Introduction
This is neither a paper on mathematical logic, nor even on logic, but in the actually not well enough explored subject of the mathematical models of language. For this reason, it connects with the grounds of Zadeh’s fuzzy sets [23], [15].
Language, that is basically for describing perceptions and covers a wide range of human activities, is a social phenomenon resulting in evolutive systems of a big complexity. Language, inextricably linked to narrative and common-sense arguing, is there viewed as the reality to be mathematically represented. Of course, once a (partial) model is introduced it should be later on tested against that to which it refers to, as the only way of knowing to what extent it reflects well enough what is done by means of language, at least when linguistically describing actual or imaginary facts. Understanding a language implies to know what its words mean, how to use them properly.
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
Alsina, C., Frank, M.J., Schweizer, B.: Associative Functions. Triangular Norms and Copulas. World Scientific, Singapore (2006)
Alsina, C., Trillas, E.: Fuzzy sets from a mathematical-naïve point of view. In: Bouchon-Meunier, B., Guitterrer-Roos, J. (eds.) Technologies for Constructing Intelligent Systems, vol. II, pp. 381–392. Springer, Heidelberg (2002)
Cock, M.D., Kerre, E.: A context-based approach to linguistic hedges. International Journal of Applied Mathematics and Computer Science 12(3), 371–382 (2002)
Goguen, J.: L-fuzzy sets. Journal of Mathematical Analysis and Applications (10), 145–174 (1967)
Horwich, P.: Meaning. Clarendon Press, Oxford (1998)
Link, G.: Algebraic semantics in language and philosophy. CSLI Publications, Stanford (1998)
Lyons, J.: Introduction to Theoretical Linguistics. Cambridge University Press, London (1968)
McGinn, C.: Logical properties. Clarendon Press, Oxford (2000)
Mora, J.F.: Diccionario de filosofía. Ariel, Barcelona (1994) (in Spanish)
Muller, F.: The implicit definition of the set-concept. Synthese (138), 417–451 (2004)
Nelsen, R.: An Introduction to Copulas. Lecture Notes in Statistics. Springer, USA (1999)
Odgen, C., Richards, I.: The meaning of meaning. Brace & World, Inc., New York (1946)
Pradera, A., Trillas, E., Renedo, E.: An overview on the construction of fuzzy set theories. New Maths and Natural Computation 1(3), 329–358 (2005)
Trillas, E.: On the words not-probable and improbable. In: Proceedings of the Eighth International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU 2000), Madrid, Spain, vol. II, pp. 780–783. Madrid (2000)
Trillas, E.: On the use of words and fuzzy sets. Information Science (176), 1463–1487 (2006)
Trillas, E.: On the genesis of fuzzy sets. Agora (forthcoming in January 2009)
Trillas, E., Alsina, C.: A reflection on what is a membership function. Mathware & Soft Computing (6), 201–215 (1999)
Trillas, E., Alsina, C., Pradera, A.: On a class of fuzzy set theories. In: Proceedings FUZZ-IEEE 2007, London, pp. 120–124 (2007)
Trillas, E., Alsina, C.: An outline of a naïve loose-set theory. In: Proceedings IPMU 2000, pp. 857–863. Madrid (2000)
Trillas, E., Guadarrama, S.: What about fuzzy logic’s linguistic soundness? Fuzzy Sets and Systems (156), 334–340 (2005)
Trillas, E., Pradera, A.: A reflection on rationality, guessing and measuring. In: Proceedings IPMU 2002, pp. 385–389 (2002)
Wittgenstein, L.: Philosophical Investigations. Basil Blackwell Pubs., Oxford (1958)
Zadeh, L.A.: Fuzzy sets. Information and Control (8), 338–353 (1965)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Information Sciences I 8(3), 199–249, II 8(4), 301–357, III 9(1), 43–80 (1975)
Zadeh, L.A.: Fuzzy logic = computing with words. IEEE Transactions on Fuzzy Systems 4, 103–111 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Trillas, E. (2009). On a Model for the Meaning of Predicates – A Naïve Approach to the Genesis of Fuzzy Sets. In: Seising, R. (eds) Views on Fuzzy Sets and Systems from Different Perspectives. Studies in Fuzziness and Soft Computing, vol 243. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93802-6_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-93802-6_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-93801-9
Online ISBN: 978-3-540-93802-6
eBook Packages: EngineeringEngineering (R0)