Computers and Mathematics with Applications, ISSN 0898-1221, 2009, Volume 57, Issue 3, pp. 367 - 378

The notions of (transitive) soft d -algebras, soft edge d -algebras, soft d ∗ -algebras, soft d -ideals, soft d ♯ -ideals, soft d ∗ -ideals, and d -idealistic...

(transitive) Soft [formula omitted]-algebra | or [formula omitted]-idealistic) soft [formula omitted]-algebra | Soft [formula omitted]-ideal | Soft edge [formula omitted]-algebra | Soft BCK-ideal | Soft BCK-algebra | [formula omitted]-idealistic ( [formula omitted]-idealistic | Soft [formula omitted]-algebra | Soft d | or d | ideal | d-idealistic (d | Soft edge d-algebra | idealistic | Soft d-ideal | algebra | idealistic) soft d-algebra | (transitive) Soft d-algebra | MATHEMATICS, APPLIED | BCK-ALGEBRAS | Soft BCK-algebra (transitive) Soft d-algebra | d-idealistic (d(#)-idealistic or d-idealistic) soft d-algebra | FUZZY IDEALS | FILTERS | Soft d(#)-ideal | Soft d-algebra | Set theory | Mathematical models

(transitive) Soft [formula omitted]-algebra | or [formula omitted]-idealistic) soft [formula omitted]-algebra | Soft [formula omitted]-ideal | Soft edge [formula omitted]-algebra | Soft BCK-ideal | Soft BCK-algebra | [formula omitted]-idealistic ( [formula omitted]-idealistic | Soft [formula omitted]-algebra | Soft d | or d | ideal | d-idealistic (d | Soft edge d-algebra | idealistic | Soft d-ideal | algebra | idealistic) soft d-algebra | (transitive) Soft d-algebra | MATHEMATICS, APPLIED | BCK-ALGEBRAS | Soft BCK-algebra (transitive) Soft d-algebra | d-idealistic (d(#)-idealistic or d-idealistic) soft d-algebra | FUZZY IDEALS | FILTERS | Soft d(#)-ideal | Soft d-algebra | Set theory | Mathematical models

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2008, Volume 56, Issue 5, pp. 1408 - 1413

Molodtsov [D. Molodtsov, Soft set theory — First results, Comput. Math. Appl. 37 (1999) 19–31] introduced the concept of soft set as a new mathematical tool...

(Trivial, whole) soft BCK/BCI-algebra | BCK/BCI-algebra | Soft set | soft set | MATHEMATICS, APPLIED | BCK-ALGEBRAS | FUZZY IDEALS | FILTERS | (trivial, whole) soft BCK/BCI-algebra | SET-THEORY | Tools | Set theory | Uncertainty | Mathematical models | Dealing

(Trivial, whole) soft BCK/BCI-algebra | BCK/BCI-algebra | Soft set | soft set | MATHEMATICS, APPLIED | BCK-ALGEBRAS | FUZZY IDEALS | FILTERS | (trivial, whole) soft BCK/BCI-algebra | SET-THEORY | Tools | Set theory | Uncertainty | Mathematical models | Dealing

Journal Article

Journal of Multiple-Valued Logic and Soft Computing, ISSN 1542-3980, 2016, Volume 27, Issue 4, pp. 353 - 406

Hilbert algebras are particular cases of BCK algebras, while BCK algebras are particular cases of BCI algebras. In Part I, starting with a list of properties...

RM algebra | BCK algebra | BE algebra | BZ algebra | Hilbert algebra | RML algebra | (generalized) Tarski algebra | BCH algebra | BCC algebra | BCI algebra | Weak BCK-algebra | Pre-BCK algebra | LOGIC | weak BCK-algebra | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | pre-BCK algebra | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS

RM algebra | BCK algebra | BE algebra | BZ algebra | Hilbert algebra | RML algebra | (generalized) Tarski algebra | BCH algebra | BCC algebra | BCI algebra | Weak BCK-algebra | Pre-BCK algebra | LOGIC | weak BCK-algebra | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | pre-BCK algebra | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Journal of Multiple-Valued Logic and Soft Computing, ISSN 1542-3980, 2016, Volume 27, Issue 4, pp. 407 - 456

Hilbert algebras are particular cases of BCK algebras, while BCK algebras are particular cases of BCI algebras. In Part I, starting with a list of properties...

