Concept lattices and similarity in non-commutative fuzzy logic. (English) Zbl 1023.03016

This paper deals with the algebraic treatment of “noncommutative concepts”. Assuming that truth values form a generalized residuated lattice, the authors define noncommutative similarity, equality and order relations. Then they define the appropriate notion of noncommutative concept lattice, and generalize Belohlavek’s results for the commutative case. The final sections of this paper deal with similarity of objects, attributes and concepts. The noncommutativity of conjunction results in two implications: as a result, in the object-oriented approach of this paper, every concept has one extension and two intensions.
Reviewer: D.Mundici (Milano)


03B52 Fuzzy logic; logic of vagueness
06B99 Lattices
68T30 Knowledge representation
06F05 Ordered semigroups and monoids