In this paper we present an approach to visualize a potentially high-dimensional and large number of (fuzzy) rules in two dimensions. This visualization presents the entire set of rules to the user as one coherent picture. We use a gradient descent based algorithm to generate a 2D-view of the rule set which minimizes the error on the pair-wise fuzzy distances between all rules. This approach is...

Let d be a metric on the set FP(X) of fuzzy subsets of a set X. A midpoint of two fuzzy subsets μ, ν ∈ FP(X) is any fuzzy subset ξ ∈ FP(X) such that d(ξ, μ) = d(ξ, ν) = 1 2d(μ, ν). These midpoints can be used to describe “middle ways” or “compromises” between two situations described by the fuzzy subsets μ and ν. In this work we explicitly compute midpoints for weighted Hamming distances and fo...

Although fuzzy operators have deserved a large attention in the Euclidean case, almost nothing exists concerning the geodesic case. In this paper, we address this question, by de"ning fuzzy geodesic distances between points in a fuzzy set, and geodesic balls in a fuzzy set (based on the comparison of fuzzy numbers), from which we derive fuzzy geodesic mathematical morphology operators. The prop...

Intuitionistic fuzzy special sets is a special case of intuitionistic fuzzy sets. In this paper, under the framework of information systems, the relationship between intuitionistic fuzzy special sets and rough sets is analyzed. Based on basic intuitionistic fuzzy special sets of information systems, intuitionistic fuzzy special σ-algebra are generated, and rough sets are embedded in the intuiti...

Given a set S, we show that there is a strict relation between the notion of similarity on S and the one of fuzzy subgroup of transformations in S . Such a relation enables us to extablish a connection between fuzzy subgroups and distances.