Fuzzy Ideals and Fuzzy Filters of Pseudocomplemented Semilattices

Abstract

In this paper, we introduce the concept of kernel fuzzy ideals and ⁎-fuzzy filters of a pseudocomplemented semilattice and investigate some of their properties. We observe that every fuzzy ideal cannot be a kernel of a ⁎-fuzzy congruence and we give necessary and sufficient conditions for a fuzzy ideal to be a kernel of a ⁎-fuzzy congruence. On the other hand, we show that every fuzzy filter is the cokernel of a ⁎-fuzzy congruence. Finally, we prove that the class of ⁎-fuzzy filters forms a complete lattice that is isomorphic to the lattice of kernel fuzzy ideals.

A Study of Fuzzy Sequence Spaces

“…The concepts of fuzzy sets were initiated by Zadeh [1], since then it has become an active area of researchers. Matloka [2] initiated the notion of ordinary convergence of a sequence of fuzzy real numbers and studied convergent and bounded sequences of fuzzy numbers and some of their properties, and proved that every convergent sequence of fuzzy numbers is bounded. Nanda [3] investigated some basic properties for these sequences and showed that the set of all convergent sequences of fuzzy real numbers form a complete metric space.…”

The Commutator of Fuzzy Congruences in Universal Algebras

“…In 1971, A.Rosenfeld [3] applied this theory and has formulated the concept of a fuzzy subgroup of a group. Since then, many researchers have been studying fuzzy subalgebras of several algebraic structures such as rings (see [4][5][6]), modules (see [7][8][9]), vector spaces (see [10,11]), lattices (see [12][13][14][15][16][17]), pseudo-complemented semi-lattice (see [18]), posets (see [19,20]), MS-algebras (see [21][22][23][24]), universal algebras (see [25][26][27][28]), etc.…”

P-Fuzzy Ideals and P-Fuzzy Filters in P-Algebras

“…Rosenfeld's paper inspired the development of fuzzy abstract algebra. Since then, several authors have developed interesting results on fuzzy theory (see [3][4][5][6][7][8][9][10][11][12][13][14]). In this paper, we introduce the concept of p-fuzzy ideals and p-fuzzy filters in p-algebra.…”