Applications of fuzzy set concepts to behavioral sciences

Abstract Because people do not seem to use hard-edged categories in everyday thought, fuzzy set theory has some intuitively appealing formalisms which appear suitable for modelling natural cognitive schema. This paper presents tools for applying fuzzy set concepts to the social and behavioral sciences, and examples of their uses. The following issues are addressed: (1) Definitions of fuzziness and its measurement; (2) The measurement of intercategory overlap or synonymy; (3) Fuzzy set inclusion and overlap as the basis for a new hierarchical clustering method; and (4) Fuzzy set union and intersection as the basis for regional-interpretive models in multidimensional scaling and fuzzy taxonomies. Most of the examples for this paper are taken from empirical research into individuals' cognitive representations of helping behavior.

[1]  E BLACKER,et al.  The generality of cognitive complexity in the perception of people and inkblots. , 1956, Journal of abnormal psychology.

[2]  S. Budner.  Intolerance of ambiguity as a personality variable. , 1962, Journal of personality.

[3]  R. Malpass,et al.  Recognition for faces of own and other race. , 1969, Journal of personality and social psychology.

[4]  Settimo Termini,et al.  A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory , 1972, Inf. Control..

[5]  J. Aitchison,et al.  The Lognormal Distribution. , 1958 .

[6]  J. Ray,et al.  Measuring the Concentration of Power in the International System , 1973 .

[7]  Lotfi A. Zadeh,et al.  A fuzzy-algorithmic approach to the definition of complex or imprecise concepts , 1976 .

[8]  S. C. Johnson.  Hierarchical clustering schemes , 1967, Psychometrika.

[9]  W. Alston.  Philosophy of Language , 1964 .

[10]  J. Knopfmacher.  On measures of fuzziness , 1975 .

[11]  Riley W. Gardner,et al.  Differentiation and abstraction in concept formation. , 1962 .

[12]  P. Allison.  Measures of Inequality , 1978 .

[13]  J. Bezdek.  Numerical taxonomy with fuzzy sets , 1974 .

[14]  H. M. Schroder,et al.  Conceptual systems and personality organization , 1963 .

[15]  J. Chang,et al.  Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition , 1970 .

[16]  Michael Smithson,et al.  An Unstudied Region of Helping: An Extension of the Pearce-Amato Cognitive Taxonomy , 1982 .

[17]  Rein Taagepera,et al.  A Generalized Index of Concentration , 1977 .

[18]  Willett Kempton,et al.  Category grading and taxonomic relations: a mug is a sort of a cup , 1978 .

[19]  Shelley E. Taylor,et al.  Categorical and contextual bases of person memory and stereotyping. , 1978 .

[20]  Henri Theil,et al.  Economics and information theory , 1967 .

[21]  Walter J.M. Kickert,et al.  Fuzzy Theories on Decision Making: A Critical Review , 1979 .

[22]  B. Gaines.  Stochastic and fuzzy logics , 1975 .

[23]  George Lakoff,et al.  Hedges: A Study In Meaning Criteria And The Logic Of Fuzzy Concepts , 1973 .

[24]  T. Pettigrew.  The measurement and correlates of category width as a cognitive variable1 , 1958 .

[25]  Enrique H. Ruspini,et al.  A New Approach to Clustering , 1969, Inf. Control..