RM algebra | BCK algebra | BE algebra | BZ algebra | Hilbert algebra | RML algebra | (generalized) Tarski algebra | BCH algebra | BCC algebra | BCI algebra | Weak BCK-algebra | Pre-BCK algebra | LOGIC | weak BCK-algebra | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | pre-BCK algebra | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS

RM algebra | BCK algebra | BE algebra | BZ algebra | Hilbert algebra | RML algebra | (generalized) Tarski algebra | BCH algebra | BCC algebra | BCI algebra | Weak BCK-algebra | Pre-BCK algebra | LOGIC | weak BCK-algebra | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | pre-BCK algebra | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Soft Computing, ISSN 1432-7643, 2018, Volume 23, Issue 13, pp. 4643 - 4654

In this paper, we introduce the notion of pseudo-CI algebras and investigate some of their properties. It is a generalization of the notion of pseudo-BE...

Pseudo-BCK algebra | (singular, commutative, distributive) Pseudo-CI algebra | Pseudo-BE algebra | Pseudo-MV algebra | Algebra

Pseudo-BCK algebra | (singular, commutative, distributive) Pseudo-CI algebra | Pseudo-BE algebra | Pseudo-MV algebra | Algebra

Journal Article

Fuzzy Sets and Systems, ISSN 0165-0114, 06/2014, Volume 244, pp. 86 - 105

In the paper, we define the notion of a state BCK-algebra and a state-morphism BCK-algebra extending the language of BCK-algebras by adding a unary operator...

Quasivariety | State BCK-algebra | Right state operator | Left state operator | BCK-algebra | State-morphism operator | State-morphism BCK-algebra | Generator | MATHEMATICS, APPLIED | THEOREM | STATISTICS & PROBABILITY | MV-ALGEBRAS | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS | Analysis | Algebra | Operators | Reasoning | Probability theory | Adjoints | Generators | Probabilistic methods | Fuzzy set theory

Quasivariety | State BCK-algebra | Right state operator | Left state operator | BCK-algebra | State-morphism operator | State-morphism BCK-algebra | Generator | MATHEMATICS, APPLIED | THEOREM | STATISTICS & PROBABILITY | MV-ALGEBRAS | SYSTEMS | COMPUTER SCIENCE, THEORY & METHODS | Analysis | Algebra | Operators | Reasoning | Probability theory | Adjoints | Generators | Probabilistic methods | Fuzzy set theory

Journal Article

Fuzzy Sets and Systems, ISSN 0165-0114, 2011, Volume 178, Issue 1, pp. 1 - 23

A special algebra called EQ-algebra has been recently introduced by Vilém Novák. Its original motivation comes from fuzzy type theory, in which the main...

EQ-algebras | Fuzzy logic | Representable algebras | Fuzzy equality | BCK-algebras | Residuated lattices | MATHEMATICS, APPLIED | ADJOINTNESS | SET | STATISTICS & PROBABILITY | FUZZY-LOGIC | TIED IMPLICATIONS | COMPUTER SCIENCE, THEORY & METHODS

EQ-algebras | Fuzzy logic | Representable algebras | Fuzzy equality | BCK-algebras | Residuated lattices | MATHEMATICS, APPLIED | ADJOINTNESS | SET | STATISTICS & PROBABILITY | FUZZY-LOGIC | TIED IMPLICATIONS | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Soft Computing, ISSN 1432-7643, 8/2017, Volume 21, Issue 16, pp. 4601 - 4616

Pseudo-equality algebras were initially introduced by Jenei and Kóródi as a possible algebraic semantic for fuzzy-type theory, and they have been revised by...

