On Neutrosophic Vague Binary BZMZ^dM Sub-algebra of BZMZ^dM-algebra in Neutrosophic Vague Binary Sets
| Autor: | P. B. Remya, A. Francina Shalini |
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| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Neutrosophic Sets and Systems, Vol 47, Pp 316-337 (2021) |
| Druh dokumentu: | article |
| ISSN: | 2331-6055 2331-608X |
| DOI: | 10.5281/zenodo.5775141 |
| Popis: | In Model theory, common algebraic structures found are Lattices and Boolean Algebras. In the broad field of research, various algebraic structures can be introduced for a set. BCK, BCI, BCH, BH etc. are some of them. In this paper, a comparatively novel mixed structure namely, de Morgan BZMV-algebra, is presented for neutrosophic vague binary sets. Obviously, this is a mixed output pattern and more effective than the already existing single output approaches. Instead of our usual Boolean approach, this model is a kind of de Morgan lattice extension. Additionally, it takes the effects of Lukasiewicz many-valued logic, combined with BZ –lattices. The logical connective operators, MV conjunction operator ⊙ and MV disjunction operator ⨁ have shown the behavior of idempotency, as same as, their underlying logical patterns, framed of ‘usual conjunction ∧ and disjunction ∨ ’. Both kind of orthocomplementations or negations, one as a fuzzy type and other one as an intuitionistic type are implemented by BZ lattices. That is, Kleene (fuzzy or Zadeh) orthocomplementation and Brouwer orthocomplementation are got implemented in BZ- structure. Here is a fuzzy type negation and is an intuitionistic type negation. In our new type, de Morgan effects are given to these orthocomplementations and hence in this paper, instead of usual negations, de Morgan negations or orthocomplementations are used. Some ideals for this new concept have also got constructed. Behaviour of its direct sum, properties and some of its related theorems are also mentioned in this paper. |
| Databáze: | Directory of Open Access Journals |
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