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Centroid of a type-2-fuzzy set. (English) Zbl 0982.03030
The authors, continuing their previous papers, define the centroid and the generalized centroid of a type-2 fuzzy set and show how to compute them, making use of the product t-norm for practical purpose. In general these computations are highly intensive, but the authors prove that, in the case of interval type-2 fuzzy sets, these procedures are very efficient. An approximation result is presented also for Gaussian type-2 fuzzy sets.

MSC:
03E72 Theory of fuzzy sets, etc.
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[1] J.L. Chaneau, M. Gunaratne, A.G. Altschaeffl, An application of type-2 sets to decision making in engineering, in: J.C. Bezdek (Ed.), Analysis of Fuzzy Information – vol. II: Artificial Intelligence and Decision Systems, CRC Press, Boca Raton, FL, 1987
[2] Driankov, D.; Hellendoorn, H.; Reinfrank, M., An introduction to fuzzy control, (1996), Springer Berlin
[3] Dubois, D.; Prade, H., Operations on fuzzy numbers, Int. J. systems sci., 9, 6, 613-626, (1978) · Zbl 0383.94045
[4] Dubois, D.; Prade, H., Operations in a fuzzy-valued logic, Inform. control, 43, 224-240, (1979) · Zbl 0434.03020
[5] Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications, (1980), Academic Press NY · Zbl 0444.94049
[6] Hisdal, E., The IF THEN ELSE statement and interval-valued fuzzy sets of higher type, Int. J. man – machine studies, 15, 385-455, (1981) · Zbl 0471.03013
[7] John, R.I., Type 2 fuzzy sets: an appraisal of theory and applications, Int. J. uncertainty, fuzziness knowledge-based systems, 6, 6, 563-576, (1998) · Zbl 1087.68639
[8] R.I. John, P.R. Innocent, M.R. Barnes, Type 2 fuzzy sets and neuro-fuzzy clustering of radiographic tibia images, in: 1998 IEEE International Conference on Fuzzy Systems, Anchorage, AK, USA, May 1998, pp. 1373-1376
[9] N.N. Karnik, Type-2 fuzzy logic systems, Ph.D. Dissertation, University of Southern California, Los Angeles, CA, 1998
[10] N.N. Karnik, J.M. Mendel, Introduction to Type-2 Fuzzy Logic Systems, presented at the 1998 IEEE FUZZ Conference, Anchorage, AK, May
[11] N.N. Karnik, J.M. Mendel, An introduction to type-2 fuzzy logic systems, October 1998, USC Report, http://sipi.usc.edu/∼mendel/report
[12] N.N. Karnik, J.M. Mendel, Type-2 Fuzzy Logic Systems: Type-Reduction, presented at the 1998 IEEE SMC Conference, San Diego, CA, October
[13] N.N. Karnik, J.M. Mendel, Operations on type-2 fuzzy set, Fuzzy Sets Systems (2000)
[14] Karnik, N.N.; Mendel, J.M.; Liang, Q., Type-2 fuzzy logic systems, IEEE trans. fuzzy systems, 7, 6, 643-658, (1999)
[15] Kaufmann, A.; Gupta, M.M., Introduction to fuzzy arithmetic: theory and applications, (1991), Van Nostrand Reinhold NY · Zbl 0754.26012
[16] Liang, Q.; Mendel, J.M., Interval type-2 fuzzy logic systems: theory and design, IEEE trans. fuzzy systems, 8, 5, (2000)
[17] J.M. Mendel, Fuzzy Logic Systems for Engineering: A Tutorial, Proc. IEEE 83 (3) (1995) 345-377
[18] J.M. Mendel, Computing with words when words can mean different things to different people, presented at Int’l. ICSC Congress on Computational Intelligence: Methods & Applications, Third Annual Symposium on Fuzzy Logic and Applications, Rochester, NY, June 22-25, 1999
[19] Mizumoto, M.; Tanaka, K., Some properties of fuzzy sets of type-2, Inform. control, 31, 312-340, (1976) · Zbl 0331.02042
[20] Mizumoto, M.; Tanaka, K., Fuzzy sets of type 2 under algebraic product and algebraic sum, Fuzzy sets systems, 5, 277-290, (1981) · Zbl 0457.04005
[21] Nieminen, J., On the algebraic structure of fuzzy sets of type-2, Kybernetica, 13, 4, (1977) · Zbl 0366.94003
[22] Wagenknecht, M.; Hartmann, K., Application of fuzzy sets of type 2 to the solution of fuzzy equation systems, Fuzzy sets systems, 25, 183-190, (1988) · Zbl 0651.04006
[23] Yager, R.R., Fuzzy subsets of type II in decisions, J. cybernet., 10, 137-159, (1980)
[24] Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning - 1, Inform. sci., 8, 199-249, (1975) · Zbl 0397.68071
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