Regular Partial Residuated Lattices and Their Filters
To express wider uncertainty, Běhounek and Daňková studied fuzzy partial logic and partial function. At the same time, Borzooei generalized t-norms and put forward the concept of partial t-norms when studying lattice valued quantum effect algebras. Based on partial t-norms, Zhang et al. studied part...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/14/2429 |
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| author | Nan Sheng Xiaohong Zhang |
| author_facet | Nan Sheng Xiaohong Zhang |
| author_sort | Nan Sheng |
| collection | DOAJ |
| description | To express wider uncertainty, Běhounek and Daňková studied fuzzy partial logic and partial function. At the same time, Borzooei generalized t-norms and put forward the concept of partial t-norms when studying lattice valued quantum effect algebras. Based on partial t-norms, Zhang et al. studied partial residuated implications (PRIs) and proposed the concept of partial residuated lattices (PRLs). In this paper, we mainly study the related algebraic structure of fuzzy partial logic. First, we provide the definitions of regular partial t-norms and regular partial residuated implication (rPRI) through the general forms of partial t-norms and partial residuated implication. Second, we define regular partial residuated lattices (rPRLs) and study their corresponding properties. Third, we study the relations among commutative quasi-residuated lattices, commutative Q-residuated lattices, partial residuated lattices, and regular partial residuated lattices. Last, in order to obtain the filter theory of regular partial residuated lattices, we restrict certain conditions and then propose special regular partial residuated lattices (srPRLs) in order to finally construct the quotient structure of regular partial residuated lattices. |
| first_indexed | 2024-03-09T10:15:25Z |
| format | Article |
| id | doaj.art-6717b975fa3346cbbaf3143fb3a681eb |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T10:15:25Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6717b975fa3346cbbaf3143fb3a681eb2023-12-01T22:24:39ZengMDPI AGMathematics2227-73902022-07-011014242910.3390/math10142429Regular Partial Residuated Lattices and Their FiltersNan Sheng0Xiaohong Zhang1School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi’an 710021, ChinaSchool of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi’an 710021, ChinaTo express wider uncertainty, Běhounek and Daňková studied fuzzy partial logic and partial function. At the same time, Borzooei generalized t-norms and put forward the concept of partial t-norms when studying lattice valued quantum effect algebras. Based on partial t-norms, Zhang et al. studied partial residuated implications (PRIs) and proposed the concept of partial residuated lattices (PRLs). In this paper, we mainly study the related algebraic structure of fuzzy partial logic. First, we provide the definitions of regular partial t-norms and regular partial residuated implication (rPRI) through the general forms of partial t-norms and partial residuated implication. Second, we define regular partial residuated lattices (rPRLs) and study their corresponding properties. Third, we study the relations among commutative quasi-residuated lattices, commutative Q-residuated lattices, partial residuated lattices, and regular partial residuated lattices. Last, in order to obtain the filter theory of regular partial residuated lattices, we restrict certain conditions and then propose special regular partial residuated lattices (srPRLs) in order to finally construct the quotient structure of regular partial residuated lattices.https://www.mdpi.com/2227-7390/10/14/2429fuzzy logicpartial t-normregular partial residuated latticeQ-residuated latticefilter |
| spellingShingle | Nan Sheng Xiaohong Zhang Regular Partial Residuated Lattices and Their Filters Mathematics fuzzy logic partial t-norm regular partial residuated lattice Q-residuated lattice filter |
| title | Regular Partial Residuated Lattices and Their Filters |
| title_full | Regular Partial Residuated Lattices and Their Filters |
| title_fullStr | Regular Partial Residuated Lattices and Their Filters |
| title_full_unstemmed | Regular Partial Residuated Lattices and Their Filters |
| title_short | Regular Partial Residuated Lattices and Their Filters |
| title_sort | regular partial residuated lattices and their filters |
| topic | fuzzy logic partial t-norm regular partial residuated lattice Q-residuated lattice filter |
| url | https://www.mdpi.com/2227-7390/10/14/2429 |
| work_keys_str_mv | AT nansheng regularpartialresiduatedlatticesandtheirfilters AT xiaohongzhang regularpartialresiduatedlatticesandtheirfilters |