Roughness based on filters in residuated multilattices
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This paper explores approximation spaces defined by residuated multilattices equipped with an equivalence relation induced by filters. It extends the work of J. Rachunek and D. Salounova on roughness in residuated lattices. Specifically, we use equivalence classes induced by filters, to define lower and upper approximations and, we provide several characterizations of these approximations.
Abstract
This paper explores approximation spaces defined by residuated multilattices equipped with an equivalence relation induced by filters. It extends the work of J. Rachunek and D. Salounova on roughness in residuated lattices. Specifically, we use equivalence classes induced by filters, to define lower and upper approximations and, we provide several characterizations of these approximations.
참고문헌 (14)
- M. Benado, "Les ensembles partiellement ordonnes et th´eor`eme de raffinement de Schreier II(Th´eorie des multistructures)", Czechoslovak Math. J, 5, pp.308~344 (1955)
- D. J. Hassen, "An axiomatic characterization of multilattices", Discrete Math, 33(1), pp.99~101 (1981)
- J. Medina, "Fuzzy logic programming via multilattices", Fuzzy Sets and Systems, 158, pp.674~688 (2007)
- J. Medina, "Fuzzy formal concept analysis via multilattices: first prospects and results", CLA, 972, pp.69~79 (2012)
- I. P. Cabrera, "Residuated operations in hyperstructures: residuated multilattices", 11th International Conference on Computational and Mathematical Methods in Science and Engineering CMMSE, pp.26~30 (2011)
- B. B. Koguep Njionou, "Formal concepts and residuation on multilattices", fundamental informaticae, 188(4), pp.1~21 (2023)
- Zdislaw Pawlak, "Rough sets", International Journal of Computer and Information Sciences, 11(5), pp.341~356 (1982)
- B. Davvaz, "Roughness in rings", Inform. Sci, 164, pp.147~163 (2004)
- S. Rasouli, "Roughness in MV-algebras", Inform. Sci, 180, pp.737~747 (2010)
- V. Leoreanu-Fotea, "Roughness in n-ary hypergroups", Inform. Sci, 178, pp.4114~4124 (2008)
- B. Davvaz, "Roughness based on fuzzy ideals", Inform. Sci, 176, pp.2417~2437 (2006)
- J. Rachunek, "Roughness in Residuated Lattices, IPMU (2012)", pp.596~603, Springer
- I. P. Cabrera, "On residuation in multilattices: Filters, congruences, and homomorphisms", Fuzzy Sets and Systems, 237, pp.1~21 (2014)
- Qingguo Li, "Approximations in multilattices", Quantitative Logic and Soft Computing, 5, pp.472~479 (2017)