nach oben

Erschienen in:

2022 | OriginalPaper | Buchkapitel

Granularity and Rational Approximation: Rethinking Graded Rough Sets

verfasst von : A. Mani

Erschienen in: Transactions on Rough Sets XXIII

Verlag: Springer Berlin Heidelberg

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

The concept of rational discourse is typically determined by subjective, normative, and rule based constraints in the context under consideration. It is typically determined by related ontologies, and coherence between associated concepts employed in the discourse. Classical rough approximations, and variants of variable precision rough sets (VPRS) including graded rough sets embody at least some aspects of potentially useful concepts of rational approximation, but can be very lacking in application contexts, and rough set theoretical frameworks for cluster validation. While the literature on knowledge from general rough perspectives is rich and diverse, not much work has been done from the perspective of rationality in explicit terms. In this research, the gap is addressed by the present author in variants of high granular partial algebras. Specifically, the nature of optimal concepts of rational approximations is examined, and formalized by her in such frameworks. Graded rough sets are generalized from a granular perspective, and the compatibility of the introduced concepts are studied over it. Further aspects of algebraic semantics of granular graded rough sets are examined. Some incorrect results in graded rough sets in the literature are also corrected.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Vorheriges Kapitel Named Entity Recognition on CORD-19 Bio-Medical Dataset with Tolerance Rough Sets

Nächstes Kapitel MADM Strategies Based on Arithmetic and Geometric Mean Operator Under Rough-Bipolar Neutrosophic Set Environment

Akama, S., Murai, T., Kudo, Y.: Reasoning with Rough Sets. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-72691-5CrossRefMATH

Banerjee, M., Chakraborty, M.K.: Rough sets through algebraic logic. Fund. Inform. 28, 211–221 (1996)MathSciNetMATH

Burkhardt, H., Seibt, J., Imaguire, G., Gerogiorgakis, S. (eds.): Handbook of Mereology. Philosophia Verlag, Munich (2017)

Burmeister, P.: A Model-Theoretic Oriented Approach to Partial Algebras. Akademie-Verlag (1986, 2002)

de Caro, F.: Graded modalities, II (canonical models). Stud. Logica. 47, 1–10 (1988). https://doi.org/10.1007/BF00374047MathSciNetCrossRefMATH

de Caro, F., Fattorsi-Barnaba, M.: Graded modalities. III. Stud. Logica. 47, 99–110 (1988). https://doi.org/10.1007/BF00370285MathSciNetCrossRef

Cattaneo, G., Ciucci, D., Dubois, D.: Algebraic models of deviant modal operators based on de Morgan and Kleene lattices. Inf. Sci. 181, 4075–4100 (2011). https://doi.org/10.1016/J.INS.2011.05.008MathSciNetCrossRefMATH

Cerrato, C.: Decidability by filtrations for graded normal logics (graded modalities V). Stud. Logica. 53(1), 61–74 (1994)MathSciNetCrossRefMATH

Chen, J., van Ditmarsch, H., Greco, G., Tzimoulis, A.: Neighbourhood semantics for graded modal logic, pp. 1–12. ArXiv:2105.09202 (2021)

10.

Fattorsi-Barnaba, M., de Caro, F.: Graded modalities. I. Stud. Logica. 44, 197–221 (1985). https://doi.org/10.1007/BF00379767MathSciNetCrossRefMATH

11.

Goble, L.F.: Grades of modality. Logique et Anal. (N.S.) 13, 323–334 (1970)MathSciNetMATH

12.

van der Hoek, W., Meyer, J.-J.C.: Graded modalities in epistemic logic. In: Nerode, A., Taitslin, M. (eds.) LFCS 1992. LNCS, vol. 620, pp. 503–514. Springer, Heidelberg (1992). https://doi.org/10.1007/BFb0023902CrossRef

13.

Katzberg, T., Ziarko, W.: Variable precision extension of rough sets. Fund. Inform. 27(2–3), 155–168 (1996)MathSciNetMATH

14.

Kolodny, N., Brunero, J.: Instrumental rationality. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (Spring 2020). Stanford University (2020). https://plato.stanford.edu/archives/spr2020/entries/rationality-instrumental/

15.

