State BCK-algebras and state-morphism BCK-algebras

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 which models probabilistic reasoning. We present a relation between state operators and state-morphism operators and measures and states on BCK...

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Published inFuzzy sets and systems Vol. 244; pp. 86 - 105
Main Authors Borzooei, R.A., Dvurečenskij, A., Zahiri, O.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.06.2014
Subjects
Adjoints
BCK-algebra
Fuzzy set theory
Generator
Generators
Left state operator
Operators
Probabilistic methods
Probability theory
Quasivariety
Reasoning
Right state operator
State BCK-algebra
State-morphism BCK-algebra
State-morphism operator
Quasivariety
State BCK-algebra
Right state operator
Left state operator
BCK-algebra
State-morphism operator
State-morphism BCK-algebra
Generator
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Summary: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 which models probabilistic reasoning. We present a relation between state operators and state-morphism operators and measures and states on BCK-algebras, respectively. We study subdirectly irreducible state (morphism) BCK-algebras. We introduce the concept of an adjoint pair in BCK-algebras and show that there is a one-to-one correspondence between adjoint pairs and state-morphism operators. In addition, we show the generators of quasivarieties of state-morphism BCK-algebras.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0165-0114
1872-6801
DOI:10.1016/j.fss.2013.12.007