The principles of fuzzy sets and their role in processing uncertain information will be discussed. The question of knowledge representation that is of significant importance in problems of system modelling will be formulated and considered at the level of fuzzy sets. Modelling and simulation realized with the aid of fuzzy sets are studied in a unified methodological framework. First a notion of the cognitive perspective is applied to articulate the problem in terms of specialized linguistic labels. Fuzzy models are constructed to capture logical relationships between the elements (linguistic labels) of the cognitive perspective. Several different classes of the models distinguished with regard to their structural dependencies will be analysed in depth. Finally a linguistic-numerical transformation constituting a type of model-environment interface will be studied.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bezdek, J. C. (1981) Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York.
Borel, E. (1950) Probabilité et Certitude, Press Université de France, Paris.
D'Ambrosio, B. (1989) Qualitative Process Theory Using Linguistic Variables, Springer-Verlag, New York, Berlin.
De Kleer, J. and Brown, J. S. (1984) A qualitative physics based on confluence. Artificial Intelligence, 24, 7–83.
Di Nola, A., Sessa, S., Pedrycz, W. and Sanchez, E. (1989) Fuzzy Relational Equations and Their Applications in Knowledge Engineering, Kluwer Academic Press, Dordrecht.
Dubois, D. and Prade, H. (1988) Possibility Theory — An Approach to Computerized Processing of Uncertainty, Plenum Press, New York.
Heshmaty, B. and Kandel, A. (1985) Fuzzy linear repression and its application to forecasting in uncertain environment, Fuzzy Sets and Systems, 15, 159–191.
Lakoff, G. (1973) Hedges: a study in meaning criteria and the logic of fuzzy concepts. Journal of Philosophical Logic, 2, 458–508.
Ledley, R. S. (1968) Digital Computer and Control Engineering, McGraw-Hill, New York, p. 196.
Martin-Clouaire, R. (1987) Semantics and computation of the generalized modus ponens: efficient deduction in fuzzy logic, in Uncertainty in Knowledge-Based Systems, Bouchon, B. and Yager, R. R. (eds), Springer-Verlag, Berlin, pp. 123–136.
Menger, K. (1942) Statistical metric spaces. Proceedings of the National Academy of Science, USA, 28, 535–537.
Pedrycz, W. (1985) On generalized fuzzy relational equations and their applications. Journal of Mathematical Analysis and Applications, 107, 520–536.
Pedrycz, W. (1990a) Processing in relational structures: fuzzy relational equations. Fuzzy Sets and Systems, 40, 77–106.
Pedrycz, W. (1990b) Fuzzy sets framework for development of a perception perspective. Fuzzy Sets and Systems, 37, 123–137.
Pedrycz, W. (1991) Neurocomputations in relational systems. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13, 289–296.
Pedrycz, W. (1992a) Selected issues of frames of knowledge representation realized by means of linguistic labels. International Journal of Intelligent Systems, 7, 155–170.
Pedrycz, W. (1992b) Fuzzy neural networks with reference neurons as pattern classifiers. IEEE Transactions on Neural Networks (in press).
Pedrycz, W. (1993) Fuzzy Control and Fuzzy Systems, Research Studies Press/J. Wiley, Taunton/New York.
Puccia, Ch. J. and Levins, R. (1985) Qualitative Modeling of Complex Systems, Harvard University Press, Cambridge MA, London.
Rudeanu, S. (1974) Boolean Functions and Equations, North Holland, Amsterdam.
Saaty, T. L. (1980) The Analytic Hierarchy Processes, McGraw-Hill, New York.
Sanchez, E. (1976) Resolution of composite fuzzy relation equations. Information and Control, 34, 38–48.
Savic, D. A. and Pedrycz, W. (1991) Evaluation of fuzzy linear regression models. Fuzzy Sets and Systems, 39, 51–63.
Shin, Y. C., Chen, Y.-T. and Kumara, S. (1992) Framework of an intelligent grinding process advisor. Journal of Intelligent Manufacturing, 3, 135–148.
Takagi, T. and Sugeno, M. (1985) Fuzzy identification of systems and the applications to modelling and control. IEEE Transactions on Systems, Man and Cybernetics, 15, 116–132.
Tanaka, H. (1987) Fuzzy data analysis by possibilistic linear models. Fuzzy Sets and Systems, 24, 363–375.
Tanaka, H., Uejima, S. and Asai, K. (1982) Linear regression analysis with fuzzy model. IEEE Transactions on Systems, Man and Cybernetics, 6, 903–907.
Yager, R. R. (1980) On measuring specificity, Technical Report, Iona College, New Rochelle, NY.
Zadeh, L. A. (1965) Fuzzy sets. Information and Control, 8, 338–353.
Zadeh, L. A. (1973) Outline of a new approach to analysis of complex systems and decision processes. IEEE Transactions on Systems, Man and Cybernetics, 1, 28–44.
Zadeh, L. A. (1978a) PRUF-a meaning representation language for natural language. International Journal of Man-Machine Studies, 10, 395–446.
Zadeh, L. A. (1978b) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems, 1, 3–28.
Zadeh, L. A. (1979) Fuzzy sets and information granularity, in Advances in Fuzzy Set Theory and Applications, Gupta, M. M., Ragade, R. K. and Yager, R. R. (eds), North Holland, Amsterdam, pp. 3–18.
Zimmermann, H. J. (1987) Fuzzy Sets, Decision Making and Expert Systems, Kluwer Academic Publishers, Boston.
Zimmermann, H. J. (1992) Approximate reasoning in manufacturing, in Intelligent Design and Manufacturing, Kusiak, A. (ed.), J. Wiley & Sons, New York, pp. 701–722.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pedrycz, W. Principles and methodology of fuzzy sets. J Intell Manuf 4, 323–340 (1993). https://doi.org/10.1007/BF00123778
Issue Date:
DOI: https://doi.org/10.1007/BF00123778