We describe weak BCC-algebras (also called BZ-algebras) in which the condition (xy)z = (xz)y is satisfied only in the case when elements x, y belong to the same branch. We also characterize branchwise commutative and branchwise implicative weak BCC-algebras satisfying this condition. We also describe connections between various types of implicative weak BCC-algebras.

In this paper, the notion of the radical of a filter in residuated lattices is defined and several characterizations of the radical of a filter are given. We show that if F is a positive implicative filter (or obstinate filter), then Rad(F ) = F . We proved the extension theorem for radical of filters in residuated lattices. Also, we study the radical of filters in linearly ordered residuated l...

In the present paper, we introduce the notion of fuzzy Aideals of MV -modules over PMV -algebras and several properties of fuzzy A-ideals are given. Using this concept, a prime fuzzy A-ideal is defined. Using a level set of a fuzzy set in MV -modules, we give a characterization of prime fuzzy A-ideals in MV -modules. Finally, we prove that the homomorphic image and preimage of prime fuzzy A-ide...

The class of radial fuzzy systems is introduced. The fuzzy systems in this class use radial functions to implement membership functions of fuzzy sets and exhibit a shape preservation property in antecedents of their rules. The property is called the radial property. It enables the radial fuzzy systems to have their computational model mathematically tractable under both conjunctive and implicat...

This paper proposes the implicative rating measure developed on the typicality measure. The paper also proposes a new recommendation model presenting the top N items to the active users. The proposed model is based on the user-based collaborative filtering approach using the implicative intensity measure to find the nearest neighbors of the active users, and the proposed measure to predict user...