Fuzzy Ideals and Fuzzy Filters of Pseudocomplemented Semilattices
| Autor: | Wondwosen Zemene Norahun, Berhanu Assaye Alaba |
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| Rok vydání: | 2019 |
| Předmět: |
lcsh:Computer software
Pure mathematics Control and Optimization Article Subject Mathematics::Commutative Algebra Mathematics::General Mathematics Fuzzy ideal Semilattice Fuzzy logic Computational Mathematics lcsh:QA76.75-76.765 ComputingMethodologies_PATTERNRECOGNITION Complete lattice Control and Systems Engineering Cokernel Lattice (order) lcsh:Electrical engineering. Electronics. Nuclear engineering ComputingMethodologies_GENERAL Fuzzy filter lcsh:TK1-9971 Mathematics |
| Zdroj: | Advances in Fuzzy Systems, Vol 2019 (2019) |
| ISSN: | 1687-711X 1687-7101 |
| DOI: | 10.1155/2019/4263923 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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