Abstract
It has been a vexing question in recent years whether concepts are fuzzy. In this paper several views on the fuzziness of concepts are pointed out to have stemmed from dubious concepts of fuzziness. The underlying notions of the roles feasibly played byprototype, set, andprobability in modeling concepts strongly suggest that the controversy originates from a vague relation between intuitive and mathematical ideas in the cognitive sciences. It is argued that the application of fuzzy sets cannot resolve this vagueness since they are one sided,viz., defined on sets. An alternative definition based on classes (in the sense of axiomatic set theory) is proposed.
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References
Bar-Hillel, M. and Falk, R.: 1982, ‘Some Teasers Concerning Conditional Probabilities’,Cognition 11, 109–22.
Berlin, B. and Kay, P.: 1969,Basic Color Terms: Their Universality and Evolution, University of California Press, Berkeley.
Carnap, R.: 1947,Meaning and Necessity, University of Chicago Press, Chicago (2nd ed. 1956).
Carnap, R.: 1950,Logical Foundations of Probability, University of Chicago Press, Chicago.
Cohen, B. and Murphy, G. L.: 1984, ‘Models of Concepts’,Cognitive Sciences 8, 27–58.
Cohen, L. J.: 1981, ‘Can Human Irrationality be Experimentally Demonstrated?’,The Behavioral and Brain Sciences 4, 317–70.
Fraenkel, A. A., Bar-Hillel, Y. and Levy, A.: 1973,Foundations of Set Theory, 2nd rev. ed., North-Holland, Amsterdam.
Fuhrmann, Gy.: 1981, ‘Modelling the Visual Cortex with ‘Modulo System’ Concept’,Biological Cybernetics 40, 39–48.
Fuhrmann, Gy.: 1982, ‘A Recognizing Neural Network: Modulo System, for Extracting and Syntactically Processing of the Important Properties of Patterns’, in: R. Trappl, G. Pask and L. M. Ricciardi (eds.),Progress in Cybernetics and Systems Research IX, pp. 305–11, Hemisphere, Washington, reprinted in R. K. Ragade (ed.), General Systems XXVII Society for General Systems Research, Louisville, 1983, pp. 147–53.
Fuhrmann, Gy.: 1984, ‘Syntax as the Model of Semantics in Brain Modelling,Cybernetica 27, 39–56.
Fuhrmann, Gy.: 1985a, ‘Interdisciplinary Approach to the Brain's Pattern Recognition’,Cybernetica 28, 107–45.
Fuhrmann, Gy.: 1985b, ‘Arithmetic Model for the Distributed Encoding in the Neuron-Module,International Journal of Neuroscience 27, 131–48.
Fuhrmann, Gy.: 1985c, ‘Mathematical Approach to Integrating the ‘Neuron-Module’ and the ‘Cell-Assembly’,International Journal of Neuroscience 28, 91–110.
Fuhrmann, Gy.: 1986, ‘Arithmetic Codes Resembling Neural Encoding’,Information Sciences 39, 197–203.
Fuhrmann, Gy.: 1988, ‘Prototypes' and ‘Fuzziness’ in the Logic of Concepts’,Synthese 75, 317–347.
Fuhrmann, Gy.: Forthcoming. ‘Note on the Generality of Fuzzy Sets’. (submitted for publication).
Goguen, J. A.: 1969, ‘The Logic of Inexact Concepts’,Synthese 19, 325–73.
Goguen, J. A.: 1974, ‘Concept Representation in Natural and Artificial Languages: Axioms, Extensions, and Applications for Fuzzy Sets’,International Journal for Man-Machine Studies 6, 513–61, reprinted in E. H. Mamdani and B. R. Gaines (eds.),Fuzzy Reasoning and Its Applications, Academic Press, New York, 1981, pp. 67–115.
Gupta, M. M., Kandel, A., Bandler, W. and Kiszka, J. B. (eds.): 1985,Approximate Reasoning in Expert Systems, North-Holland, Amsterdam.
Halmos, P. R.: 1950,Measure Theory, Van Nostrand, New York.
Johnson-Laird, P. N.: 1983,Mental Models, Harvard University Press, Cambridge, MA.
Kandel, A.: 1982,Fuzzy Techniques in Pattern Recognition, Wiley, New York.
