| Title:
|
An investigation on the $n$-fold IVRL-filters in triangle algebras (English) |
| Author:
|
Zahiri, Saeide |
| Author:
|
Borumand Saeid, Arsham |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
145 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
75-91 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The present study aimed to introduce $n$-fold interval valued residuated lattice (IVRL for short) filters in triangle algebras. Initially, the notions of $n$-fold (positive) implicative IVRL-extended filters and $n$-fold (positive) implicative triangle algebras were defined. Afterwards, several characterizations of the algebras were presented, and the correlations between the $n$-fold IVRL-extended filters, $n$-fold (positive) implicative algebras, and the Gödel triangle algebra were discussed. (English) |
| Keyword:
|
interval-valued structure |
| Keyword:
|
triangle algebra |
| Keyword:
|
interval valued residuated lattice filter |
| Keyword:
|
$n$-fold interval valued residuated lattice extended filter |
| MSC:
|
03B50 |
| MSC:
|
03B52 |
| MSC:
|
08A30 |
| MSC:
|
08A72 |
| idZBL:
|
07217182 |
| idMR:
|
MR4088695 |
| DOI:
|
10.21136/MB.2019.0104-17 |
| . |
| Date available:
|
2020-03-12T08:21:01Z |
| Last updated:
|
2020-11-18 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148066 |
| . |
| Reference:
|
[1] Hájek, P.: Metamathematics of Fuzzy Logic.Trends in Logic---Studia Logica Library 4. Kluwer Academic Publishers, Dordrecht (1998). Zbl 0937.03030, MR 1900263, 10.1007/978-94-011-5300-3 |
| Reference:
|
[2] Piciu, D.: Algebras of Fuzzy Logic.Ed. Universtaria, Craiova (2007). |
| Reference:
|
[3] Gasse, B. Van, Cornelis, C., Deschrijver, G., Kerre, E. E.: A characterization of interval-valued residuated lattices.Int. J. Approx. Reasoning 49 (2008), 478-487. Zbl 1195.03060, MR 2460281, 10.1016/j.ijar.2008.04.006 |
| Reference:
|
[4] Gasse, B. Van, Cornelis, C., Deschrijver, G., Kerre, E. E.: Triangle algebras: A formal logic approach to interval-valued residuated lattices.Fuzzy Sets Syst. 159 (2008), 1042-1060. Zbl 1174.03028, MR 2418783, 10.1016/j.fss.2007.09.003 |
| Reference:
|
[5] Gasse, B. Van, Deschrijver, G., Cornelis, C., Kerre, E. E.: Filters of residuated lattices and triangle algebras.Inf. Sci. 180 (2010), 3006-3020. Zbl 1206.03058, MR 2653329, 10.1016/j.ins.2010.04.010 |
| Reference:
|
[6] Ward, M., Dilworth, R. P.: Residuated lattices.Trans. Am. Math. Soc. 45 (1939), 335-354. Zbl 0021.10801, MR 1501995, 10.1090/S0002-9947-1939-1501995-3 |
| Reference:
|
[7] Zahiri, S., Saeid, A. Borumand, Eslami, E.: A new approach to filters in triangle algebras.Publ. Inst. Math., Nouv. Sér. 101 (115) (2017), 267-283. MR 3700422, 10.2298/PIM1715267Z |
| . |
