scholarly journals L-Fuzzy Congruences and L-Fuzzy Kernel Ideals in Ockham Algebras

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Teferi Getachew Alemayehu ◽  
Derso Abeje Engidaw ◽  
Gezahagne Mulat Addis
Keyword(s):  
Complete Lattice ◽  
Ockham Algebra ◽  
Truth Values ◽  
Kernel Ideal ◽  
Congruence Relations ◽  
Fuzzy Ideal ◽  
Fuzzy Congruence ◽  
Distributive Law ◽  
Ockham Algebras ◽  
Equivalent Conditions

In this paper, we study fuzzy congruence relations and kernel fuzzy ideals of an Ockham algebra A , f , whose truth values are in a complete lattice satisfying the infinite meet distributive law. Some equivalent conditions are derived for a fuzzy ideal of an Ockham algebra A to become a fuzzy kernel ideal. We also obtain the smallest (respectively, the largest) fuzzy congruence on A having a given fuzzy ideal as its kernel.

scholarly journals On Fuzzy Deductive Systems of Hilbert Algebras

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Gezahagne Mulat Addis ◽  
Derso Abeje Engidaw
Keyword(s):  
Fuzzy Set ◽  
Complete Lattice ◽  
Algebraic Closure ◽  
Lattice Isomorphism ◽  
Hilbert Algebra ◽  
Hilbert Algebras ◽  
Deductive Systems ◽  
Congruence Relations ◽  
Fuzzy Congruence ◽  
Distributive Law

In this paper, we study fuzzy deductive systems of Hilbert algebras whose truth values are in a complete lattice satisfying the infinite meet distributive law. Several characterizations are obtained for fuzzy deductive systems generated by a fuzzy set. It is also proved that the class of all fuzzy deductive systems of a Hilbert algebra forms an algebraic closure fuzzy set system. Furthermore, we obtain a lattice isomorphism between the class of fuzzy deductive systems and the class of fuzzy congruence relations in the variety of Hilbert algebras.

scholarly journals Fuzzy Ideals and Fuzzy Filters of Pseudocomplemented Semilattices

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Berhanu Assaye Alaba ◽  
Wondwosen Zemene Norahun
Keyword(s):  
Complete Lattice ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Fuzzy Filter ◽  
Pseudocomplemented Semilattice ◽  
Fuzzy Ideal ◽  
Fuzzy Congruence ◽  
Necessary And Sufficient ◽  
Fuzzy Filters

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.

scholarly journals L -Fuzzy Prime Spectrums of ADLs

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Natnael Teshale Amare ◽  
Srikanya Gonnabhaktula ◽  
Ch. Santhi Sundar Raj
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattice ◽  
Complete Lattice ◽  
Prime Ideals ◽  
Truth Values ◽  
Boolean Rings ◽  
Distributive Law

The notion of an Almost Distributive Lattice (ADL) is a common abstraction of several lattice theoretic and ring theoretic generalizations of Boolean algebra and Boolean rings. In this paper, the set of all L -fuzzy prime ideals of an ADL with truth values in a complete lattice L satisfying the infinite meet distributive law is topologized and the resulting space is discussed.

Lattice structure on fuzzy congruence relations of a hypergroupoid

2007 ◽  
Vol 177 (16) ◽  
pp. 3305-3313 ◽  
Author(s):  
M. Bakhshi ◽  
R.A. Borzooei
Keyword(s):  
Lattice Structure ◽  
Congruence Relations ◽  
Fuzzy Congruence

On an algebra of lattice-valued logic

2005 ◽  
Vol 70 (1) ◽  
pp. 282-318
Author(s):  
Lars Hansen
Keyword(s):  
Boolean Algebra ◽  
Complete Lattice ◽  
Algebraic Theory ◽  
Propositional Calculus ◽  
Boolean Lattice ◽  
Finite Chain ◽  
Axiomatic Theory ◽  
Truth Values ◽  
Algebraic Generalization

AbstractThe purpose of this paper is to present an algebraic generalization of the traditional two-valued logic. This involves introducing a theory of automorphism algebras, which is an algebraic theory of many-valued logic having a complete lattice as the set of truth values. Two generalizations of the two-valued case will be considered, viz., the finite chain and the Boolean lattice. In the case of the Boolean lattice, on choosing a designated lattice value, this algebra has binary retracts that have the usual axiomatic theory of the propositional calculus as suitable theory. This suitability applies to the Boolean algebra of formalized token models [2] where the truth values are, for example, vocabularies. Finally, as the actual motivation for this paper, we indicate how the theory of formalized token models [2] is an example of a many-valued predicate calculus.

scholarly journals Fuzzy congruence relations on pseudo BE-algebras

2020 ◽  
Vol 1 (2) ◽  
pp. 31-43
Author(s):  
Akbar Rezaei ◽  
Arsham Borumand Saeid ◽  
Qiuyan Zhan
Keyword(s):  
Congruence Relations ◽  
Fuzzy Congruence

Fuzzy congruence relations in CI-algebras

2012 ◽  
Vol 21 (S1) ◽  
pp. 319-328 ◽  
Author(s):  
Akbar Rezaei ◽  
Arsham Borumand Saeid
Keyword(s):  
Congruence Relations ◽  
Fuzzy Congruence

scholarly journals Rough sets based on fuzzy ideals in distributive lattices

2020 ◽  
Vol 18 (1) ◽  
pp. 122-137
Author(s):  
Yongwei Yang ◽  
Kuanyun Zhu ◽  
Xiaolong Xin
Keyword(s):  
Distributive Lattice ◽  
Rough Set ◽  
Rough Sets ◽  
Congruence Relation ◽  
Distributive Lattices ◽  
Model Based ◽  
Congruence Relations ◽  
Fuzzy Ideal ◽  
Lower And Upper Approximations ◽  
Generalized Rough Sets

Abstract In this paper, we present a rough set model based on fuzzy ideals of distributive lattices. In fact, we consider a distributive lattice as a universal set and we apply the concept of a fuzzy ideal for definitions of the lower and upper approximations in a distributive lattice. A novel congruence relation induced by a fuzzy ideal of a distributive lattice is introduced. Moreover, we study the special properties of rough sets which can be constructed by means of the congruence relations determined by fuzzy ideals in distributive lattices. Finally, the properties of the generalized rough sets with respect to fuzzy ideals in distributive lattices are also investigated.

A RING-THEORETIC BASIS FOR LOGIC PROGRAMMING

1990 ◽  
Vol 01 (01) ◽  
pp. 23-48 ◽  
Author(s):  
V.S. SUBRAHMANIAN
Keyword(s):  
Logic Programming ◽  
Algebraic Structure ◽  
Complete Lattice ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Truth Values ◽  
Partially Ordered

Investigations into the semantics of logic programming have largely restricted themselves to the case when the set of truth values being considered is a complete lattice. While a few theorems have been obtained which make do with weaker structures, to our knowledge there is no semantical characterization of logic programming which does not require that the set of truth values be partially ordered. We derive here semantical results on logic programming over a space of truth values that forms a commutative pseudo-ring (an algebraic structure a bit weaker than a ring) with identity. This permits us to study the semantics of multi-valued logic programming having a (possibly) non-partially ordered set of truth values.

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