Measure morphism | Pseudo-valuation | Pseudo-BCK-meet-semilattice | Commutative pseudo-equality algebra | Pseudo-equality algebra | Pseudo-BCK-algebra | Engineering | Computational Intelligence | Control, Robotics, Mechatronics | Artificial Intelligence (incl. Robotics) | Measure | Commutative deductive system | Mathematical Logic and Foundations | BCK-ALGEBRAS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Valuation | Algebra | Equality

Measure morphism | Pseudo-valuation | Pseudo-BCK-meet-semilattice | Commutative pseudo-equality algebra | Pseudo-equality algebra | Pseudo-BCK-algebra | Engineering | Computational Intelligence | Control, Robotics, Mechatronics | Artificial Intelligence (incl. Robotics) | Measure | Commutative deductive system | Mathematical Logic and Foundations | BCK-ALGEBRAS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Valuation | Algebra | Equality

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2009, Volume 58, Issue 7, pp. 1383 - 1390

More general form of the notion of quasi-coincidence of a fuzzy point with a fuzzy set is considered, and generalizations of results in the papers [Y. B. Jun,...

[formula omitted]-level subalgebra | BCK/BCI-algebra | [formula omitted]-fuzzy subalgebra | q | level subalgebra | fuzzy subalgebra | MATHEMATICS, APPLIED | SOFT SET-THEORY | BCK-ALGEBRAS | (epsilon, q(k))-fuzzy subalgebra | FUZZY IDEALS | (epsilon boolean OR q(k))-level subalgebra | (epsilon, epsilon boolean OR q(k))-fuzzy subalgebra | SUBGROUP

[formula omitted]-level subalgebra | BCK/BCI-algebra | [formula omitted]-fuzzy subalgebra | q | level subalgebra | fuzzy subalgebra | MATHEMATICS, APPLIED | SOFT SET-THEORY | BCK-ALGEBRAS | (epsilon, q(k))-fuzzy subalgebra | FUZZY IDEALS | (epsilon boolean OR q(k))-level subalgebra | (epsilon, epsilon boolean OR q(k))-fuzzy subalgebra | SUBGROUP

Journal Article

Studia Logica: An International Journal for Symbolic Logic, ISSN 0039-3215, 12/2012, Volume 100, Issue 6, pp. 1201 - 1209

A new structure, called equality algebras, will be introduced. It has two connectives, a meet operation and an equivalence, and a constant. A closure operator...

Equivalence relation | Substructural logic | Algebra | Mathematical theorems | Axioms | Residuated lattices | Equivalential logic | Heyting algebras | Heyting algebra | Computational Linguistics | Term equivalence | Equivalential algebra | Closure operator | BCK-algebra with meet | Equational characterization | Logic | Equivalential fragment | Philosophy | Mathematical Logic and Foundations | MATHEMATICS | PHILOSOPHY | LOGIC

Equivalence relation | Substructural logic | Algebra | Mathematical theorems | Axioms | Residuated lattices | Equivalential logic | Heyting algebras | Heyting algebra | Computational Linguistics | Term equivalence | Equivalential algebra | Closure operator | BCK-algebra with meet | Equational characterization | Logic | Equivalential fragment | Philosophy | Mathematical Logic and Foundations | MATHEMATICS | PHILOSOPHY | LOGIC

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 12/2018, Volume 68, Issue 6, pp. 1327 - 1338

In this paper we define and study the weak pseudo-BCK algebras as generalizations of weak BCK-algebras, extending some results given by Cı⃖rulis for weak...

commutative weak pseudo-BCK algebra | quasi pseudo-BCK algebra | pseudo-BCK algebra | 06B75 | weak pseudo-BCK algebra | weak pseudo-BCK(E) algebra | Primary 06F35 | 03G25 | pseudo-BE algebra | MATHEMATICS | HILBERT-ALGEBRAS | Equivalence | Theorems | Algebra

commutative weak pseudo-BCK algebra | quasi pseudo-BCK algebra | pseudo-BCK algebra | 06B75 | weak pseudo-BCK algebra | weak pseudo-BCK(E) algebra | Primary 06F35 | 03G25 | pseudo-BE algebra | MATHEMATICS | HILBERT-ALGEBRAS | Equivalence | Theorems | Algebra

Journal Article

Soft Computing, ISSN 1432-7643, 1/2018, Volume 22, Issue 1, pp. 31 - 40

In this paper, we show that the going up and lying over theorems hold in PMV-algebras, and we prove that every $$\cdot $$ · -prime ideal in a PMV-subalgebra is...

