuzzy Shapley value is the barycenter of the core. Surprisingly, the core and the Weber set coincide ∗This paper was written while the authors were research fellows at the ZiF (Bielefeld) for the project ”Procedural Approaches to Conflict Res...

For a non-degenerate convex subset Y of the n-dimensional Euclidean space Rn , let K(Y ) be the family of all fuzzy sets of Rn , which are upper-semicontinuous, fuzzy convex and normal with compact supports contained in Y. We show that the space K(Y ) with the topology of endograph metric is homeomorphic to the Hilbert cube Q = [−1, 1] iff Y is compact; and the space K(Y ) is homeomorphic to {(...

The aim of this paper is to propose a convex risk measure in the framework of fuzzy random theory and verify its advantage over the conventional variance approach. For this purpose, this paper defines the quadratic deviation (QD) of fuzzy random variable as the mathematical expectation of QDs of fuzzy variables. As a result, the new risk criterion essentially describes the variation of a fuzzy ...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  Ulrich Hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. Many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. Using Hohle's idea, we show that for a (universal) algebra $A$, th...

An orthogonal approach to the fuzzification of both multisets and hybridsets is presented. In particular, we introduce $L$-multi-fuzzy and$L$-fuzzy hybrid sets, which are general enough and in spirit with thebasic concepts of fuzzy set theory. In addition, we study the properties ofthese structures. Also, the usefulness of these structures is examined inthe framework of mechanical multiset proc...