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.

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 Construction of some algebras of logics by using intuitionistic fuzzy filters on hoops

2021 ◽  
Vol 6 (11) ◽  
pp. 11950-11973
Author(s):  
Mona Aaly Kologani ◽  
◽  
Rajab Ali Borzooei ◽  
Hee Sik Kim ◽  
Young Bae Jun ◽  
...  
Keyword(s):  
Distributive Lattice ◽  
Algebraic Structure ◽  
Congruence Relation ◽  
Heyting Algebra ◽  
Bounded Distributive Lattice ◽  
Intuitionistic Fuzzy ◽  
Brouwerian Semilattice ◽  
Fuzzy Filters

<abstract><p>In this paper, we define the notions of intuitionistic fuzzy filters and intuitionistic fuzzy implicative (positive implicative, fantastic) filters on hoops. Then we show that all intuitionistic fuzzy filters make a bounded distributive lattice. Also, by using intuitionistic fuzzy filters we introduce a relation on hoops and show that it is a congruence relation, then we prove that the algebraic structure made by it is a hoop. Finally, we investigate the conditions that quotient structure will be different algebras of logics such as Brouwerian semilattice, Heyting algebra and Wajesberg hoop.</p></abstract>

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.

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.

Perfect residuated lattice ordered monoids

2010 ◽  
Vol 60 (6) ◽  
Author(s):  
Jiří Rachůnek ◽  
Dana Šalounová
Keyword(s):  
Probability Measure ◽  
Residuated Lattice ◽  
Residuated Lattices ◽  
Heyting Algebras ◽  
Effect Algebras ◽  
Quantum Logics ◽  
Mv Algebras ◽  
Intuitionistic Logics

AbstractBounded Rℓ-monoids form a large subclass of the class of residuated lattices which contains certain of algebras of fuzzy and intuitionistic logics, such as GMV-algebras (= pseudo-MV-algebras), pseudo-BL-algebras and Heyting algebras. Moreover, GMV-algebras and pseudo-BL-algebras can be recognized as special kinds of pseudo-MV-effect algebras and pseudo-weak MV-effect algebras, i.e., as algebras of some quantum logics. In the paper, bipartite, local and perfect Rℓ-monoids are investigated and it is shown that every good perfect Rℓ-monoid has a state (= an analogue of probability measure).

scholarly journals Essential extensions of filters in residuated lattices

2021 ◽  
Author(s):  
Masoud Haveshki
Keyword(s):  
Boolean Algebra ◽  
Residuated Lattice ◽  
Residuated Lattices ◽  
Essential Extension ◽  
Mv Algebra ◽  
Essential Extensions

Abstract We define the essential extension of a filter in the residuated lattice A associated to an ideal of L(A) and investigate its related properties. We prove the residuated lattice A is a Boolean algebra, G(RL)-algebra or MV -algebra if and only if the essential extension of {1} associated to A \ P is a Boolean filter, G-filter or MV -filter (for all P ∈ SpecA), respectively. Also, some properties of lattice of essential extensions are studied.

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