Fuzzy quantic nuclei and conuclei with applications to fuzzy semi-quantales and (L, M)-quasi-fuzzy topologies | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 27, Issue 1, 2019, Pages 1-17 PDF (524.27 K) | ||
| DOI: 10.1186/s42787-019-0031-z | ||
| Authors | ||
| Kamal El-Saady; Saad Sharqawy; Ayat A. Temraz | ||
| Department of Mathematics, Faculty of Science, South Valley University, Qena, 83523, Egypt | ||
| Abstract | ||
| The aim of this paper is to introduce and study the notions of M-fuzzy quantic nuclei and conuclei on quantales. Firstly, the concept of an M-fuzzy quantic nuclei is introduced and some of its properties are discussed. Secondly, the concept of an M-fuzzy quantic conuclei is introduced. As an application of M-fuzzy quantic conuclei on quantales, a characterization of an (L, M)-quasi-fuzzy interior operator on a non-empty set X is given and the relationship between it and an (L, M)-quasi-fuzzy topology is discussed. Finally, the concept of an M-fuzzy left (resp., right) ideal conucleus is introduced and the relationship with the concept of M-fuzzy left (resp., right) ideal is introduced. | ||
| Keywords | ||
| Quantale; Semi-quantale; Fuzzy semi-quantale; Quantic nucleus and conucleus | ||
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