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Transitivity-preserving fuzzification schemes for cardinality-based similarity measures.
Bernard De Baets,Hans De Meyer +1 more
- pp 37-48
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A family of fuzzification schemes is proposed that can be used to transform cardinality-based similarity measures for ordinary sets into similarity Measures for fuzzy sets in a finite universe, based on rules for fuzzy set cardinality and for the standard operations on fuzzy sets.Abstract:
Abstract A family of fuzzification schemes is proposed that can be used to transform cardinality-based similarity measures for ordinary sets into similarity measures for fuzzy sets in a finite universe. The family is based on rules for fuzzy set cardinality and for the standard operations on fuzzy sets. In particular, the fuzzy set intersections are pointwisely generated by Frank t -norms. The fuzzification schemes are applied to a variety of previously studied rational cardinality-based similarity measures for ordinary sets and it is demonstrated that transitivity is preserved in the fuzzification process.read more
Citations
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Journal ArticleDOI
Similarity and dissimilarity measures between fuzzy sets: A formal relational study
TL;DR: A self-contained picture of these relationships, by providing formal results and counterexamples that reflect which of the (dis)similarity definitions in the literature are connected by implication relations and which of them are not.
Journal ArticleDOI
On the transitivity of a parametric family of cardinality-based similarity measures
TL;DR: A parametric family of cardinality-based similarity measures for ordinary sets harbouring numerous well-known similarity measures is introduced, and transitivity, and the corresponding dual metric interpretation, is preserved along this fuzzification process.
Journal ArticleDOI
Bell-type inequalities for quasi-copulas
TL;DR: For the important parametric family of Frank t-norms, it is proved that for each of the inequalities the parameter values for which it is fulfilled, thereby completing the results of Pykacz and D'Hooghe.
Book ChapterDOI
Information Affinity: A New Similarity Measure for Possibilistic Uncertain Information
TL;DR: A new measure so-called Information Affinity is proposed to overcome the limits of the existing ones and is based on a classical informative distance, e.g. Manhattan distance, which evaluates the difference between two normalized possibility distributions.
Journal ArticleDOI
On the cycle-transitive comparison of artificially coupled random variables
B. De Baets,H. De Meyer +1 more
TL;DR: The main result of this paper pertains to the transitivity of this probabilistic relation: Provided the commutative copula satisfies some additional condition, this transitivity can be described elegantly within the cycle-transitivity framework.
References
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Fuzzy sets
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A statistical method for evaluating systematic relationships
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Similarity relations and fuzzy orderings
TL;DR: An extended version of Szpilrajn's theorem is proved and various properties of similarity relations and fuzzy orderings are investigated and, as an illustration, a fuzzy preordering is investigated which is reflexive and antisymmetric.
Book
Fuzzy Preference Modelling and Multicriteria Decision Support
János Fodor,Marc Roubens +1 more
TL;DR: This dissertation aims to provide a history of web exceptionalism from 1989 to 2002, a period chosen in order to explore its roots as well as specific cases up to and including the year in which descriptions of “Web 2.0” began to circulate.
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