Engineering | Lying over theorem | Computational Intelligence | Control, Robotics, Mechatronics | Artificial Intelligence (incl. Robotics) | PMV -algebra | Going up theorem | Localization | Mathematical Logic and Foundations | PMV-algebra | BCK-ALGEBRAS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODULES | CODES | MV-ALGEBRAS | IDEALS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algebra

Engineering | Lying over theorem | Computational Intelligence | Control, Robotics, Mechatronics | Artificial Intelligence (incl. Robotics) | PMV -algebra | Going up theorem | Localization | Mathematical Logic and Foundations | PMV-algebra | BCK-ALGEBRAS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MODULES | CODES | MV-ALGEBRAS | IDEALS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algebra

Journal Article

Soft Computing, ISSN 1432-7643, 6/2016, Volume 20, Issue 6, pp. 2091 - 2101

Recently Jenei introduced a new structure called equality algebras which is inspired by ideas of BCK-algebras with meet. These algebras were generalized by...

Engineering | Pseudo hoop | JK-algebra | Congruence relation | Computational Intelligence | Control, Robotics, Mechatronics | Artificial Intelligence (incl. Robotics) | Pseudo equality algebra | Mathematical Logic and Foundations | Pseudo BCK-meet-semilattice | Normal deductive system | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algebra | Equality

Engineering | Pseudo hoop | JK-algebra | Congruence relation | Computational Intelligence | Control, Robotics, Mechatronics | Artificial Intelligence (incl. Robotics) | Pseudo equality algebra | Mathematical Logic and Foundations | Pseudo BCK-meet-semilattice | Normal deductive system | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algebra | Equality

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 12/2018, Volume 68, Issue 6, pp. 1327 - 1338

Journal Article

Soft Computing, ISSN 1432-7643, 11/2019, Volume 23, Issue 21, pp. 10587 - 10600

In this paper, we introduce the very true operators on pseudo-BCK algebras and we study their properties. We prove that the composition of two very true...

Very true pseudo-BCK algebra | Engineering | Interior operator | Computational Intelligence | Very true homomorphism | Control, Robotics, Mechatronics | Artificial Intelligence | Truth-depressing hedge | Mathematical Logic and Foundations | Very true deductive system | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HEDGES | FUZZY | LATTICES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algebra

Very true pseudo-BCK algebra | Engineering | Interior operator | Computational Intelligence | Very true homomorphism | Control, Robotics, Mechatronics | Artificial Intelligence | Truth-depressing hedge | Mathematical Logic and Foundations | Very true deductive system | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HEDGES | FUZZY | LATTICES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algebra

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 2009, Volume 58, Issue 10, pp. 2060 - 2068

Molodtsov [D. Molodtsov, Soft set theory–First results, Comput. Math. Appl. 37 (1999) 19–31] introduced the concept of soft set as a new mathematical tool for...

Soft set | Soft [formula omitted]-ideal | ( [formula omitted]-idealistic) soft BCI-algebra | Soft ideal | (p-idealistic) soft BCI-algebra | Soft p-ideal | MATHEMATICS, APPLIED | FUZZY IDEALS | FILTERS | SET-THEORY | BCK/BCI-ALGEBRAS

Soft set | Soft [formula omitted]-ideal | ( [formula omitted]-idealistic) soft BCI-algebra | Soft ideal | (p-idealistic) soft BCI-algebra | Soft p-ideal | MATHEMATICS, APPLIED | FUZZY IDEALS | FILTERS | SET-THEORY | BCK/BCI-ALGEBRAS

Journal Article

Soft Computing, ISSN 1432-7643, 11/2018, Volume 22, Issue 21, pp. 7119 - 7128

Hoop algebras or hoops are naturally ordered commutative residuated integral monoids, introduced by Bosbach (Fundam Math 64:257–287, 1969, Fundam Math 69:1–14,...