Lin, T.Y.: Granular computing-1: the concept of granulation and its formal model. Int. J. Granular Comput. Rough Sets Intell. Syst. 1(1), 21–42 (2009)

16.

Lin, T., Liu, Q.: Rough approximate operators: axiomatic rough set theory. In: Ziarko, W.P. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery. WORKSHOPS COMP., pp. 256–260. Springer, London (1994). https://doi.org/10.1007/978-1-4471-3238-7_31CrossRef

17.

Lipscomb, D.: Basics of Cladistic Analysis. George Washington University, Washington D.C. (1998). https://www.researchgate.net/publication/221959140

18.

Ljapin, E.S.: Partial Algebras and Their Applications. Kluwer Academic (1996)

19.

Mani, A.: Esoteric rough set theory: algebraic semantics of a generalized VPRS and VPFRS. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets VIII. LNCS, vol. 5084, pp. 175–223. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85064-9_9CrossRef

20.

Mani, A.: Algebraic semantics of similarity-based bitten rough set theory. Fund. Inform. 97(1–2), 177–197 (2009)MathSciNetMATH

21.

Mani, A.: Dialectics of counting and the mathematics of vagueness. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets XV. LNCS, vol. 7255, pp. 122–180. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31903-7_4CrossRef

22.

Mani, A.: Generalized ideals and co-granular rough sets. In: Polkowski, L., et al. (eds.) IJCRS 2017. LNCS (LNAI), vol. 10314, pp. 23–42. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60840-2_2CrossRefMATH

23.

Mani, A.: Algebraic methods for granular rough sets. In: Mani, A., Cattaneo, G., Düntsch, I. (eds.) Algebraic Methods in General Rough Sets. TM, pp. 157–335. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01162-8_3CrossRefMATH

24.

Mani, A.: Dialectical rough sets, parthood and figures of opposition-I. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets XXI. LNCS, vol. 10810, pp. 96–141. Springer, Heidelberg (2019). https://doi.org/10.1007/978-3-662-58768-3_4CrossRef

25.

Mani, A.: Comparative approaches to granularity in general rough sets. In: Bello, R., Miao, D., Falcon, R., Nakata, M., Rosete, A., Ciucci, D. (eds.) IJCRS 2020. LNCS (LNAI), vol. 12179, pp. 500–517. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-52705-1_37CrossRef

26.

Mani, A.: Functional extensions of knowledge representation in general rough sets. In: Bello, R., Miao, D., Falcon, R., Nakata, M., Rosete, A., Ciucci, D. (eds.) IJCRS 2020. LNCS (LNAI), vol. 12179, pp. 19–34. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-52705-1_2CrossRef

27.

Mani, A.: Towards student centric rough concept inventories. In: Bello, R., Miao, D., Falcon, R., Nakata, M., Rosete, A., Ciucci, D. (eds.) IJCRS 2020. LNCS (LNAI), vol. 12179, pp. 251–266. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-52705-1_19CrossRef

28.

Mani, A.: A note on graded granular rough sets. In: FRSA International Conference on Z Pawlak’s 95th Birth Anniversary, pp. 1–9. Preprint, November 2021. https://doi.org/10.5281/zenodo.5623951

29.

Mani, A.: General rough modeling of cluster analysis. In: Ramanna, S., Cornelis, C., Ciucci, D. (eds.) IJCRS 2021. LNCS (LNAI), vol. 12872, pp. 75–82. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-87334-9_6CrossRefMATH

30.

Orlowska, E.: Logic of indiscernible relations. Bull. Pol. Acad. Sci. (Math.) 33, 475–485 (1987)MATH

31.

Pagliani, P.: Three lessons on the topological and algebraic hidden core of rough set theory. In: Mani, A., Cattaneo, G., Düntsch, I. (eds.) Algebraic Methods in General Rough Sets. TM, pp. 337–415. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01162-8_4CrossRefMATH

32.

Pagliani, P., Chakraborty, M.: A Geometry of Approximation: Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns. Springer, Berlin (2008). https://doi.org/10.1007/978-1-4020-8622-9CrossRefMATH

33.

