Abstract
This communication is a first step towards a general approach to fuzzy set-theoretic operators, i.e. algebraic operators which coincide with set-operators when membership values are crisp. Some properties of subclasses of such fuzzy set-theoretic operators are investigated. Specific examples are given. An attempt to discuss a possible interpretation of these operators is proposed. The choice of a good operator in a given practical situation can be crucial in decision analysis, information retrieval, pattern recognition for the purpose of aggregating several pieces of information.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
A. D. Allen, “Measuring the Empirical Properties of Sets,” IEEE Trans. on Systems, Man, and Cybernetics 4 (1974), 66–73.
R. E. Bellman, M. Giertz, “On the Analytic Formalism of the Theory of Fuzzy Sets,” Inf. Sci. 5 (1973), 149–156.
R. E. Bellman, L. A. Zadeh, “Decision-making in a Fuzzy Environment,” Mngt. Sci. 17 (1970), 141–164.
D. Dubois, “Selection Automatique par Spécifications Floues,” Rapport Interne ADEPA, Montrouge, France (1979).
D. Dubois, H. Prade, “Fuzzy Sets and Systems: Theory and Applications,” to be published (Academic Press, 1980).
L. W. Fung, K. S. Fu, “An Axiomatic Approach to Rational Decision-Making in a Fuzzy Environment,” in: Fuzzy Sets and Their Applications to Cognitive and Decision Processes, L. A. Zadeh, K. S. Fu, K. Tanaka, M. Shimura, eds. (1975), 227–256.
G. Jumarie, “A Relativistic Approach to Modelling Dynamic Systems Involving Human Factors,” Int. J. Systems Sci., 10 No. 1 (1979), 89–112.
G. C. Oden, “Integration of Fuzzy Logical Information,” J. Exp. Psych. (Human Perception and Performance), 106 (1977), 565–575.
W. Silvert, “Symmetric Summation: A Class of Operations on Fuzzy Sets,” IEEE Trans. on Systems, Man and Cybernetics, 9, 657–659 (1979).
U. Thole, H. J. Zimmermann, P. Zysno, “On the Suitability of Minimum and Product Operators for the Intersection of Fuzzy Sets,” Fuzzy Sets and Systems 2 (1979), 167–180.
S. Watanabe, “Modified Concepts of Logic, Probability and Information Based on Generalized Continuous Characteristic Functions,” Inf. and Cont. 15 (1969), 1–21.
R. R. Yager, “Some Procedures for Selecting Operators for Fuzzy Operations,” Tech. Rep. RRY-79–05, Iona College New Rochelle, NY (1979).
L. A. Zadeh, “Fuzzy Sets,” Inf. and Cont., 8 (1965), 338–353.
L. A. Zadeh, “The Concept of a Linguistic Variable and its Application to Approximate Reasoning,” Inf. Sci. (I) 8, 199–249, (II) 8, 301–357, (III) 9, 43–80 (1975).
L. A. Zadeh, “Fuzzy Sets as a Basis for a Theory of Possibility,” Fuzzy Sets and Systems 1 (1978), 1–28.
H. J. Zimmermann, “Fuzzy Programming and Linear Programming with Several Objective Functions,” Fuzzy Sets and Systems 1 (1978), 45–55.
H. J. Zimmermann, “Results of Empirical Studies in Fuzzy Set Theory,” in: Applied General Systems Research, G. Klir, ed. (1978), 303–312.
B. Schweizer, A. Sklar, “Associative Functions and Abstract Semigroups,” Publ. Math. Debrecen, Vol. 10 (1963), 69–81.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1980 Plenum Press, New York
About this chapter
Cite this chapter
Dubois, D., Prade, H. (1980). New Results about Properties and Semantics of Fuzzy Set-Theoretic Operators. In: Wang, P.P., Chang, S.K. (eds) Fuzzy Sets. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-3848-2_6
Download citation
DOI: https://doi.org/10.1007/978-1-4684-3848-2_6
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-3850-5
Online ISBN: 978-1-4684-3848-2
eBook Packages: Springer Book Archive