RELATION BETWEEN (FUZZY) GODEL IDEALS AND ¨ (FUZZY) BOOLEAN IDEALS IN BL-ALGEBRAS
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2016, Vol 36, Issue 1
Abstract
In this paper, we study relationships between among (fuzzy) Boolean ideals, (fuzzy) G¨odel ideals, (fuzzy) implicative filters and (fuzzy) Boolean filters in BL-algebras. In [9], there is an example which shows that a G¨odel ideal may not be a Boolean ideal, we show this example is not true and in the following we prove that the notions of (fuzzy) G¨odel ideals and (fuzzy) Boolean ideals in BL-algebras coincide.
Authors and Affiliations
Akbar Paad
GENERALIZED PELL EQUATIONS FOR 2 × 2 MATRICES
In this paper we consider the solutions of the generalized matrix Pell equations X^2 − dY^2 = cI, where X and Y are 2 × 2 matrices over Z, d is a non-zero (positive or negative) square-free integer, c is an arbitrary int...
WEAK-HYPERLATTICES DERIVED FROM FUZZY CONGRUENCES
In this paper we explore the connections between fuzzy congruence relations, fuzzy ideals and homomorphisms of hyperlattices. Indeed, we introduce the concept of fuzzy quotient set of hyperlattices as it was done in the...
Congruences and Trajectories in Planar Semimodular Lattices
A 1955 result of J. Jakub´ık states that for the prime intervals p and q of a finite lattice, con(p) ≥ con(q) iff p is congruence-projective to q (via intervals of arbitrary size). The problem is how to determine whether...
A VARIATION OF ZERO-DIVISOR GRAPHS
In this paper, we define a new graph for a ring with unity by extending the definition of the usual ‘zero-divisor graph’. For a ring R with unity, Γ1(R) is defined to be the simple undirected graph having all non-zero el...
ON THE SUBSEMIGROUP GENERATED BY ORDERED IDEMPOTENTS OF A REGULAR SEMIGROUP
An element e of an ordered semigroup S is called an ordered idempotent if e ≤ e^2. Here we characterize the subsemigroup < E≤(S) > generated by the set of all ordered idempotents of a regular ordered semigroup S. If S is...