A fuzzy-set-theoretic feature model and its application to asymmetric similarity data analysis

KENPEI SHIINA

doi:10.4992/psycholres1954.30.95

KENPEI SHIINA

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Keywords: features, fuzzy sets, similarities, Tversky's contrast model, asymmetry

JOURNAL FREE ACCESS

1988 Volume 30 Issue 3 Pages 95-104

DOI https://doi.org/10.4992/psycholres1954.30.95

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Published: October 25, 1988 Received: December 24, 1985 Available on J-STAGE: February 24, 2009 Accepted: January 16, 1988 Advance online publication: - Revised: -
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Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : Araki, Y. 1984 Generalization of EBA model using fuzzy sets: Application to political choice. Japanese Journal of Psychology, 55, 88-94. (In Japanese with English summary)
Goguen, J. A. 1968 The logic of inexact concepts. Synthese, 19, 325-373.
Hersh, H. M., & Caramazza, A. 1976 A fuzzy set approach to modifiers and vagueness in natural language. Journal of Experimental Psychology: General, 105, 254-276.
Jacoby, S. L. S., Kowalik, J. S., & Pizzo, J. T. 1972 Iterative methods for nonlinear optimazation problems. New York: Prentice-Hall.
Kandel, A. 1986 Fuzzy mathematical techniques with applications. Massachusetts: Addison-Wesley.
Keren, G., & Baggen, S. 1981 Recognition models of alphanumeric characters. Perception _??_ Psychophysics, 29, 234-246.
Klir, G. J., & Folger, T. A. 1988 Fuzzy sets, uncertainty and information. New York: Prentice Hall.
Krumhansl, C. L. 1978 Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85, 445-463.
Kruskal, J. B. 1964 Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29, 115-129.
Oden, G. C. 1977a Integration of fuzzy logical information. Journal of Experimental Psychology: Human Perception and Performance, 3, 565-575.
Oden, G. C. 1977b Fuzziness in semantic memory: Choosing exemplars of subjective categories. Memory and Cognition, 5, 198-204.
Oden, G. C. 1979 A fuzzy logical model of letter identification. Journal of Experimental Psychology: Human Perception and Performance, 5, 336-352.
Oden, G. C., & Massaro, D. W. 1978 Integration of featural model in speech perception. Psychological Review, 85, 172-191.
Ruspini, E. H. 1969 A new approach to clustering. Information and Control, 15, 22-32.
Ruspini, E. H. 1973 New experimental results in fuzzy clustering. Information Sciences, 5, 273-384.
Shepard, R. N., & Arabic, P. 1979 Additive clustering: Representation of similarities as combination of discrete overlapping properties. Psychological Review, 86, 87-123.
Smithson, M. 1987 Fuzzy set analysis for behavioral and social sciences. Springer-Verlag.
Tversky, A. 1977 Features of similarity. Psychological Review, 84, 327-352.
Watanabe, S. 1985 Pattern recognition: Human and mechanical. New York: Wiley
Zadeh, L. A. 1965 Fuzzy sets. Information and Control, 8, 338-353.

Right : Araki, Y. 1984 Generalization of EBA model using fuzzy sets: Application to political choice. Japanese Journal of Psychology, 55, 88-94.(In Japanese with English summary)
Goguen, J. A. 1968 The logic of inexact con-cepts. Synthese, 19, 325-373.
Hersh, H. M., & Caramazza, A. 1976 A fuzzy set approach to modifiers and vagueness in na-tural language. Journal of Experimental Psycholo-gy: General, 105, 254-276.
Jacoby, S. L. S., Kowalik, J. S., & Pizzo, J. T. 1972 Iterative methods for nonlinear optimazation problems. New York: Prentice-Hall.
Kandel, A. 1986 Fuzzy mathematical techniques with applications. Massachusetts: Addison-Wesley.
Keren, G., & Baggen, S. 1981 Recognition models of alphanumeric characters. Perception Psychophysics, 29, 234-246.
Klir, G. J., & Folger, T. A. 1988 Fuzzy sets, uncertainty and information. New York: Prentice-Hall.
Krumhansl, C. L. 1978 Concerning the applica-bility of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85, 445-463.
Kruskal, J. B. 1964 Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29, 115-129.
Oden, G. C. 1977a Integration of fuzzy logical information. Journal of Experimental Psychology: Human Perception and Performance, 3, 565-575.
Oden, G. C. 1977b Fuzziness in semantic mem-ory: Choosing exemplars of subjective categories. Memory and Cognition, 5, 198-204.
Oden, G. C. 1979 A fuzzy logical model of letter identification. Journal of Experimental Psychology: Human Perception and Performance, 5, 336-352.
Oden, G. C., & Massaro, D. W. 1978 Integration of featural model in speech perception. Psychological Review, 85, 172-191.
Ruspini, E. H. 1969 A new approach to clustering. Information and Control, 15, 22-32.
Ruspini, E. H. 1973 New experimental results in fuzzy clustering. Information Sciences, 5, 273-384.
Shepard, R. N., & Arabic, P. 1979 Additive clus-tering: Representation of similarities as combination of discrete overlapping properties. Psychological Review, 86, 87-123.
Smithson, M. 1987 Fuzzy set analysis for behavioral and social sciences. Springer-Verlag.
Tversky, A. 1977 Features of similarity. Psy-chological Review, 84, 327-352.
Watanabe, S. 1985 Pattern recognition: Human and mechanical. New York: Wiley Zadeh, L. A. 1965 Fuzzysets. Information and Control, 8, 338-353.

