Recently, three-way concept lattice is studied to handle the uncertainty and incompleteness in the given attribute set based on acceptation, rejection, and uncertain regions. This paper aimed at analyzing the uncertainty and incompleteness in the given fuzzy attribute set characterized by truth-membership, indeterminacy-membership, and falsity membership functions of a defined single-valued neu...

The present paper has been an attempt to investigate the general fuzzy automata on the basis of complete residuated lattice-valued ($L$-GFAs). The study has been chiefly inspired from the work by Mockor cite{15, 16, 17}. Regarding this, the categorical issue of $L$-GFAs has been studied in more details. The main issues addressed in this research include: (1) investigating the relationship betwe...

In this article, we formalize the definition of divisible Z-module and its properties in the Mizar system [3]. We formally prove that any non-trivial divisible Z-modules are not finitely-generated. We introduce a divisible Z-module, equivalent to a vector space of a torsion-free Z-module with a coefficient ring Q. Z-modules are important for lattice problems, LLL (Lenstra, Lenstra and Lovász) b...

In this paper, we characterize residuated lattices for which the topological space of prime ideals is a Noetherian space. The notion i-Noetherian lattice introduced and related properties are investigated. We proved that iff every ideal principal. Moreover, show has spectrum it i-Noetherian.

The first part of this paper provides a comprehensive and self-contained account of the interrelationships between algebraic properties of varieties and properties of their free algebras and equational consequence relations. In particular, proofs are given of known equivalences between the amalgamation property and the Robinson property, the congruence extension property and the extension prope...

We show that adding compatible operations to Heyting algebras and to commutative residuated lattices, both satisfying the Stone law ¬x∨¬¬x = 1, preserves filtering (or directed) unification, that is, the property that for every two unifiers there is a unifier more general then both of them. Contrary to that, often adding new operations to algebras results in changing the unification type. To pr...