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1999 | 46 | 1 | 63-91
Tytuł artykułu

A theory of refinement structure of hedge algebras and its applications to fuzzy logic

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In [13], an algebraic approach to the natural structure of domains of linguistic variables was introduced. In this approach, every linguistic domain can be interpreted as an algebraic structure called a hedge algebra. In this paper, a refinement structure of hedge algebras based on free distributive lattices generated by linguistic hedge operations will be examined in order to model structure of linguistic domains more properly. In solving this question, we restrict our consideration to the specific hedge algebras called PN-homogeneous hedge algebras. It is shown that any PN-homogeneous hedge algebra can be refined to a refined hedge algebra (RHA, for short) and every RHA with a chain of the primary generators is a distributive lattice. Especially, we shall examine RHAs with exactly two distinct generators, which will be called symmetrical RHAs. Furthermore, in the symmetrical RHAs of the linguistic truth variable, we are able to define negation and implication operation, which, according to their properties, may be interpreted as logical negation and implication in a kind of fuzzy logic called linguistic-valued logic. Some elementary properties of these operations will be also examined. This yields a possibility to construct a method in linguistic reasoning, which is based on linguistic-valued fuzzy logic corresponding to the symmetrical RHAs of the linguistic truth variable.
Słowa kluczowe
Rocznik
Tom
46
Numer
1
Strony
63-91
Opis fizyczny
Daty
wydano
1999
Twórcy
  • Institute of Information Technology, NCST, Hanoi, Vietnam
  • Department of Mathematics, Quinhon University of Pedagogy, 170 Nguyen Hue, Quinhon, Vietnam
Bibliografia
  • [1] G. Birkhoff, Lattice Theory (Providence, Rhode Island, 1973).
  • [2] S. Burris & H. P. Sankappanavar, A Course in Universal Algebras, (Springer-Verlag: New York-Heidelberg-Berlin, 1981).
  • [3] Z. Cao and A. Kandel, Applicability of some fuzzy implication operators, Fuzzy Sets and Systems 31(1989), 151-186.
  • [4] N. Cat Ho, Generalized Post algebras and their application to some infinitary many-valued logic, Dissertationes Math. 107 (1973) 1-76.
  • [5] N. Cat Ho, Fuzziness in structure of linguistic truth values: A foundation for development of fuzzy reasoning, Proc. of ISMVL 87, Boston, USA (IEEE Computer Society Press, New York),1987, 326-335.
  • [6] N. Cat Ho, Linguistic-valued logic and a deductive method in linguistic reasoning, Proc. of the Fifth IFSA 93, Seoul, Korea, July 4-9, 1993.
  • [7] N. Cat Ho, A method in linguistic reasoning on a knowledge base representing by sentences with linguistic belief degree, Fundamenta Informaticae Vol. 28(3,4) (1996), 247-259.
  • [8] N. Cat Ho & H. Rasiowa, Plain semi-Post algebras and their representability, Studia Logica 48(4) (1989), 509-530.
  • [9] N. Cat Ho & H. Van Nam, A refinement structure of hedge algebras, Proc. of the NCST of Vietnam, Vol. 9(1) (1997), 15-28.
  • [10] N. Cat Ho & H. Van Nam, Lattice character of the refinement structure of hedge algebras, J. of Comp. Sci. and Cyber., Vol. 12(1) (1996), 7-20.
  • [11] N. Cat Ho & H. Van Nam, Refinement of hedge algebras based on free distributive lattices generated by hedge operations, Research Report at Workshop on Information Technology: R & D, IOIT, 5-6 Dec. 1996, 156-182 (in Vietnamese).
  • [12] N. Cat Ho & H. Van Nam, Refinement structure of hedge algebras: An algebraic basis for a linguistic-valued fuzzy logic, Present at Inter. Conf. on Discrete Mathematics and Allied Topics, 10-13 Nov. 1997, India.
  • [13] N. Cat Ho & W. Wechler, Hedge algebras: An algebraic approach to structure of sets of linguistic truth values, Fuzzy Sets and Systems 35(1990), 281-293.
  • [14] N. Cat Ho & W. Wechler, Extended hedge algebras and their application to fuzzy logic, Fuzzy Sets and Systems 52(1992), 259-281.
  • [15] R. Giles, Łukasiewicz logic and fuzzy set theory, Inter. J. of Man-Machine stud. 8 (1976), 313-327.
  • [16] J. B. Kiszka, M. E. Kochańska and S. Śliwińska, The influence of some fuzzy implication operators on the accuracy of a fuzzy model-Part I, Fuzzy Sets and Systems 15(1983), 111-128.
  • [17] J. B. Kiszka, M. E. Kochańska and S. Śliwińska, The influence of some fuzzy implication operators on the accuracy of a fuzzy model-Part II, Fuzzy Sets and Systems 15(1983), 223-240.
  • [18] G. Lakoff, Hedges: A study in meaning criteria and the logic of fuzzy concepts, J. Philos. Logic 2 (1973) 458-508 (also presented at the 8th Regional Meeting of the Chicago Linguistic Society, 1972).
  • [19] M. Mizumoto and H.-J. Zimmermann, Comparison of fuzzy reasoning methods, Fuzzy Sets and Systems 8(1982), 253-283.
  • [20] H. Rasiowa, An Algebraic Approach to Non-classical Logic (North-Holland, Amsterdam-New York, 1974).
  • [21] H. Rasiowa & R. Sikorski, The Mathematics of Metamathematics, second edition (Polish Scientific Publ., Warszawa, 1968).
  • [22] D. B. Rinks, A heuristic approach to aggregate production scheduling using linguistic variables, Proc. of Inter. Congr. on Appl. Systems Research and Cybernetics, Vol. VI (1981) 2877-2883.
  • [23] R. Sikorski, Boolean Algebras, third edition, (Springer-Verlag, Berlin-Heidelberg-New York, 1969).
  • [24] H. J. Skala, On many-valued logics, fuzzy sets, fuzzy logics and their applications, Fuzzy Sets and Systems 1 (1978) 129-149.
  • [25] Y. Tsukamoto, An approach to fuzzy reasoning method, in M. M. Gupta, R. K. Ragade, R. R. Yager, Eds., Advances in Fuzzy Set Theory and Applications (North-Holland, Amsterdam, 1979) 137-149.
  • [26] L. A. Zadeh, Fuzzy-set-theoretic interpretation of linguistic hedges, J. of Cybernetics 2 (1972) 4-34.
  • [27] L. A. Zadeh, A theory of approximate reasoning, in: R. R. Yager, S. Ovchinnikov, R. M. Tong and H. T. Nguyen, Eds., Fuzzy Sets and Applications: The selected papers by L. A. Zadeh (Wiley, New York, 1987) 367-411.
  • [28] L. A. Zadeh, The concept of linguistic variable and its application to approximate reasoning Inform. Sci. (I) 8(1975) 199-249; (II) 8(1975) 310 -357; (III) 9(1975) 43-80.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv46i1p63bwm
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