On fuzzy α-lattices

Mezzomo, Ivan; Bedregal, Benjamín R. C.

doi:10.1109/fuzz-ieee.2016.7737766

Cited by 3 publications

(2 citation statements)

References 25 publications

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“…Definition A.8 (Composition of fuzzy binary relations). The (max-min) composition of two fuzzy binary relations R and Q on a finite set X is the fuzzy binary relation R We adopt the definitions of lower bounds, greatest lower bounds and fuzzy lattice from [48]- [50]. The following proposition states that the support (S, | •|) of a fuzzy lattice (S, •) is a lattice.…”

Section: Definition A5 (Fuzzy Binary Relation)mentioning

confidence: 99%

Similarity-Based Reasoning With Order-Sorted Feature Logic

Milanese,

Pasi

2024

IEEE Trans. Fuzzy Syst.

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Order-Sorted Feature (OSF) logic is a knowledge representation and reasoning language based on sorts -symbols that denote concepts ordered in a subsumption relation -and features -symbols that denote functional attributes. Reasoning with OSF logic is based on the unification of OSF terms, recordlike structures that denote classes of objects and that are themselves ordered in a subsumption relation. OSF term unification aims to combine the constraints expressed by two terms in a consistent way, and it takes into account the subsumption relation between sort symbols, providing an efficient calculus of type subsumption. This paper presents an approach to define approximate reasoning with OSF logic by extending its language with a similarity relation on sorts. In order for the OSF term unification algorithm to take into account this similarity and its interaction with the subsumption relation, we propose to combine the two relations into a single fuzzy subsumption relation. The advantage is that the same unification rules of OSF logic can then be applied to this fuzzy setting. We conclude by discussing potential applications of OSF logic extended with a sort similarity relation.

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Section: Definition A5 (Fuzzy Binary Relation)mentioning

confidence: 99%

Similarity-Based Reasoning With Order-Sorted Feature Logic

Milanese,

Pasi

2024

IEEE Trans. Fuzzy Syst.

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“…In [30] the triples formed by a t-norm, t-conorm and standard complement are called De Morgan triples if it fulfills De Morgan laws. Some new important results about t-norm and t-conorm theory are discussed and many of them are not readily found in the literature.…”

Section: Introductionmentioning

confidence: 99%

n-Dimensional (S,N)-implications

Zanotelli

Reiser

Bedregal

2020

International Journal of Approximate Reasoning

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The n -dimensional fuzzy logic ( n -DFL) has been contributed to overcome the insufficiency of traditional fuzzy logic in modeling imperfect and imprecise information, coming from different opinions of many experts by considering the possibility to model not only ordered but also repeated membership degrees. Thus, n -DFL provides a consolidated logical strategy for applied technologies since the ordered evaluations provided by decision makers impact not only by selecting the best solutions for a decision making problem, but also by enabling their comparisons. In such context, this paper studies the n -dimensional fuzzy implications ( n -DI) following distinct approaches: (i) analytical studies, presenting the most desirable properties as neutrality, ordering, (contra-)symmetry, exchange and identity principles, discussing their interrelations and exemplifications; (ii) algebraic aspects mainly related to left- and right-continuity of representable n -dimensional fuzzy t-conorms; and (iii) generating n -DI from existing fuzzy implications. As the most relevant contribution, the prospective studies in the class of n -dimensional interval (S,N)-implications include results obtained from t-representable n -dimensional conorms and involutive n -dimensional fuzzy negations. And, these theoretical results are applied to model approximate reasoning of inference schemes, dealing with based-rule in n -dimensional interval fuzzy systems. A synthetic case-study illustrates the solution for a decision-making problem in medical diagnoses.

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Conjunctive Reasoning on Fuzzy Taxonomies with Order-Sorted Feature Logic

Milanese

Pasi

2021

2021 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE)

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On fuzzy α-lattices

Cited by 3 publications

References 25 publications

Similarity-Based Reasoning With Order-Sorted Feature Logic

Similarity-Based Reasoning With Order-Sorted Feature Logic

n-Dimensional (S,N)-implications

Conjunctive Reasoning on Fuzzy Taxonomies with Order-Sorted Feature Logic

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