Journal Article10.1080/03081071003791339
Central fuzzy sets
Radim Belohlavek,Michal Krupka +1 more
TL;DR: This paper uses complete residuated lattices as the structures of truth degrees, covering thus the real unit interval with left-continuous t-norm and its residuum as an important but particular case and presents results describing central fuzzy sets and optimal central fuzzy set, provided similarity of fuzzy sets is assessed by Leibniz rule.
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Abstract: Let B be a collection of fuzzy sets. What are the fuzzy sets which are sufficiently similar to every fuzzy set from B, i.e. ‘central’ fuzzy sets for B? Such a question naturally arises if B is large and one wishes to replace B by a single fuzzy set – the representative of B. In this paper, we develop a framework which enables us to answer this question and related ones. We use complete residuated lattices as the structures of truth degrees, covering thus the real unit interval with left-continuous t-norm and its residuum as an important but particular case. We present results describing central fuzzy sets and optimal central fuzzy sets, provided similarity of fuzzy sets is assessed by Leibniz rule.
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Citations
Relationship Between L-Fuzzy Quasi-Proximity and L-Fuzzy Closure (Interior) Operators
Abeer Ramadan
TL;DR: Relationship between L-fuzzy quasi-proximity and L-fuzzy closure operators is studied. Properties of the spaces and Galois connections are investigated.
The axiomatic characterizations on L-generalized fuzzy neighborhood system-based approximation operators
TL;DR: This paper will seek the axiomatic sets to characterize the approximation operators generated by serial, reflexive, unary and transitive L-generalized fuzzy neighborhood systems, respectively.
Central points and approximation in residuated lattices
Radim Belohlavek,Michal Krupka +1 more
TL;DR: The paper presents results on approximation in residuated lattices given that closeness is assessed by means of biresiduum, and presents algorithms for two problems regarding optimal approximation.
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