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Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. (English) Zbl 0988.03040
The author is well known for his continuing inspiration for the development of fuzzy set methodology. In this paper he explains his ideas on how to combine approaches toward fuzzy logic, approximate reasoning, and fuzzified functions into a common framework. This framework has the idea of information granulation (into fuzzy pieces) as its core idea.
This is essentially not a mathematical paper. As it may be expected, however, that it will be influential in applications of fuzzy sets, it is likely to be a source of mathematical problems.

MSC:
03B52 Fuzzy logic; logic of vagueness
68T30 Knowledge representation
94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
68T37 Reasoning under uncertainty in the context of artificial intelligence
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[1] Driankov, D.; Hellendoorn, H.; Reinfrank, M., An introduction to fuzzy control, (1993), Springer Berlin
[2] Dubois, D.; Fargier, H.; Prade, H., Possibility theory in constraint satisfaction problems: handling priority, preference and uncertainty, Applied intelligence, 6, 287-309, (1996) · Zbl 1028.91526
[3] Dubois, D.; Lang, J.; Prade, H., Possibilistic logic, (), 439-513
[4] Dubois, D.; Prade, H.; Dubois, D.; Prade, H., Fuzzy sets in approximate reasoning, part II: logical approaches (with J. lang), Fuzzy sets and systems, Fuzzy sets and systems, Vol. 40, 203-244, (1991) · Zbl 0722.03018
[5] Dubois, D.; Prade, H., Putting rough sets and fuzzy sets together, (), 203-232
[6] ()
[7] ()
[8] Goguen, J.A., The logic of inexact concepts, Synthese, 19, 325-373, (1969) · Zbl 0184.00903
[9] ()
[10] Klir, G.; Yuan, B., Fuzzy sets and fuzzy logic, (1995), Prentice-Hall Englewood Cliffs
[11] Kosko, B., Neural networks and fuzzy systems: A dynamical systems approach to machine intelligence, (1991), Prentice-Hall Englewood Cliffs
[12] Kruse, R.; Gebhardt, J.; Klawonn, F., Foundations of fuzzy systems, (1994), Wiley New York · Zbl 0843.68109
[13] Lee, C.C., Fuzzy logic in control systems: fuzzy logic controller, parts I and II, IEEE trans. systems, man cybernet., 20, 404-418, (1990) · Zbl 0707.93036
[14] ()
[15] Mares, M., Computation over fuzzy quantities, (1994), CRC Press Boca Raton · Zbl 0859.94035
[16] Novak, V., Fuzzy logic, fuzzy sets, and natural languages, Internat. J. general systems, 20, 1, 83-97, (1991) · Zbl 0741.03011
[17] ()
[18] Pawlak, Z., Rough sets, Internat. J. comput. inform. sci., 11, 341-356, (1982) · Zbl 0501.68053
[19] Pedrycz, W., Fuzzy control and fuzzy systems, (1989), Wiley New York · Zbl 0800.68750
[20] Terano, T.; Asai, K.; Sugeno, M., Fuzzy systems theory and its applications, (1992), Academic Press New York
[21] von Altrock, C., Fuzzy logic & neurofuzzy applications explained, (1995), PTR Prentice-Hall Englewood, NJ
[22] Wang, L.-X., Adaptive fuzzy systems and control: design stability analysis, (1994), PTR Prentice-Hall Englewood Cliffs, NJ
[23] ()
[24] Zadeh, L.A., Fuzzy sets, Inform. and control, 8, 338-353, (1965) · Zbl 0139.24606
[25] Zadeh, L.A., Shadows of fuzzy sets, Prob. trans. inform., 2, 37-44, (1966) · Zbl 0263.02028
[26] Zadeh, L.A., Toward a theory of fuzzy systems, (), 469-490
[27] Zadeh, L.A., Outline of a new approach to the analysis of complex system and decision processes, IEEE trans. systems. man, cybernet., 3, 28-44, (1973) · Zbl 0273.93002
[28] Zadeh, L.A., On the analysis of large scale systems, (), 23-37 · Zbl 0263.02028
[29] Zadeh, L.A.; Zadeh, L.A.; Zadeh, L.A., The concept of a linguistic variable and its applications to approximate reasoning part III, Inform. sci., Inform. sci., Inform. sci., 9, 43-80, (1975) · Zbl 0404.68075
[30] Zadeh, L.A., A fuzzy-algorithmic approach to the definition of complex or imprecise concepts, Internat. J. man-machine stud., 8, 249-291, (1976) · Zbl 0332.68068
[31] Zadeh, L.A., Fuzzy sets and information granularity, (), 3-18 · Zbl 0377.04002
[32] Zadeh, L.A., Outline of a computational approach to meaning and knowledge representation based on a concept of a generalized assignment statement, (), 198-211
[33] Zadeh, L.A., Outline of a theory of usuality based on fuzzy logic, (), 79-97 · Zbl 0626.03016
[34] Zadeh, L.A., Fuzzy logic, neural networks and soft computing, Commun. ACM, 37, 3, 77-84, (1994)
[35] Zadeh, L.A., Why the success of fuzzy logic is not paradoxical, IEEE expert, 9, 4, 43-45, (1994) · Zbl 1009.03532
[36] Zadeh, L.A., Fuzzy logic and the calculi of fuzzy rules and fuzzy graphs, Multiple valued logic, 1, 1-38, (1996) · Zbl 0906.03022
[37] Zadeh, L.A., Fuzzy logic = computing with words, IEEE trans. on fuzzy systems, 4, 103-111, (1996)
[38] Zimmerman, H.J., Fuzzy set theory and its applications, (1996), Kluwer-Nijhoff Amsterdam
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