Kandel, A.: 1986,Fuzzy Mathematical Techniques with Applications, Addison-Wesley, Reading, MA.
Kaufmann, A.: 1975,Introduction to the Theory of Fuzzy Subsets 1, Academic Press, New York.
Kaufmann, A. and Gupta, M. M.: 1985,An Introduction to Fuzzy Arithmetic, Van Nostrand, New York.
Klir, G. L.: 1985,Architecture of Systems Problem Solving, Plenum Press, New York.
Kocprzyk, J. and Yager, R. R.: 1985,Management Decision-Support Systems, Using Fuzzy Sets and Possibility Theory, TÜV Rheinland, Köln.
Kolmogorov, A. N.: 1933,Foundations of the Theory of Probability (in German), English ed. Chelsea Publishing Co., New York, 1950.
McCloskey, M. E. and Glucksberg, S.: 1979, ‘Decision Processes in Verifying Category Membership Statements: Implications for Models of Semantic Memory’,Cognitive Psychology 11, 1–37.
Mervis, C. B. and Rosch, E.: 1981, ‘Categorization of Natural Objects’,Annual Review of Psychology 32, 89–115.
Oden, G. C.: 1977, ‘Integration of Fuzzy Logical Information’,Journal of Experimental Psychology: Human Perception and Performance 3, 565–75.
Osheron, D. N. and Smith, E. E.: 1981, ‘On the Adequacy of Prototype Theory as a Theory of Concepts’,Cognition 9, 35–58.
Posner, M. I. and Keele, S. W.: 1968, ‘On the Genesis of Abstract Ideas’,Journal of Experimental Psychology 77, 353–63.
Révész, P.: 1967,The Laws of Large Numbers, Akadémiai Kiadó, Budapest.
Roth, E. M. and Mervis, C. B.: 1983, ‘Fuzzy Set Theory and Class Inclusion Relations in Semantic Categories’,Journal of Verbal Learning and Verbal Behavior 22, 509–25.
Sanchez, E. (ed.): 1984,Fuzzy Information, Knowledge Representation and Decision Analysis, Pergamon Press, Oxford.
Smith, E. E. and Osheron, D. N.: 1984, ‘Conceptual Combination with Prototype Concepts’,Cognitive Science 8, 337–61.
Tversky, A.: 1977, ‘Features of Similarity’,Psychological Review 84, 327–52.
Tversky, A. and Gati, I.: 1978, ‘Studies of Similarity’, in E. Rosch and B. B. Lloyd (eds.),Cognition and Categorization, L. Erlbaum, Hillsdale, NJ, pp. 79–98.
Tversky, A. and Kahmenan, D.: 1983, ‘Extensional Versus Intuitive Reasoning: The Conjunction Fallacy in Probability Judgment’,Psychological Review 90, 293–315.
Zadeh, L. A.: 1965, ‘Fuzzy Sets’,Information and Control 8, 338–53.
Zadeh, L. A.: 1971, ‘Quantitative Fuzzy Semantics’,Information Sciences 3, 159–76.
Zadeh, L. A.: 1975, ‘Calculus of Fuzzy Restrictions’, in: L. A. Zadeh, K. S. Fu, K. Tanaka and M. Shimura (eds.),Fuzzy Sets and Their Applications to Cognitive and Decision Processes, Academic Press, New York, pp. 1–39.
Zadeh, L. A.: 1976, ‘A Fuzzy-Algorithmic Approach to the Definition of Complex or Imprecise Concepts’,International Journal for Man-Machine Studies 8, 249–91.
Zadeh, L. A.: 1978, ‘PRUF — A Meaning Representation Language for Natural Languages’,International Journal for Man-Machine Studies 10, 395–460.
Zétényi, T. (ed.): 1988,Fuzzy Sets and Psychology, North-Holland, Amsterdam.
Zimmermann, H. J.: 1985,Fuzzy Set Theory and Its Applications, Kluwer-Academic, Dordrecht.
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Fuhrmann, G. Fuzziness of concepts and concepts of fuzziness. Synthese 75, 349–372 (1988). https://doi.org/10.1007/BF00869405
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DOI: https://doi.org/10.1007/BF00869405