zbMATH — the first resource for mathematics

Operations on type-2 fuzzy sets. (English) Zbl 1010.03047
Summary: We discuss set operations on type-2 fuzzy sets (including join and meet under minimum/product t-norm), algebraic operations, properties of membership grades of type-2 sets, and type-2 relations and their compositions. All this is needed to implement a type-2 fuzzy logic system (FLS).

03E72 Theory of fuzzy sets, etc.
03B52 Fuzzy logic; logic of vagueness
Full Text: DOI
[1] Chaneau, J.L.; Gunaratne, M.; Altschaeffl, A.G., An application of type-2 sets to decision making in engineering, ()
[2] Dubois, D.; Prade, H., Operations on fuzzy numbers, Internat. J. systems sci., 9, 6, 613-626, (1978) · Zbl 0383.94045
[3] Dubois, D.; Prade, H., Operations in a fuzzy-valued logic, Inform. and control, 43, 224-240, (1979) · Zbl 0434.03020
[4] Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications, (1980), Academic Press, Inc. New York · Zbl 0444.94049
[5] Hisdal, E., The IF THEN ELSE statement and interval-valued fuzzy sets of higher type, Internat. J. man-Mach. stud., 15, 385-455, (1981) · Zbl 0471.03013
[6] John, R.I., Type 2 fuzzy setsan appraisal of theory and applications, Internat. J. uncertainty, fuzziness knowledge-based systems, 6, 6, 563-576, (1998) · Zbl 1087.68639
[7] R.I. John, C. Czarnecki, A type 2 adaptive fuzzy inferencing system, 1998 IEEE Internat Conf. on Systems, Man, and Cybernetics, San Diego, CA, USA, October 1998, pp. 2068-2073.
[8] R.I. John, P.R. Innocent, M.R. Barnes, Type 2 fuzzy sets and neuro-fuzzy clustering of radiographic tibia images, 1998 IEEE Internat. Conf. on Fuzzy Systems, Anchorage, AK, USA, May 1998, pp. 1373-1376.
[9] Karnik, N.N., Type-2 fuzzy logic systems, ph.D. dissertation, (1998), University of Southern California Los Angeles, CA
[10] N.N. Karnik, J.M. Mendel, Introduction to type-2 fuzzy logic systems, Presented at the 1998 IEEE FUZZ Conf. Anchorage, AK, May 1998.
[11] N.N. Karnik, J.M. Mendel, An introduction to type-2 fuzzy logic systems, USC Report, October 1998, http://sipi.usc.edu\(/∼\)mendel/report.
[12] Karnik, N.N.; Mendel, J.M., Applications of type-2 fuzzy logic systems: handling the uncertainty associated with surveys, Proc. FUZZ-IEEE ’99, (1999), Seoul Korea
[13] Karnik, N.N.; Mendel, J.M.; Liang, Q., Type-2 fuzzy logic systems, IEEE trans. fuzzy systems, 7, 6, 643-658, (1999)
[14] Kaufmann, A.; Gupta, M.M., Introduction to fuzzy arithmetic: theory and applications, (1991), Van Nostrand Reinhold New York · Zbl 0754.26012
[15] Klir, G.J.; Folger, T.A., Fuzzy sets, uncertainty, and information, (1988), Prentice-Hall Upper Saddle River, NJ · Zbl 0675.94025
[16] Klir, G.J.; Yuan, B., Fuzzy sets and fuzzy logic: theory and applications, (1995), Prentice-Hall Upper Saddle River, NJ · Zbl 0915.03001
[17] Q. Liang, J.M. Mendel, Interval type-2 fuzzy logic systems: theory and design, IEEE Trans. Fuzzy Systems (2000), to appear.
[18] Q. Liang, J.M. Mendel, MPEG VBR video traffic modeling and classification using fuzzy techniques, IEEE Trans. Fuzzy Systems, submitted.
[19] Mabuchi, S., An interpretation of membership functions and the properties of general probabilistic operators as fuzzy set operators. II. extension to three-valued and interval-valued fuzzy sets, Fuzzy sets and systems, 92, 1, 31-50, (1997) · Zbl 0938.94025
[20] Mendel, J.M., Fuzzy logic systems for engineeringa tutorial, Proc. IEEE, 83, 3, 345-377, (1995)
[21] J.M. Mendel, Computing with words when words can mean different things to different people, Presented at Internat. ICSC Congress on Computational Intelligence: Methods & Applications, 3rd Annual Symp. on Fuzzy Logic and Applications, Rochester, New York, June 22-25, 1999.
[22] Mendel, J.M., Uncertainty, fuzzy logic, and signal processing, Signal processing, 80, 913-933, (2000) · Zbl 1034.94527
[23] Mizumoto, M.; Tanaka, K., Some properties of fuzzy sets of type-2, Inform. and control, 31, 312-340, (1976) · Zbl 0331.02042
[24] Mizumoto, M.; Tanaka, K., Fuzzy sets of type 2 under algebraic product and algebraic sum, Fuzzy sets and systems, 5, 277-290, (1981) · Zbl 0457.04005
[25] Nieminen, J., On the algebraic structure of fuzzy sets of type-2, Kybernetica, 13, 4, (1977) · Zbl 0366.94003
[26] Schwartz, D.G., The case for an interval-based representation of linguistic truth, Fuzzy sets and systems, 17, 153-165, (1985) · Zbl 0595.03017
[27] Wagenknecht, M.; Hartmann, K., Application of fuzzy sets of type 2 to the solution of fuzzy equation systems, Fuzzy sets and systems, 25, 183-190, (1988) · Zbl 0651.04006
[28] Wang, L.X., A course in fuzzy systems and control, (1997), Prentice-Hall Upper Saddle River, NJ
[29] Yager, R.R., Fuzzy subsets of type II in decisions, J. cybernet., 10, 137-159, (1980)
[30] 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.