Classes of η-fold implicative fuzzy filters of residuated lattice ordered monoids

2018 ◽  
Author(s):  
Somayeh Motamed ◽  
Javad Moghaderi
Keyword(s):  
Residuated Lattice ◽  
Fuzzy Filters

INTUITIONISTIC FUZZY FILTERS OF RESIDUATED LATTICES

2011 ◽  
Vol 07 (03) ◽  
pp. 499-513 ◽  
Author(s):  
SHOKOOFEH GHORBANI
Keyword(s):  
Fuzzy Sets ◽  
Complete Lattice ◽  
Residuated Lattice ◽  
Intuitionistic Fuzzy Sets ◽  
Residuated Lattices ◽  
Intuitionistic Fuzzy ◽  
Correspondence Theorem ◽  
Fuzzy Filters

In this paper, the concept of intuitionistic fuzzy sets is applied to residuated lattices. The notion of intuitionistic fuzzy filters of a residuated lattice is introduced and some related properties are investigated. The characterizations of intuitionistic fuzzy filters are obtained. We show that the set of all the intuitionistic fuzzy filters of a residuated lattice forms a complete lattice and we find the distributive sublattices of it. Finally, the correspondence theorem for intuitionistic fuzzy filters is established.

scholarly journals Fuzzy stabilizers in BL-algebras

Filomat ◽  
2018 ◽  
Vol 32 (5) ◽  
pp. 1783-1788 ◽  
Author(s):  
Xiaoyun Cheng ◽  
Xiaolong Xin ◽  
Juntao Wang ◽  
Pengfei He
Keyword(s):  
Fuzzy Logic ◽  
Residuated Lattice ◽  
Algebraic Foundation ◽  
Fuzzy Filters

The primary goal of this paper is to develop fuzzy stabilizer theory in BL-algebras. Two types of fuzzy stabilizers are introduced and their related properties are given. Also, the relationships between fuzzy stabilizers and several fuzzy filters are discussed. Finally, by means of fuzzy stabilizers, it is proven that the collection of all fuzzy filters in BL-algebras forms a residuated lattice. These results will provide a solid algebraic foundation for the consequence connectives in fuzzy logic.

Several types of hesitant fuzzy filters on residuated lattices

2020 ◽  
Vol 39 (3) ◽  
pp. 3949-3956
Author(s):  
Zhi Qiang Liu ◽  
Zhen Ming Ma
Keyword(s):  
Residuated Lattice ◽  
Residuated Lattices ◽  
Fuzzy Filter ◽  
One To One ◽  
Boolean Filters ◽  
Fuzzy Filters

The present paper investigates the hesitant fuzzy filters on residuated lattices. A one-to-one correspondence between the set of all hesitant fuzzy filters and the set of all hesitant fuzzy congruences is established and a quotient residuated lattice with respect to a hesitant fuzzy filter is induced. Furthermore, several special types of hesitant fuzzy filters such as hesitant fuzzy implicative, regular and Boolean filters are introduced, and some alternative definitions of them are obtained, then some typical logical algebras are characterized by these identity forms.

scholarly journals The Lattice of Intuitionistic Fuzzy Filters in Residuated Lattices

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Zhen Ming Ma
Keyword(s):  
Distributive Lattice ◽  
Residuated Lattice ◽  
Residuated Lattices ◽  
Bounded Distributive Lattice ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Filters

The notion of tip-extended pair of intuitionistic fuzzy filters is introduced by which it is proved that the set of all intuitionistic fuzzy filters in a residuated lattice forms a bounded distributive lattice.

scholarly journals Classes of fuzzy filters of residuated lattice ordered monoids

2010 ◽  
Vol 135 (1) ◽  
pp. 81-97
Author(s):  
Jiří Rachůnek ◽  
Dana Šalounová
Keyword(s):  
Residuated Lattice ◽  
Fuzzy Filters

FUZZY FILTERS ON THE RESIDUATED LATTICES

2006 ◽  
Vol 02 (01) ◽  
pp. 11-28 ◽  
Author(s):  
JIA-LU ZHANG ◽  
HONG-JUN ZHOU
Keyword(s):  
Boolean Algebra ◽  
Residuated Lattice ◽  
Residuated Lattices ◽  
Adjoint Pair ◽  
Fuzzy Filters

In this paper, the lattice operations and the adjoint pair on the fuzzy filters set on residuated lattices are defined, the conclusion that the fuzzy filters lattice defined as such is a distributive residuated lattice is obtained. An order-reversing involution on the fuzzy strong-prime filters sublattice is introduced. It is proved that the fuzzy strong-prime filters sublattice is a quasi-Boolean algebra.

scholarly journals Some Types of Generalized Fuzzyn-Fold Filters in Residuated Lattices

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhen Ming Ma
Keyword(s):  
Residuated Lattice ◽  
Residuated Lattices ◽  
Fuzzy Filter ◽  
One To One ◽  
Boolean Filters ◽  
Fuzzy Filters

Fuzzy filters and their generalized types have been extensively studied in the literature. In this paper, a one-to-one correspondence between the set of all generalized fuzzy filters and the set of all generalized fuzzy congruences is established, a quotient residuated lattice with respect to generalized fuzzy filter is induced, and several types of generalized fuzzyn-fold filters such as generalized fuzzyn-fold positive implicative (fantastic and Boolean) filters are introduced; examples and results are provided to demonstrate the relations among these filters.

L-Fuzzy Filters of Almost Distributive Lattices

2018 ◽  
Vol 8 (1) ◽  
pp. 35
Author(s):  
U. M. Swamy ◽  
Ch. Santhi Sundar Raj ◽  
A. Natnael Teshale
Keyword(s):  
Distributive Lattices ◽  
Fuzzy Filters

Fuzzy filters of MTL-algebras

2005 ◽  
Vol 175 (1-2) ◽  
pp. 120-138 ◽  
Author(s):  
Young Bae Jun ◽  
Yang Xu ◽  
Xiao Hong Zhang
Keyword(s):  
Fuzzy Filters
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