Fuzziness measure on complete hedge algebras and quantifying semantics of terms in linear hedge algebras. (English) Zbl 1108.68118
Summary: We examine the Fuzziness Measure (FM) of terms or of complete and linear hedge algebras of a linguistic variable. The notion of Semantically Quantifying Mappings (SQMs), previously examined by the first author, is redefined more generally and a closed relation between the FM of linguistic terms and a family of SQMs with the parameters to be the FM of primary terms and linguistic hedges is established. A semantics-based topology of hedge algebras and a closed and interesting relation between this topology, the FM and the above family of SQMs are discovered and examined. An applicability of the FM and SQMs is shown by an examination of some application examples.
MSC:
| 68T37 | Reasoning under uncertainty in the context of artificial intelligence |
Keywords:
linear hedge algebras; fuzziness measure of linguistic terms; semantically quantifying mappings; interpolative reasoning method; membership functions; fuzziness of linguistic termsReferences:
| [1] | B. De Baets, E.E. Kerre, S. Nasuto, Measuring fuzziness: an evaluation problem, Proc. Second Internat. Symp. on Uncertainty Modeling and Analysis, April 25-28, 1993, publication date: 25-28 April 1993, pp. 65-72.; B. De Baets, E.E. Kerre, S. Nasuto, Measuring fuzziness: an evaluation problem, Proc. Second Internat. Symp. on Uncertainty Modeling and Analysis, April 25-28, 1993, publication date: 25-28 April 1993, pp. 65-72. |
| [2] | Cao, Z.; Kandel, A., Applicability of some fuzzy implication operators, Fuzzy Sets and systems, 31, 151-186 (1989) |
| [3] | X. Hang, F. Xiong, Measures of fuzziness and entropy of fuzzy information, Intelligent Control and Automation, 2000. Proc. Third World Congress, vol. 4, pp. 2448-2452.; X. Hang, F. Xiong, Measures of fuzziness and entropy of fuzzy information, Intelligent Control and Automation, 2000. Proc. Third World Congress, vol. 4, pp. 2448-2452. |
| [4] | 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, IEEE Computer Society Press, Boston University, Boston, MA, 1987, pp. 325-335.; 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, IEEE Computer Society Press, Boston University, Boston, MA, 1987, pp. 325-335. |
| [5] | 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.; 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. |
| [6] | N.C. Ho, A topological completion of refined hedge algebras and a model of fuzziness of linguistic terms, Fuzzy Sets and Systems, submitted for publication.; N.C. Ho, A topological completion of refined hedge algebras and a model of fuzziness of linguistic terms, Fuzzy Sets and Systems, submitted for publication. |
| [7] | N.C. Ho, N.H. Chau, Quantitative semantics in hedge algebras and interpolation methods, Proc. of ICT, Hanoi, 2003.; N.C. Ho, N.H. Chau, Quantitative semantics in hedge algebras and interpolation methods, Proc. of ICT, Hanoi, 2003. |
| [8] | Ho, N. C.; Nam, H. V., Towards an algebraic foundation for a zadeh fuzzy logic, Fuzzy Sets and System, 129, 229-254 (2002) · Zbl 1001.03023 |
| [9] | Ho, N. C.; Nam, H. V.; Khang, T. D.; Chau, L. H., Hedge algebras, linguistic-valued logic and their application to fuzzy reasoning, Inter. J. Uncertainty Fuzziness Knowledge-Based Syst., 7, 4, 347-361 (1999) · Zbl 1113.03319 |
| [10] | Ho, N. C.; Wechler, W., Hedge algebras: an algebraic approach to structures of sets of linguistic domains of linguistic truth variable, Fuzzy Sets and Systems, 35, 3, 281-293 (1990) · Zbl 0704.03007 |
| [11] | Ho, N. C.; Wechler, W., Extended hedge algebras and their application to Fuzzy logic, Fuzzy Sets and Systems, 52, 259-281 (1992) · Zbl 0786.03018 |
| [12] | W.H. Hsiao, S.M. Chen, C.H. Lee, A new interpolative reasoning method in sparse rule-based systems, 93(1) (1998).; W.H. Hsiao, S.M. Chen, C.H. Lee, A new interpolative reasoning method in sparse rule-based systems, 93(1) (1998). · Zbl 0936.68096 |
| [13] | Koczy, L. T.; Hirota, K., Interpolative reasoning with insufficient evidence in sparse fuzzy rules bases, Inform. Sci., 71, 169-201 (1993) · Zbl 0800.68882 |
| [14] | Di Lascio, L.; Gisolfi, A., Averaging linguistic truth values in fuzzy approximate reasoning, Internat. J. Intelligent Syst., 13, 301-318 (1998) · Zbl 0924.03032 |
| [15] | Di Lascio, L.; Gisolfi, A.; Loia, V., A new model for linguistic modifiers, Internat. J. Approx. Reason., 15, 25-47 (1996) · Zbl 0935.03042 |
| [16] | Li, F.; Su, L.; Luo, S., A general model of fuzziness measure, Proc. 2004 Internat. Conf. on Machine Learning and Cybernetics, 3, 1831-1835 (2004) |
| [17] | Pal, N. R.; Bezdek, J. C., Measuring fuzzy uncertainty, IEEE Trans. Fuzzy Systems, 2, 2, 107-118 (1994) |
| [18] | Pedrycz, W., Fuzzy equalization in the construction of fuzzy sets, Fuzzy Sets and Systems, 119, 329-335 (2001) · Zbl 1033.94025 |
| [19] | Ross, T. J., Fuzzy Logic With Engineering Application (1997), McGraw-Hill Inc: McGraw-Hill Inc New York |
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