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 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.

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 μ -Fuzzy Filters in Distributive Lattices

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Wondwosen Zemene Norahun
Keyword(s):  
Distributive Lattice ◽  
Special Class ◽  
Distributive Lattices ◽  
Fuzzy Filter ◽  
One To One ◽  
Fuzzy Filters

In this paper, we introduce the concept of μ -fuzzy filters in distributive lattices. We study the special class of fuzzy filters called μ -fuzzy filters, which is isomorphic to the set of all fuzzy ideals of the lattice of coannihilators. We observe that every μ -fuzzy filter is the intersection of all prime μ -fuzzy filters containing it. We also topologize the set of all prime μ -fuzzy filters of a distributive lattice. Properties of the space are also studied. We show that there is a one-to-one correspondence between the class of μ -fuzzy filters and the lattice of all open sets in X μ . It is proved that the space X μ is a T 0 space.

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.

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 Generalizations of(∈,∈∨q)-Fuzzy Filters inR0-Algebras

2010 ◽  
Vol 2010 ◽  
pp. 1-19
Author(s):  
Young Bae Jun ◽  
Seok Zun Song ◽  
Jianming Zhan
Keyword(s):  
Fuzzy Filter ◽  
Fuzzy Filters

Generalizations of a part of the paper (Ma et al., 2009) are considered. As a generalization of an(∈,∈∨q)-fuzzy filter, the notion of an(∈,∈∨qk)-fuzzy filter is introduced, and its characterizations are provided. The implication-based fuzzy filters of anR0-algebra are discussed.

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.

scholarly journals Left residuated lattices induced by lattices with a unary operation

2019 ◽  
Vol 24 (2) ◽  
pp. 723-729
Author(s):  
Ivan Chajda ◽  
Helmut Länger
Keyword(s):  
Orthomodular Lattice ◽  
Residuated Lattice ◽  
Unary Operation ◽  
Residuated Lattices ◽  
Boolean Algebras ◽  
Natural Question ◽  
Similar Technique ◽  
Orthomodular Lattices

Abstract In a previous paper, the authors defined two binary term operations in orthomodular lattices such that an orthomodular lattice can be organized by means of them into a left residuated lattice. It is a natural question if these operations serve in this way also for more general lattices than the orthomodular ones. In our present paper, we involve two conditions formulated as simple identities in two variables under which this is really the case. Hence, we obtain a variety of lattices with a unary operation which contains exactly those lattices with a unary operation which can be converted into a left residuated lattice by use of the above mentioned operations. It turns out that every lattice in this variety is in fact a bounded one and the unary operation is a complementation. Finally, we use a similar technique by using simpler terms and identities motivated by Boolean algebras.

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