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Q-Filters of Quantum B-Algebras and Basic Implication Algebras
- Source :
- Symmetry, Vol 10, Iss 11, p 573 (2018), Symmetry, Volume 10, Issue 11
- Publication Year :
- 2018
- Publisher :
- MDPI AG, 2018.
-
Abstract
- The concept of quantum B-algebra was introduced by Rump and Yang, that is, unified algebraic semantics for various noncommutative fuzzy logics, quantum logics, and implication logics. In this paper, a new notion of q-filter in quantum B-algebra is proposed, and quotient structures are constructed by q-filters (in contrast, although the notion of filter in quantum B-algebra has been defined before this paper, but corresponding quotient structures cannot be constructed according to the usual methods). Moreover, a new, more general, implication algebra is proposed, which is called basic implication algebra and can be regarded as a unified frame of general fuzzy logics, including nonassociative fuzzy logics (in contrast, quantum B-algebra is not applied to nonassociative fuzzy logics). The filter theory of basic implication algebras is also established.
- Subjects :
- Physics and Astronomy (miscellaneous)
General Mathematics
quotient algebra
Quotient algebra
02 engineering and technology
q-filter
01 natural sciences
Fuzzy logic
quantum B-algebra
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
0202 electrical engineering, electronic engineering, information engineering
Computer Science (miscellaneous)
Frame (artificial intelligence)
basic implication algebra
0101 mathematics
Filter (mathematics)
Quantum
Quotient
Mathematics
lcsh:Mathematics
010102 general mathematics
fuzzy implication
lcsh:QA1-939
Noncommutative geometry
Algebra
Algebraic semantics
Chemistry (miscellaneous)
020201 artificial intelligence & image processing
Subjects
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 10
- Issue :
- 11
- Database :
- OpenAIRE
- Journal :
- Symmetry
- Accession number :
- edsair.doi.dedup.....3eb2c35aca256c3ecfce02aaf75cfb69