Polkowski, L.: A rough-neural computation model based on rough mereology. In: Pal, S.K., et al. (eds.) Rough-Neural Computing. COGTECH, pp. 85–108. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-642-18859-6_4CrossRef

34.

Polkowski, L.: Approximate Reasoning by Parts. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22279-5CrossRef

35.

Polkowski, L., Semeniuk–Polkowska, M.: Reasoning about concepts by rough mereological logics. In: Wang, G., Li, T., Grzymala-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 205–212. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-79721-0_31CrossRefMATH

36.

Polkowski, L., Skowron, A.: Rough mereology: a new paradigm for approximate reasoning. Int. J. Approximate Reasoning 15(4), 333–365 (1996)MathSciNetCrossRefMATH

37.

Qiao, J., Hu, B.Q.: Granular variable precision L-fuzzy rough sets based on residuated lattices. Fuzzy Sets Syst. 336, 148–166 (2018)MathSciNetCrossRefMATH

38.

de Rijke, M.: A note on graded modal logic. Stud. Logica. 64(2), 271–283 (2000). https://doi.org/10.1023/A:1005245900406MathSciNetCrossRefMATH

39.

Sands, D., Parker, M., Hedgeland, H., Jordan, S., Galloway, R.: Using concept inventories to measure understanding. High. Educ. Pedagogies 3(1), 173–182 (2018)CrossRef

40.

Skowron, A., Jankowski, A., Dutta, S.: Interactive granular computing. Granular Comput. 1(2), 95–113 (2016). https://doi.org/10.1007/s41066-015-0002-1MathSciNetCrossRefMATH

41.

Syau, Y.R., Lin, E.B., Liau, C.J.: Neighborhood systems and variable precision generalized rough sets. Fund. Inform. 153, 271–290 (2017)MathSciNetMATH

42.

Vakarelov, D.: A modal logic for similarity relations in Pawlak knowledge representation systems. Fund. Inform. 15, 61–79 (1991)MathSciNetMATH

43.

Velesaca, H.O., Suárez, P.L., Mira, R., Sappa, A.D.: Computer vision based food grain classification: a comprehensive survey. Comput. Electron. Agric. 187, 106287:1–106287:13 (2021)

44.

Yao, Y.: The art of granular computing. In: Kryszkiewicz, M., Peters, J.F., Rybinski, H., Skowron, A. (eds.) RSEISP 2007. LNCS (LNAI), vol. 4585, pp. 101–112. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73451-2_12CrossRef

45.

Yao, Y.Y., Lin, T.Y.: Generalizing rough sets using modal logics. Intell. Autom. Soft Comput. 2(2), 103–120 (1996)CrossRef

46.

Zadeh, L.A.: Fuzzy sets and information granularity. In: Gupta, N., et al. (eds.) Advances in Fuzzy Set Theory and Applications, pp. 3–18. North Holland, Amsterdam (1979)

47.

Zadeh, L.A.: Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst. 90(2), 111–127 (1997)MathSciNetCrossRefMATH

48.

Zhang, D.: Triangular norms on partially ordered sets. Fuzzy Sets Syst. 153, 195–209 (2005)MathSciNetCrossRefMATH

49.

Zhang, X., Mo, Z., Xiong, F., Cheng, W.: Comparative study of variable precision rough set model and graded rough set model. Int. J. Approximate Reasoning 53, 104–116 (2012)MathSciNetCrossRefMATH

50.

Zhao, S., Tsang, E.C., Chen, D.: The model of fuzzy variable precision rough sets. IEEE Trans. Fuzzy Syst. 17(2), 451–467 (2009). https://doi.org/10.1109/TFUZZ.2009.2013204CrossRef

51.

Ziarko, W.: Variable precision rough set model. J. Comput. Syst. Sci. 46, 39–59 (1993)MathSciNetCrossRefMATH

Titel: Granularity and Rational Approximation: Rethinking Graded Rough Sets
verfasst von: A. Mani
Verlag: Springer Berlin Heidelberg
Buch: Transactions on Rough Sets XXIII
Print ISBN: 978-3-662-66543-5

Electronic ISBN: 978-3-662-66544-2

Copyright-Jahr: 2022
DOI: https://doi.org/10.1007/978-3-662-66544-2_4

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Premium Partner