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Abstrakty
We show that finite IUML-algebras, which are residuated lattices arising from an idempotent uninorm, can be interpreted as algebras of sequences of orthopairs whose main operation is defined starting from the three-valued Sobociński operator between rough sets. Our main tool is the representation of finite IUML-algebras by means of finite forests.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
139--163
Opis fizyczny
Bibliogr. 27 poz., rys., tab.
Twórcy
autor
- Università di Milano, Milano, Italy
autor
- Università di Milano-Bicocca, Milano, Italy
autor
- Università dell'Insubria, Varese, Italy
autor
- Università dell'Insubria, Varese, Italy
Bibliografia
- [1] Aguzzoli S, Boffa S, Ciucci D, Gerla B. Refinements of Orthopairs and IUML-algebras. In: Flores V, Gomide F, Janusz A, Meneses C, Miao D, Peters G, Slezak D, Wang G, Weber R, Yao Y (eds.), Rough Sets-International Joint Conference, IJCRS 2016, Santiago de Chile, Chile, October 7-11, 2016, Proceedings, volume 9920 of Lecture Notes in Computer Science. 2016 pp. 87-96. doi:10.1007/978-3-319-47160-0_8.
- [2] Fodor JC, Yager RR, Rybalov AN. Structure of Uninorms. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 1997. 5(4):411-428. doi:10.1142/S0218488597000312.
- [3] Ciucci D, Dubois D. Three-Valued Logics, Uncertainty Management and Rough Sets. Trans. Rough Sets, 2014. 17:1-32. doi:10.1007/978-3-642-54756-0_1.
- [4] Aguzzoli S, Flaminio T, Marchioni E. Finite forests. Their algebras and logics, 2018. Submitted.
- [5] Ciucci D. Orthopairs: A Simple and Widely UsedWay to Model Uncertainty. Fundam. Inform., 2011. 108(3-4):287-304. doi:10.3233/FI-2011-424.
- [6] Pawlak Z. Rough sets. International Journal of Parallel Programming, 1982. 11(5):341-356. doi:10.1007/BF01001956.
- [7] Pagliani P. Rough Set Theory and Logic-Algebraic Structures, volume 13, chapter 6, pp. 109-190. Physica-Verlag HD, Heidelberg. ISBN 978-3-7908-1888-8, 1998. doi:10.1007/978-3-7908-1888-8_6.
- [8] Pal SK, Polkowski L, Skowron A (eds.). Rough-Neural Computing: Techniques for Computing with Words. Cognitive Technologies. Springer, 2004. ISBN 978-3-540-43059-9.
- [9] Bianchi M. A temporal semantics for Nilpotent Minimum logic. Int. J. Approx. Reasoning, 2014. 55(1):391-401. doi:10.1016/j.ijar.2013.10.007.
- [10] Sobociński B. Axiomatization of a partial system of three-value calculus of propositions. Journal of Computing Systems, 1952. 1:23-55. URL https://books.google.pl/books?id=ys9ptwAACAAJ.
- [11] Swietorzecka K. Boleslaw Sobocinski: The Ace of the Second Generation of the LWS, chapter 1, pp. 599-613. Studies in Universal Logic. Birkhuser, Cham, 2018.
- [12] Metcalfe G, Montagna F. Substructural fuzzy logics. J. Symb. Log., 2007. 72(3):834-864. doi:10.2178/jsl/1191333844.
- [13] Anderson A, Belnap N. Entailment: The Logic of Relevance and Necessity, volume 1. Princeton University Press, 1975. ISBN-13: 978-0691071923, 10: 0691071926.
- [14] Stone MH. Topological Representations of Distributive Lattices and Brouwerian Logics. Journal of Symbolic Logic, 1938. 3(2):90-91.
- [15] Priestley HA. Representation of distributive lattices by means of ordered Stone spaces. Bulletin of the London Mathematical Society, 1970. 2:186-190. URL https://doi.org/10.1112/blms/2.2.186.
- [16] Priestley HA. Ordered topological spaces and the representation of distributive lattices. Proc. Lond. Math. Soc. (3), 1972. 24:507-530. URL https://doi.org/10.1112/plms/s3-24.3.507.
- [17] Esakia LL. Topological Kripke models. Sov. Math., Dokl., 1974. 15:147-151.
- [18] Esakia LL. Heyting Algebras I: duality theory. Tbilisi: ”Metsniereba”. 104 p. R. 0.85 (1985)., 1985.
- [19] Baets BD. Idempotent uninorms. European Journal of Operational Research, 1999. 118(3):631-642. doi:10.1016/S0377-2217(98)00325-7.
- [20] Fussner W, Galatos N. Categories of Models of R-mingle, 2018. ArXiv:1710.04256.
- [21] Ciucci D, Mihálydeák T, Csajbók ZE. On Definability and Approximations in Partial Approximation Spaces. In: Miao D, Pedrycz W, Slezak D, Peters G, Hu Q, Wang R (eds.), Rough Sets and Knowledge Technology - 9th International Conference, RSKT 2014, Shanghai, China, October 24-26, 2014, Proceedings, volume 8818 of Lecture Notes in Computer Science. Springer, 2014 pp. 15-26. doi:10.1007/978-3-319-11740-9_2.
- [22] Csajbók Z. Approximation of sets based on partial covering. Theor. Comput. Sci., 2011. 412(42):5820-5833. doi:10.1016/j.tcs.2011.05.037.
- [23] Stefanowski J, Tsoukiàs A. On the Extension of Rough Sets under Incomplete Information. In: Zhong N, Skowron A, Ohsuga S (eds.), New Directions in Rough Sets, Data Mining, and Granular-Soft Computing, 7th International Workshop, RSFDGrC ’99, Yamaguchi, Japan, November 9-11, 1999, Proceedings, volume 1711 of Lecture Notes in Computer Science. Springer, 1999 pp. 73-81. doi:10.1007/978-3-540-48061-7_11.
- [24] Ciucci D. Orthopairs and granular computing. Granular Computing, 2016. 1:159-170. doi:10.1007/s41066-015-0013-y.
- [25] Calegari S, Ciucci D. Granular computing applied to ontologies. Int. J. Approx. Reasoning, 2010. 51(4):391-409. doi:10.1016/j.ijar.2009.11.006.
- [26] Zhu W, Wang F. Reduction and axiomization of covering generalized rough sets. Information Sciences, 2003. 152:217-230. URL https://doi.org/10.1016/S0020-0255(03)00056-2.
- [27] Boffa S, Gerla B. Kleene Algebras as Sequences of Orthopairs. In: Kacprzyk J, Szmidt E, Zadrozny S, Atanassov KT, Krawczak M (eds.), Advances in Fuzzy Logic and Technology 2017 – Proceedings of: EUSFLAT-2017-The 10th Conference of the European Society for Fuzzy Logic and Technology, September 11-15, 2017, Warsaw, Poland IWIFSGN’2017, volume 641 of Advances in Intelligent Systems and Computing. Springer, 2017 pp. 235-248. doi:10.1007/978-3-319-66830-7_22.
Typ dokumentu
Bibliografia
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