The property of transitivity is one of the most important for fuzzy binary relations, especially in the cases when they are used for the representation of real life similarity or ordering information. As far as the algorithmic part of the actual calculation of the transitive closure of such relations is concerned, works in the literature mainly focus on crisp symmetric relations, paying little ...

Morphisms of some categories of sets with similarity relations (Ω-sets) are investigated, where Ω is a complete residuated lattice. Namely a category SetF(Ω) with morphisms (A, δ) → (B, γ) defined as special maps A → B and a category SetR(Ω) with morphisms defined as a special relations A × B → Ω. It is proved that arbitrary maps A → Ω and A × B → Ω can be extended onto morphisms (A, δ) → (Ω,↔)...

This is an extended abstract of the published paper “Approximate Similarity and Poincaré Paradox to be published in Notre Dame Journal of Formal Logic, 49, 2008”. The startin point is an observation by De Cock and Kerre, in which, in considering Poincaré paradox, one observes that the intuitive notion of “approximate similarity” cannot be adequately represented by the fuzzy equivalence relation...

The notion of fuzzy function based on many-valued equivalence relations (many-valued similarity relations (equalities) [17, 18, 19], fuzzy equivalence relations [4, 6, 7, 21, 22, 26], similarity relations [1, 2, 3, 15, 28], indistinguishability operators [27], etc.) has been introduced by several authors, and applied to category theory [5], approximate reasoning and fuzzy control theory [8, 10,...

The problem of obtaining of a minimal polygonal representation of a plane digital curve is treated. Means of a fuzzy clustering method are used. The fuzzy clustering is realized by relations of similarity and dissimilarity that are defined on a planar digital curve.

A sound and complete Automated Prover for the Fuzzy Simplification Logic (FSL logic) is introduced and based on it a method for efficiently reasoning about fuzzy functional dependencies over domains with similarity relations. The complexity of the algorithm is the same as that of equivalent algorithms for crisp functional dependencies that appear in the literature.

In this work, we shall present some novel process to measure the similarity between picture fuzzy sets. Firstly, we adopt the concept of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and picture fuzzy sets. Secondly, we develop some similarity measures between picture fuzzy sets, such as, cosine similarity measure, weighted cosine similarity measure, set-theoretic similar...

We study rules A ⇒ B describing attribute dependencies in tables over domains with similarity relations. A ⇒ B reads “for any two table rows: similar values of attributes from A imply similar values of attributes from B”. The rules generalize ordinary functional dependencies in that they allow for processing of similarity of attribute values. Similarity is modeled by reflexive and symmetric fuz...

This article will introduce abductive case-based reasoning (CBR) and attempt to show that abductive CBR and deductive CBR can be integrated in clinical process and problem solving. Then it provides a unified formalization for integration of abduction, abductive CBR, deduction and deductive CBR. This article also investigates abductive case retrieval and deductive case retrieval using similarity...

In this work, we address the transposition of a fragment of the modeling of the Sociology of Organized Action to the fuzzy setting. We present two different ways of developing fuzzy models in this context, that depend on the kind of available data furnished by the user: one based on the extension principle and another using fuzzy rule-based inference with similarity relations. We illustrate our...