Heyting algebra | Node | Kleene algebra | Semi-De Morgan algebra | Hoop | Engineering | Computational Intelligence | Control, Robotics, Mechatronics | Hertz algebra | Hilbert algebra | BCK-algebra | Artificial Intelligence (incl. Robotics) | Nodal filter | Mathematical Logic and Foundations | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algebra

Heyting algebra | Node | Kleene algebra | Semi-De Morgan algebra | Hoop | Engineering | Computational Intelligence | Control, Robotics, Mechatronics | Hertz algebra | Hilbert algebra | BCK-algebra | Artificial Intelligence (incl. Robotics) | Nodal filter | Mathematical Logic and Foundations | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Algebra

Journal Article

Soft Computing, ISSN 1432-7643, 7/2008, Volume 12, Issue 9, pp. 835 - 856

Since all the algebras connected to logic have, more or less explicitly, an associated order relation, it follows, by duality principle, that they have two...

IMTL algebra | Hájek(P) algebra | Divisible BCK(P) lattice | Engineering | Weak-BL algebra | Artificial Intelligence (incl. Robotics) | BL algebra | Wajsberg algebra | Generalized-MV algebra | Heyting algebra | BCK(P) lattice | R 0 algebra | WNM algebra | Generalized-Wajsberg algebra | t-norm | MV algebra | BCK algebra | MTL algebra | Generalized-BL algebra | Residuated lattice | NM algebra | Control Engineering | Numerical and Computational Methods in Engineering | Pocrim | Mathematical Logic and Foundations | MTLalgebra | algebra | RESIDUATED LATTICES | Haijek(P) algebra | FUZZY-LOGIC | PROPOSITIONAL CALCULUS | VARIETIES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SYSTEMS | R-0 algebra

IMTL algebra | Hájek(P) algebra | Divisible BCK(P) lattice | Engineering | Weak-BL algebra | Artificial Intelligence (incl. Robotics) | BL algebra | Wajsberg algebra | Generalized-MV algebra | Heyting algebra | BCK(P) lattice | R 0 algebra | WNM algebra | Generalized-Wajsberg algebra | t-norm | MV algebra | BCK algebra | MTL algebra | Generalized-BL algebra | Residuated lattice | NM algebra | Control Engineering | Numerical and Computational Methods in Engineering | Pocrim | Mathematical Logic and Foundations | MTLalgebra | algebra | RESIDUATED LATTICES | Haijek(P) algebra | FUZZY-LOGIC | PROPOSITIONAL CALCULUS | VARIETIES | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SYSTEMS | R-0 algebra

Journal Article

Fuzzy Sets and Systems, ISSN 0165-0114, 05/2018, Volume 339, pp. 1 - 16

Pseudo-BCI-algebras generalize both BCI-algebras and pseudo-BCK-algebras, which are a non-commutative generalization of BCK-algebras. In this paper, following...

Ideal term | Pseudo-BCI-algebra | Filter | Prefilter | Relative congruence modularity | Pseudo-BCK-algebra | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | MONOIDS | IDEALS | LATTICES | COMPUTER SCIENCE, THEORY & METHODS | QUASIVARIETIES | Mathematics - Rings and Algebras

Ideal term | Pseudo-BCI-algebra | Filter | Prefilter | Relative congruence modularity | Pseudo-BCK-algebra | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | MONOIDS | IDEALS | LATTICES | COMPUTER SCIENCE, THEORY & METHODS | QUASIVARIETIES | Mathematics - Rings and Algebras

Journal Article

International Journal of Engineering and Technology(UAE), 2018, Volume 7, Issue 4, pp. 1199 - 1202

A pseudo completely closed ideal of a pseudo BH-algebra | A pseudo Smarandache ideal of BH -algebra | BH-algebra | Apseudo ideal of a pseudo BH-algebra | a pseudo BH-algebra | Ideal of BH-algebra | A pseudo closed ideal of a pseudo BH-algebra | A pseudo Smarandache closed ideal of BH-algebra | BCK-algebra | A Smarandache of BH-algebra | A pseudo Smarandache completely closed ideal of BH -algebra

Journal Article

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