An investigation on the $n$-fold IVRL-filters in triangle algebras

Saeide Zahiri; Arsham Borumand Saeid

Mathematica Bohemica (2020)

  • Volume: 145, Issue: 1, page 75-91
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Zahiri, Saeide, and Borumand Saeid, Arsham. "An investigation on the $n$-fold IVRL-filters in triangle algebras." Mathematica Bohemica 145.1 (2020): 75-91. <http://eudml.org/doc/297000>.

@article{Zahiri2020,
abstract = {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.},
author = {Zahiri, Saeide, Borumand Saeid, Arsham},
journal = {Mathematica Bohemica},
language = {eng},
number = {1},
pages = {75-91},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An investigation on the $n$-fold IVRL-filters in triangle algebras},
url = {http://eudml.org/doc/297000},
volume = {145},
year = {2020},
}

TY - JOUR
AU - Zahiri, Saeide
AU - Borumand Saeid, Arsham
TI - An investigation on the $n$-fold IVRL-filters in triangle algebras
JO - Mathematica Bohemica
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 145
IS - 1
SP - 75
EP - 91
AB - 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.
LA - eng
UR - http://eudml.org/doc/297000
ER -

References

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  1. Hájek, P., 10.1007/978-94-011-5300-3, Trends in Logic---Studia Logica Library 4. Kluwer Academic Publishers, Dordrecht (1998). (1998) Zbl0937.03030MR1900263DOI10.1007/978-94-011-5300-3
  2. Piciu, D., Algebras of Fuzzy Logic, Ed. Universtaria, Craiova (2007). (2007) 
  3. Gasse, B. Van, Cornelis, C., Deschrijver, G., Kerre, E. E., 10.1016/j.ijar.2008.04.006, Int. J. Approx. Reasoning 49 (2008), 478-487. (2008) Zbl1195.03060MR2460281DOI10.1016/j.ijar.2008.04.006
  4. Gasse, B. Van, Cornelis, C., Deschrijver, G., Kerre, E. E., 10.1016/j.fss.2007.09.003, Fuzzy Sets Syst. 159 (2008), 1042-1060. (2008) Zbl1174.03028MR2418783DOI10.1016/j.fss.2007.09.003
  5. Gasse, B. Van, Deschrijver, G., Cornelis, C., Kerre, E. E., 10.1016/j.ins.2010.04.010, Inf. Sci. 180 (2010), 3006-3020. (2010) Zbl1206.03058MR2653329DOI10.1016/j.ins.2010.04.010
  6. Ward, M., Dilworth, R. P., 10.1090/S0002-9947-1939-1501995-3, Trans. Am. Math. Soc. 45 (1939), 335-354. (1939) Zbl0021.10801MR1501995DOI10.1090/S0002-9947-1939-1501995-3
  7. Zahiri, S., Saeid, A. Borumand, Eslami, E., 10.2298/PIM1715267Z, Publ. Inst. Math., Nouv. Sér. 101 (115) (2017), 267-283. (2017) MR3700422DOI10.2298/PIM1715267Z

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