Some studies in the approximation of $$(\in _{\gamma }, \in _{\gamma }\vee q_{\delta })$$-fuzzy substructures in quantales
| Autor: | Saqib Mazher Qurashi, Muhammad Shabir |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
0209 industrial biotechnology Algebraic structure Astrophysics::High Energy Astrophysical Phenomena Applied Mathematics Quantale Binary multiplication 02 engineering and technology Prime (order theory) Combinatorics Computational Mathematics 020901 industrial engineering & automation Complete lattice Algebraic theory 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Topological theory |
| Zdroj: | Computational and Applied Mathematics. 39 |
| ISSN: | 1807-0302 2238-3603 |
| DOI: | 10.1007/s40314-020-01142-6 |
| Popis: | The notion of quantale, which designates a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins, was used for the first time by Mulvey in 1986. In many applied disciplines like theoretical computer science, algebraic theory, rough set theory, topological theory and linear logic, the use of fuzzified algebraic structures specially quantales plays an important role. In the present paper, the concept of generalized roughness for $$\left( \in _{\gamma },\in _{\gamma }\vee q_{\delta }\right) $$-fuzzy filters in quantales, is introduced. The concept is extended to the approximations of $$\left( \in _{\gamma },\in _{\gamma }\vee q_{\delta }\right) $$-fuzzy ideals and $$\left( \in _{\gamma },\in _{\gamma }\vee q_{\delta }\right) $$-fuzzy subquantales. Moreover, this concept is applied to study the approximations of $$\left( \in _{\gamma },\in _{\gamma }\vee q_{\delta }\right) $$-fuzzy prime ideals and $$\left( \in _{\gamma },\in _{\gamma }\vee q_{\delta }\right) $$-fuzzy semi-prime ideals. |
| Databáze: | OpenAIRE |
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