A topological completion of refined hedge algebras and a model of fuzziness of linguistic terms and hedges

Fuzzy Sets and Systems

Volumn 158, Issue 4, 2007, Pages 436-451

  Cat Ho, Nguyen ^a  

^a INSTITUTE OF INFORMATION TECHNOLOGY   (Viet Nam)

Author keywords

Algebra; Fuzziness of terms; Hedge algebra; Linguistic domain; Semantic based topology; Semantically ordering relation

Indexed keywords

FUZZY SETS; LINGUISTICS; MATHEMATICAL MODELS; SEMANTICS; TOPOLOGY;

AXIOMATIZATION WAY; HEDGE ALGEBRA; LINGUISTIC DOMAIN; SEMANTIC-BASED TOPOLOGY; SEMANTICALLY ORDERING RELATION;

ALGEBRA;

EID: 33845700114     PISSN: 01650114     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.fss.2006.09.013     Document Type: Article

References (24)

1. Burris S., and Sankappanavar H.P. A Course in Universal Algebra (1981), Springer, New York
2. B. De Baets E.E. Kerre, S. Nasuto, Measuring fuzziness: an evaluation problem, in: Proc. Second Internat. Symp. Uncertainty Modeling and Analysis, April 25-28, 1993, Publication Date: 25-28 April 1993, pp. 65-72.
3. Di Lascio L., Gasilfi A., and Loia V. A new model for linguistic modifiers. Internat. J. Approx. Reason. 15 (1996) 25-47
4. Di Lascio L., and Gisolfi A. Averaging linguistic truth values in fuzzy approximate reasoning. Internat. J. Intell. Systems 13 (1998) 301-318
5. Grätzer G. Universal Algebra. second ed. (1979), Springer, New York
6. X. Hang, F. Xiong, Measures of fuzziness and entropy of fuzzy information, Intelligent Control and Automation, 2000, in: Proc. of the Third World Congress, vol. 4, pp. 2448-2452.
7. N.C. Ho, Fuzziness in structure of linguistic truth values: a foundation for development of fuzzy reasoning, Proc. Internat. Symp. on Multiple-Valued Logic, May 26-28, 1987, Boston University, Boston, MA, IEEE Computer Society Press, 1987, pp. 325-335.
8. Ho N.C. A method in linguistic reasoning on a knowledge base represented by sentences with linguistic belief degree. Fund. Inform. 28 3,4 (1996) 247-260
9. N.C. Ho, Quantifying hedge algebras and interpolation methods in approximate reasoning, Proc. Fifth Internat. Conf. on Fuzzy Information Processing, Beijing, March 1-4, 2003, pp. 105-112.
10. Ho N.C., Chau L.H., Khang T.D., and Nam H.V. Hedge algebras, linguistic-valued logic and their application to fuzzy reasoning. Internat. J. Uncertainty, Fuzziness Knowledge-Based System 7 4 (1999) 347-361
11. Ho N.C., and Nam H.V. Lattice character of the refinement structure of Hedge Algebras. J. Informatics Cybern. 12 1 (1996) 7-20
12. N.C. Ho, H.V. Nam, A refinement structure of Hedge Algebras, in: Proceedings of NCST of Vietnam, vol. 9, No.1, 1997, pp. 15-28.
13. Ho N.C., and Nam H.V. A theory of refinement structure of hedge algebras and its application to linguistic-valued fuzzy logic. In: Niwinski D., and Zawadowski M. (Eds). Logic, Algebra and Computer Science, Banach Center Publications vol. 46 (1999), PWN-Polish Scientific Publishers, Warsaw
14. N.C. Ho, H.V. Nam, Ordered structure-based semantics of linguistic terms of linguistic variables and approximate reasoning, AIP Conf. Proceed. on Computing Anticipatory Systems, CASYS'99, Third Internat. Conf., pp. 98-116.
15. Ho N.C., and Nam H.V. Towards an Algebraic Foundation for a Zadeh Fuzzy Logic. Fuzzy Set and System 129 (2002) 229-254
16. Ho N.C., and Son T.T. On distance between values of linguistic variable based on the structure of hedge algebras. J. Informatics Cybernet. 11 1 (1995) (in Vietnamese)
17. Ho N.C., and Wechler W. Hedge algebras: an algebraic approach to structures of sets of linguistic domains of linguistic truth variable. Fuzzy Sets and Systems 35 3 (1990) 281-293
18. Ho N.C., and Wechler W. Extended hedge algebras and their application to fuzzy logic. Fuzzy Sets and Systems 52 (1992) 259-281
19. F. Li, L. Su, S. Luo, A general model of fuzziness measure, Proc. of 2004 Internat. Conf. on Machine Learning and Cybernetics, vol. 3, 2004, pp. 1831-1835.
20. Rasiowa H. An Algebraic Approach to Non-classical Logic (1974), North-Holland, Amsterdam, New York
21. Rasiowa H., and Sikorski R. The Mathematics of Metamathematics. second ed. (1968), Polish Scientific Publ., Warszawa
22. R. Sikorski, Boolean Algebras, Berlin, Goettingen, Heidelberg, 1960.
23. Zadeh L.A. 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
24. Zadeh L.A. A theory of approximate reasoning. In: Yager R.R., Ovchinnikov S., Tong R.M., and Nguyen H.T. (Eds). Fuzzy Sets and Applications: The Selected Papers by L.A. Zadeh (1987), Wiley, New York 367-411