Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
In this work, we would like to discuss rough inclusions defined in Rough Mereology - a paradigm for approximate reasoning introduced by Polkowski and Skowron [20] - as a basis for common models for rough as well as fuzzy set theories. We would like to adhere to the point of view that tolerance (or, similarity) is the leading motif common to both theories and in this area paths between the two lie. To this end, we demonstrate that rough inclusions (which represent a hierarchy of tolerance relations) induce rough set theoretic approximations as well as partitions and equivalence relations in the sense of fuzzy set theory. For completeness sake, we also discuss granulation mechanisms based on rough inclusions with applications to Rough-Neuro Computing and Computing with Words. These considerations are also carried out in specialized cases of Menger's as well as Łukasiewicz's rough inclusions introduced in the paper.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
67--88
Opis fizyczny
bibliogr. 28 poz.
Twórcy
autor
- Polish-Japanese Institute of Information Technology Koszykowa 86, 02-008 Warsaw, Poland, lech.Polkowski@pjwstk.edu.pl
Bibliografia
- [1] D. Becchio. Logique trivalente de Łukasiewicz. Ann. Sci. Univ. Clermont–Ferrand, 16 (1978), pp. 38-89.
- [2] L. Borkowski (ed.). Jan Łukasiewicz. Selected Works. North Holland – Polish Sci. Publ., 1970.
- [3] D. Dubois and H. Prade.Putting rough sets and fuzzy sets together.In: R. Słowi´nski (ed.). Intelligent Decision Support. Handbook of Applications and Advances of the Rough Sets Theory. Kluwer, 1992, pp. 203-232.
- [4] J.A. Goguen. The logic of inexact concepts. Synthese, 18/19 (1968/69), pp. 325-373.
- [5] U. Hoehle. Quotients with respect to similarity relations. Fuzzy Sets Syst., 27 (1988), pp. 31-44.
- [6] S. Le´sniewski. On the foundations of mathematics. Topoi, 2 (1982), pp. 7-52.
- [7] J. Łukasiewicz. Farewell Lecture, Warsaw Univ., March 1918. In: [2], pp. 84-86.
- [8] J. Łukasiewicz and A. Tarski. Untersuchungen ueber den Aussagenkalkuls. In: [2], pp. 130-152.
- [9] C.-H. Ling. Representation of associative functions. Publ. Math. Debrecen, 12 (1965), pp. 189-212.
- [10] E. Marczewski. A general scheme of independence in mathematics. Bull. Polish Acad. Math. Sci., 6 91958), pp. 731-736.
- [11] M, Novotny and Z. Pawlak. On rough equalities. Bull. Polish Acad. Sci. Math., 33 (1985), pp. 99-104.
- [12] P. Pagliani. Rough set theory and logic–algebraic structures. In: E. Orlowska (ed.). Incomplete information. Rough Set Analysis. Studies in Fuzziness and Soft Computing vol. 13, Physica, Heidelberg, 1998, pp. 109-192.
- [13] S. K. Pal, L. Polkowski, and A. Skowron (eds.). Rough–Neuro Computing. Techniques for Computing with Words. Springer, in print.
- [14] J. Pavelka. On fuzzy logic I,II,III. Zeit. Math. Logik Grund. Math., 25, 1979, pp. 45-52, 119 - 134, 447 -464.
- [15] Z. Pawlak. Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer, 1992.
- [16] Z. Pawlak. Rough sets. Intern. J. Comp. Inf. Sci., 11 (1982), pp. 341-356.
- [17] Z. Pawlak and A. Skowron. Rough membership functions. In: R. R. Yager, M. Fedrizzi, and J. Kacprzyk (eds.). Advances in the Dempster-Schafer Theory of Evidence. Wiley, 1994, pp. 251-271.
- [18] L. Polkowski. Rough Sets. Mathematical Foundations. Physica, Heidelberg, 2002.
- [19] L. Polkowski and A. Skowron. Rough mereological calculi of granules: A Rough set approach to computation. Computational Intelligence, 17(3) (2001), pp. 472-492.
- [20] L. Polkowski and A. Skowron. Rough mereology: a new paradigm for approximate reasoning. International Journal of Approximate Reasoning, 15(4), 1997, pp. 333-365.
- [21] H. Rasiowa and R. Sikorski. The Mathematics of Metamathematics. PWN – Polish Sci. Publ., Warszawa, 1963.
- [22] A. Rose and J. B. Rosser. Fragments of many – valued statement calculi. Trans. Amer. Math.Soc., 87 (1958), pp. 1-53.
- [23] Son H. Nguyen, A. Skowron, and J. Stepaniuk. Granular computing: A Rough set approach. Computational Intelligence, 17(3) (2001), pp. 514-545.
- [24] L. Valverde. On the structure of F–indistinguishability operators. Fuzzy Sets Syst., 17 (1985), pp. 313-328.
- [25] M. Wajsberg. Axiomatization of the three–valued sentential calculus (in Polish). C.R. Soc. Sci. Lettr. Varsovie, 24 (1931), pp. 126-148.
- [26] L. A. Zadeh. Fuzzy sets. Information and Control, 8 (1965), pp. 338-353.
- [27] L. A. Zadeh. Similarity relations and fuzzy orderings. Information Sciences, 3 (1971), pp. 177-200.
- [28] L. A. Zadeh and J. Kacprzyk (eds.). Computing with Words in Information/Intelligent Systems 1. Physica, Heidelberg, 1999.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS2-0004-0082