Abstract
This paper considers fuzzy sets just as science tries to domesticate concepts once abstracted from reality: identifying them with quantities, using these quantities for building up mathematical models, escaping from just a formal logic setting, and testing the models against reality before provisionally accepting them. Its aim is that of trying to go towards a new experimental science of ‘the imprecise’; to something like a ‘physics of linguistic imprecision’. It contains a way for looking at fuzzy sets that, if continued, could offer a new perspective for seeing linguistic imprecision, and whose possible value lies on the idea that several forms of theorizing always can be better than a single one.
To professor Lotfi A. Zadeh, with a professional high admiration to his impressive work, and a deep personal esteem for him.
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
Similar content being viewed by others
References
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Trillas, E.: On the genesis of fuzzy sets. Agora 27(1), 7–33 (2008)
Trillas, E., García-Honrado, I.: A Layperson reflection on sorites. In: Seising, R., Tabacchi, M.E. (eds.) Fuzziness and Medicine: Philosophical Reflections and Application Systems in Health Care, pp. 217–231 (2013)
Trillas, E., Moraga, C., Termini, S.: A Naïve Way of Looking at Fuzzy Sets, Forthcoming in Fuzzy Sets and Systems (2015)
Trillas, E.: On a model for the meaning of predicates. In: Seising, R. (ed.) Views on Fuzzy Sets and Systems from Different Perspectives, pp. 175–205, Springer (2009)
Trillas, E., Moraga, C., Guadarrama, S., Cubillo, S., Castiñeira, E.: Computing with antonyms. In: Nikravesh, M., et al., (eds.) Forging New Frontiers, vol. I, pp. 133–154, Springer, New York (2007)
Trillas, E.: Sobre funciones de negación en la teoría de conjuntos difusos (in Spanish). Stochastica III(1), 47–59 (1979)
Alsina, C., Frank, J.M., Schweizer, B.: Associative Functions. Triangular Norms and Copulas, World Scientific, Singapore (2006)
Trillas, E.: A model for ‘Crisp Reasoning’ with fuzzy sets. Int. J. Intell. Syst. 27, 859–872 (2012)
Trillas, E., Alsina, C., Renedo, E.: On some schemes of reasoning in fuzzy logic. New Math. Natural Comput. 7(3), 433–451 (2011)
Trillas, E., Alsina, C.: On standard theories of fuzzy sets with the law (\(\mu \) \(\cdot \) \(\sigma \)’)’ = \(\sigma \) + \(\mu \)’ \(\cdot \) \(\sigma \)’. Int. J. Approximate Reasoning 37(2), 87–92 (2004)
Watanabe, S.: Knowing and Guessing. John Wiley & Sons, New York (1969)
Mendel, J.: Type-2 Fuzzy Sets and Systems: How to Learn About Them, eNewsletter Systems. Man and Cybernetics Society, Issue 27 (2009)
See [5]
Nakama, T., Trillas, E., García-Honrado, I.: Axiomatic Investigation of fuzzy probabilities. In: Seising, R., Sanz, V. (eds.) Soft Computing in Humanities and Social Sciences, pp. 125–140, Springer, (2012)
Zadeh, L.A.: Probability measures of fuzzy events. J. Math. Anal. Appl. 23(2), 421–427 (1968)
Trillas, E.: Some uncertain reflections on uncertainty. Arch. Philos. Hist. Soft Comput. 1, 1–16 (2013)
Trillas, E.: Short Note: A Scrutiny on Imprecision, ECSC Research Report (available upon request) (2014)
Trillas, E., Guadarrama, S.: Fuzzy representations need a careful design. Int. J. Gen. Syst. 39(3), 329–346 (2010)
Trillas, E., Moraga, C.: Reasons for a careful design of fuzzy sets. In: Proceedings IPMU-Milan (2013)
Wigner, E.: The unreasonable effectiveness of mathematics in the natural sciences. Commun. Pure Appl. Math. 13/1 (1960)
Zadeh, L.A.: Computing with Words: Principal Concepts and Ideas. Springer, New York (2012)
Thompson (Lord Kelvin), W.: Lecture on Electrical Units of Measurement, Popular Lectures and Addresses, McMillan, London, vol. 1:73 (1889)
Mamdani, E.H., Trillas, E.: Correspondence between an experimentalist and a theoretician. In: Trillas, E., et al. (ed.) Combining Experimentation and Theory, Springer, Berlin, pp. 1–18 (2012)
Mendel, J., Zadeh, L.A., Trillas, E., Yager, R., Lawry, J., Hagras, H., Guadarrama, S.: What computing with words means to me (discussion forum). In: Computational Intelligence Magazine IEEE, pp. 20–26 (2010)
Trillas, E., Pradera, A.: Non-functional fuzzy connectives: the case of negations. In: Proceedings XI-ESTYLF (León), pp. 21–27 (2002)
Black, M.: Vagueness: an exercise in logical analysis. Philos. Sci. 4(4), 427–455 (1937)
Black, M.: Reasoning with loose concepts. Dialogue 2, 1–12 (1963)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Inf. Sci. 8, 199–249 (1975)
Trillas, E.: On the words probable and improbable. Proc. IPMU (Madrid) II, 780–783 (2000)
Wittgenstein, L.: Philosophical Investigations. Basil Blackwell, Oxford (1958)
Goguen, J.A.: L-fuzzy sets. J. Math. Anal. Appl. 10, 145–174 (1967)
Acknowledgments
This paper is partially funded by the Foundation for the Advancement of Soft Computing (Asturias, Spain), and by the Government of Spain Project MICIIN/TIN 2011-29827-C02-01.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Trillas, E. (2015). Fuzzy Sets: Towards the Scientific Domestication of Imprecision. In: Tamir, D., Rishe, N., Kandel, A. (eds) Fifty Years of Fuzzy Logic and its Applications. Studies in Fuzziness and Soft Computing, vol 326. Springer, Cham. https://doi.org/10.1007/978-3-319-19683-1_29
Download citation
DOI: https://doi.org/10.1007/978-3-319-19683-1_29
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19682-4
Online ISBN: 978-3-319-19683-1
eBook Packages: EngineeringEngineering (R0)