## Abstract

The paper is an overview on an algebraic approach to domains of linguistic variables and somefirst applications to show the applicability of this new approach. In this approach, each linguistic domain can be considered as a hedge algebra (HA for short) and based on the structure of HAs,a notion of fuzziness measure of linguistic hedges and terms can be defined. In order to apply hedge algebras to those problems, the results of which are needed, a notion of semantically quantifying mappings (SQMs) will be introduced. It shown that there is a closed connection between SQMs and fuzziness measure of hedge and primary terms (the generators of linguistic domains). To show the applicability of this approach, new met hods to solve a Fuzzy Multiple Conditional Reasoning problem, the problem of Balancing an Inverted Pendulum will be presented.## References

Cao Z. and Kandel A. (1989), Applicability of some fuzzy implication operators, Fuzzy sets and systems, vol. 31, pp. 151-186.

Hsiao, W.H., Chen, S.M., and Lee C.H. (1998), A new interpolative reasoning method in sparse rule-based systems, vol. 93(1).

Koczy, L.T. and Hirota, K. (1993), Interpolative reasoning with insufficient evidence in sparse fuzzy rules bases, Inform. Sci., vol. 71, pp. 169-201.

Koczy, L.T. and Hirota, K. (1993), Approximate reasoning by linear rule interpolation and general approximation, Internat. J. Approx. Reason, vol. 9, pp. 197-225.

Nguyen Cat Ho (1997), A consideration of some factors influencing on the accuracy of fuzzy conditional reasoning, Proceeding of Artificial Intelligence and Information-Control

System of Robots conference of Slovak (AIICSR 97 Conf,), Bratislava, Sep 10-14.

Nguyen Cat Ho and Tran Thai Son (1995), On the distance between values of linguistic variables in hedge algebra, Journal of Computer Science and Cybernetics, vol. 11(1), pp. 10-20 (in Vietnamese).

Nguyen Cat Ho and Huynh Van Nam (1999), Ordered Structure-Based Semantics of Linguistic Terms of Linguistic Variables and Approximate Reasoning, AIP Conf. Proceed. on Computing Anticipatory Systems, CASYS’99, 3thInter. Conf., pp. 98-116.

Nguyen Cat Ho and Tran Thai Son (1997), On fuzzy model error, Journal of Informatics and Cybernetics, vol. 13(1) pp. 66-72 (in Vietnamese).

Nguyen Cat Ho (1987), Fuzziness in structure of linguistic truth values: a foundation for development of fuzzy reasoning. Proc. of Int. Symp. on Multiple-Valued Logic, May 26-28, 1987, Boston University, Boston, Massachusetts, IEEE Computer Society Press, pp. 325-335.

Nguyen Cat Ho et al.(1999), HAs, Linguistic-valued Logic and Their Application to Fuzzy Reasoning, Internat. J. of Uncertainty, Fuzzin

ess and Knowledge-Based Systems, vol.7(4), pp. 347-361.

Nguyen Cat Ho and Wechler, W. (1990), Hedge algebra: An algebraic approach to structures of sets of linguistic truth values, Fuzzy sets and systems, vol. 35, pp. 281-293.

Nguyen Cat Ho and Wechler, W. (1992), Extended algebra and their application to fuzzy logic, Fuzzy sets and systems, vol. 52, pp. 259-281.

Shi, Y. and Mizumoto, M. (1997), Reasoning conditions on Koczy’s interpolative reasoning method in sparse fuzzy rule bases, Part II, Fuzzy sets and systems, vol. 87, pp. 47-56.

Shi, Y. and Mizumoto, M. (1998), A note on reasoning conditions of Kocy’s interpolative reasoning method (Short Communication), Fuzzy Sets and Systems, vol. 96, pp. 373-379.

Shi, Y., Mizumoto, M. and Wu, Z.Q. (1995), Reasoning conditions on Koczy’s interpolative reasoning methods in sparse fuzzy rules bases, Fuzzy Sets and Systems, vol.

, pp. 63-71.

Bezdek J. (1993), Fuzzy models-what are they, and Why ?, IEEE Trans. Fuzzy Systems, vol. 1, pp. 1-5.

Cao Z. and Kandel A.(1989), Applicability of some fuzzy implication operators, Fuzzy sets and systems, vol. 31, pp. 151-186.

Dubois D. and Prade H. (1996), New trends and open problems in fuzzy logic and approximate reasoning , Theoria, vol. 11(27), pp. 109-121.

Hajek P. (1998), Mathematics of Fuzzy logic. Kluwer, Dordrecht .

Hsiao, W.H., Chen, S.M., and Lee, C.H. (1998), A new interpolative reasoning method in sparse rule-based systems,vol. 93(1), January 1,

Kiszka, J.B., Kochanska, M., and Sliwinska, D.S. (1985), The inference of some fuzzy implication operators on the accur

acy of a fuzzy model, part 1,Fuzzy sets and systems, vol.15, pp. 111-128.

Kiszka, J.B., Kochanska, M., and Sliwinska, D.S. (1985), The inference of some fuzzy implication operators on the accur

acy of a fuzzy model, part 1Fuzzy sets and systems, vol.

, pp. 223-240.

Klawonn, F. and Novak, V. (1996), The relations between inference and interpolation in frame work of fuzzy systems, Fuzzy Sets and Systems, vol. 81, pp. 336-354.

Mamdani, E.H.(1977), Application of fuzzy logic to approximate reasoning using linguistic synthesis, IEEE Transaction on computer,

vol. 26, pp. 1182-1191.

Mizumoto, M. (1985), Extended fuzzy reasoning, Approximate reasoning in expert systems (M.M. Gupta, A.Kandel, W. Bandler, J.B. Kiszka Ed.), Elsevier Science Publishers North-Holland.

Mizumoto, M. and Zimmermann, H.J. (1982), Comparison of fuzzy reasoning methods, Fuzzy sets and systems, vol. 18, pp. 253-283.

Novak, V. (1994), Fuzzy control from logical point of view. Fuzzy Sets and Systems, vol. 66, pp. 154-173.

Ross, T.J. (1997), Fuzzy logic with Engineering application.International Edition. Mc Graw-Hill, Inc.

Yager, R.R. (1994), Aggregation operators and fuzzy systems modelling. Fuzzy Sets and Systems, vol. 67, pp. 129-145.

Zadeh, L.A. (1972), Fuzzy set theoretic interpretation of linguistic hedges. J. Cybernetics, vol.2, pp. 4-34.

Zadeh, L.A. (1975), The concept of linguistic variable and its application to approximate reasoning. Inform. Sci., vol. 8, pp. 199-249.