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Finite IUML-algebras, Finite Forests and Orthopairs

Aguzzoli S., Ciucci D., Boffa S., Gerla B.

Fundamenta Informaticae

2018

Vol. 163, nr 2

139--163

We show that finite IUML-algebras, which are residuated lattices arising from an idempotent uninorm, can be interpreted as algebras of sequences of orthopairs whose main operation is defined starting from the three-valued Sobociński operator between rough sets. Our main tool is the representation of finite IUML-algebras by means of finite forests.

Similarity MV-algebras

Gerla B., Leustean I.

Fundamenta Informaticae

2006

Vol. 69, nr 3

287-300

Similarities are an extension of equivalence relations to a fuzzy context. In this paper we introduce the class of similarity MV-algebras obtained as a generalization of the variety of MV-algebras by adding a binary operator playing the role of similarity. We further introduce the similarity ukasiewicz logic and we prove a completeness theorem.