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Date of correction: February 24, 2009 Reason for correction: - Correction: TITLE Details: [in Japanese]

Date of correction: February 24, 2009 Reason for correction: - Correction: AUTHOR Details: [in Japanese]

Date of correction: February 24, 2009 Reason for correction: - Correction: AFFILIATION Details: [in Japanese]

Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : Araki, Y. 1984 Generalization of EBA model using fuzzy sets: Application to political choice. Japanese Journal of Psychology, 55, 88-94.(In Japanese with English summary)
Goguen, J. A. 1968 The logic of inexact con-cepts. Synthese, 19, 325-373.
Hersh, H. M., & Caramazza, A. 1976 A fuzzy set approach to modifiers and vagueness in na-tural language. Journal of Experimental Psycholo-gy: General, 105, 254-276.
Jacoby, S. L. S., Kowalik, J. S., & Pizzo, J. T. 1972 Iterative methods for nonlinear optimazation problems. New York: Prentice-Hall.
Kandel, A. 1986 Fuzzy mathematical techniques with applications. Massachusetts: Addison-Wesley.
Keren, G., & Baggen, S. 1981 Recognition models of alphanumeric characters. Perception Psychophysics, 29, 234-246.
Klir, G. J., & Folger, T. A. 1988 Fuzzy sets, uncertainty and information. New York: Prentice-Hall.
Krumhansl, C. L. 1978 Concerning the applica-bility of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85, 445-463.
Kruskal, J. B. 1964 Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29, 115-129.
Oden, G. C. 1977a Integration of fuzzy logical information. Journal of Experimental Psychology: Human Perception and Performance, 3, 565-575.
Oden, G. C. 1977b Fuzziness in semantic mem-ory: Choosing exemplars of subjective categories. Memory and Cognition, 5, 198-204.
Oden, G. C. 1979 A fuzzy logical model of letter identification. Journal of Experimental Psychology: Human Perception and Performance, 5, 336-352.
Oden, G. C., & Massaro, D. W. 1978 Integration of featural model in speech perception. Psychological Review, 85, 172-191.
Ruspini, E. H. 1969 A new approach to clustering. Information and Control, 15, 22-32.
Ruspini, E. H. 1973 New experimental results in fuzzy clustering. Information Sciences, 5, 273-384.
Shepard, R. N., & Arabic, P. 1979 Additive clus-tering: Representation of similarities as combination of discrete overlapping properties. Psychological Review, 86, 87-123.
Smithson, M. 1987 Fuzzy set analysis for behavioral and social sciences. Springer-Verlag.
Tversky, A. 1977 Features of similarity. Psy-chological Review, 84, 327-352.
Watanabe, S. 1985 Pattern recognition: Human and mechanical. New York: Wiley Zadeh, L. A. 1965 Fuzzysets. Information and Control, 8, 338-353.

Right : Araki, Y. 1984 Generalization of EBA model using fuzzy sets: Application to political choice. Japanese Journal of Psychology, 55, 88-94.(In Japanese with English summary)
Goguen, J. A. 1968 The logic of inexact concepts. Synthese, 19, 325-373.
Hersh, H. M., & Caramazza, A. 1976 A fuzzy set approach to modifiers and vagueness in natural language. Journal of Experimental Psychology: General, 105, 254-276.
Jacoby, S. L. S., Kowalik, J. S., & Pizzo, J. T. 1972 Iterative methods for nonlinear optimazation problems. New York: Prentice-Hall.
Kandel, A. 1986 Fuzzy mathematical techniques with applications. Massachusetts: Addison-Wesley.
Keren, G., & Baggen, S. 1981 Recognition models of alphanumeric characters. Perception & Psychophysics, 29, 234-246.
Klir, G. J., & Folger, T. A. 1988 Fuzzy sets, uncertainty and information. New York: Prentice-Hall.
Krumhansl, C. L. 1978 Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85, 445-463.
Kruskal, J. B. 1964 Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29, 115-129.
Oden, G. C. 1977a Integration of fuzzy logical information. Journal of Experimental Psychology: Human Perception and Performance, 3, 565-575.
Oden, G. C. 1977b Fuzziness in semantic memory: Choosing exemplars of subjective categories. Memory and Cognition, 5, 198-204.
Oden, G. C. 1979 A fuzzy logical model of letter identification. Journal of Experimental Psychology: Human Perception and Performance, 5, 336-352.
Oden, G. C., & Massaro, D. W. 1978 Integration of featural model in speech perception. Psychological Review, 85, 172-191.
Ruspini, E. H. 1969 A new approach to clustering. Information and Control, 15, 22-32.
Ruspini, E. H. 1973 New experimental results in fuzzy clustering. Information Sciences, 5, 273-384.
Shepard, R. N., & Arabic, P. 1979 Additive clustering: Representation of similarities as combination of discrete overlapping properties. Psychological Review, 86, 87-123.
Smithson, M. 1987 Fuzzy set analysis for behavioral and social sciences. Springer-Verlag.
Tversky, A. 1977 Features of similarity. Psychological Review, 84, 327-352.
Watanabe, S. 1985 Pattern recognition: Human and mechanical. New York: Wiley Zadeh, L. A. 1965 Fuzzy sets. Information and Control, 8, 338-353.

Abstract

Feature representation models are too restricted in that they consider features as dichotomous variables. In an attempt to construct a more general feature model, it is argued that fuzzy set theory (Zadeh, 1965) gives a natural and promising solution to the problem. Using fuzzy set theory in place of ordinary set theory, a fuzzy feature matching model, which is a generalization of Tversky's contrast model (1977) of similarity, is proposed and is applied to the analysis of an asymmetric similarity matrix, which was obtained by asking 42 undergraduates to judge pairwise similarity among eight countries.

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