In this paper our aim is to explore a new look at formal systems of fuzzy logics using the framework of (fuzzy) formal concept analysis (FCA). Let L be an extension of MTL complete with respect to a given L-chain. We investigate two possible approaches. The first one is to consider fuzzy formal contexts arising from L where attributes are identified with L-formulas and objects with L-evaluations: every Levaluation (object) satisfies a formula (attribute) to a given degree, and vice-versa. The corresponding fuzzy concept lattices are shown to be isomorphic to quotients of the Lindenbaum algebra of L. The second one, following an idea in a previous paper by two of the authors for the particular case of G¨odel fuzzy logic, is to use a result by Ganter and Wille in order to interpret the (lattice reduct of the) Lindenbaum algebra of L-formulas as a (classical) concept lattice of a given context.

Connecting Systems of Mathematical Fuzzy Logic with Fuzzy Concept Lattices / P. Codara, F. Esteva, L. Godo, D. Valota - In: Information Processing and Management of Uncertainty in Knowledge-Based Systems : Theory and Foundations / [a cura di] J. Medina, M. Ojeda-Aciego, J.L. Verdegay, D.A. Pelta, I.P. Cabrera, B. Bouchon-Meunier, R.R. Yager. - [s.l] : Springer, 2018 May 18. - ISBN 9783319914756. - pp. 275-286 (( Intervento presentato al 17. convegno IPMU tenutosi a Cádiz nel 2018.

Connecting Systems of Mathematical Fuzzy Logic with Fuzzy Concept Lattices

P. Codara;D. Valota
2018-05-18

Abstract

In this paper our aim is to explore a new look at formal systems of fuzzy logics using the framework of (fuzzy) formal concept analysis (FCA). Let L be an extension of MTL complete with respect to a given L-chain. We investigate two possible approaches. The first one is to consider fuzzy formal contexts arising from L where attributes are identified with L-formulas and objects with L-evaluations: every Levaluation (object) satisfies a formula (attribute) to a given degree, and vice-versa. The corresponding fuzzy concept lattices are shown to be isomorphic to quotients of the Lindenbaum algebra of L. The second one, following an idea in a previous paper by two of the authors for the particular case of G¨odel fuzzy logic, is to use a result by Ganter and Wille in order to interpret the (lattice reduct of the) Lindenbaum algebra of L-formulas as a (classical) concept lattice of a given context.
Mathematical fuzzy logics; MTL; Concept lattices; FCA; Łukasiewicz logic
Settore INF/01 - Informatica
Settore MAT/01 - Logica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/592747
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