Abstract
This chapter examines the foundations of IFC by analyzing the concepts of deduction, fuzziness, and induction. The first subsection explains the classical concepts of sharp and deductive logic and classification; in this section, it is presupposed that all terms are clearly defined. The second section explains what happens when those definitions have fuzzy boundaries and provides the tools, fuzzy logic and fuzzy classification, to reason about this. However, there are many terms that do not only lack a sharp boundary of term definition but also lack a priori definitions. Therefore, the third subsection discusses how such definitions can be inferred through inductive logic and how such inferred propositional functions define inductive fuzzy classes. Finally, this chapter proposes a method to derive precise definitions of vague concepts—membership functions—from data. It develops a methodology for membership function induction using normalized likelihood comparisons, which can be applied to fuzzy classification of individuals.
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References
Boole, G. (1847). The matematical analysis of logic, being an essay towards a calculus of deductive reasoning. London: George Bell.
Chmielecki, A. (1998). What is information? In Proceedings of the Twentieth World Congress of Philosophy. Boston.
Del Amo, A., Montero, J., & Cutello, V. (1999). On the principles of fuzzy classification. Proceedings 18th North American Fuzzy Information Processing Society Annual Conference, (pp. 675–679).
Dianhui, W., Dillon, T., & Chang, E. J. (2001). A data mining approach for fuzzy classification rule generation. IFSA World Congress and 20th NAFIPS International Conference, (pp. 2960–2964).
Dubois, D. J., & Prade, H. (1980). Fuzzy sets and systems. Theory and applications. New York: Academic Press.
Glubrecht, J.-M., Oberschelp, A., & Todt, G. (1983). Klassenlogik. Mannheim: Wissenschaftsverlag.
Greene, B. (2011). The hidden reality. Parallel universes and the deep laws of the cosmos. New York: Random House.
Hajek, P. (2006). Fuzzy logic. In E. N. Zalta (Ed.), Stanford encyclopedia of philosophy. Stanford: The Metaphysics Research Lab, Stanford University.
Hájek, A. (2009). Interpretations of probability. In E. N. Zalta (Ed.), Stanford encyclopedia of philosophy. Stanford: The Metaphysics Research Lab, Stanford University.
Hawthorne, J. (2008). Inductive logic. In E. N. Zalta (Ed.), Stanford encyclopedia of philosophy. Stanford: The Metaphysics Research Lab, Stanford University.
Hu, Y., Chen, R., & Tzeng, G. (2003). Finding fuzzy classification rules using data mining techniques. Pattern Recognition Letters, 24(1–3), 509–514.
Joyce, J. (2003). Bayes’ Theorem. In E. N. Zalta (Ed.), Stanford encyclopedia of philosophy. Stanford: The Metaphysics Research Lab, Stanford University.
Kaniza, G. (1976). Subjective contours. Scientific American, 234, 48–52.
Meier, A., Schindler, G., & Werro, N. (2008). Fuzzy classification on relational databases. In M. Galindo (Ed.), Handbook of research on fuzzy information processing in databases (Vol. II, pp. 586–614). London: Information Science Reference.
merriam-webster.com. (2012b). Heap. Retrieved from Merriam Webster Online Dictionnary http://www.merriam-webster.com/dictionary/heap
Mill, J. S. (1843). A system of logic. London: John W. Parker, West Strand.
Oberschelp, A. (1994). Allgemeine mengenlehre. Mannheim: Wissenschaftsverlag.
Precht, R. D. (2007). Wer bin ich - und wenn ja wie viele? Eine philosophische reise. MĂĽnchen: Goldmann.
Roubos, J. A., Setnes, M., & Abonyi, J. (2003). Learning fuzzy classification rules from labeled data. Information Sciences, 150(1–2), 77–93.
Russell, B. (1919). Introduction to mathematical philosophy. London: George Allen & Unwin, Ltd.
Shannon, C. (1948). A mathematical theory of communication. The Bell Systems Technical Journal, 27, 379–423, 623–656.
Sorensen, R. (2008). Vagueness. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy. Stanford: The Metaphysics Research Lab, Stanford University.
Vickers, J. (2009). The problem of induction. In E. N. Zalta (Ed.), Stanford encyclopedia of philosophy. Stanford: The Metaphysics Research Lab, Stanford University.
Wang, L., & Mendel, J. (1992). Generating Fuzzy Rules by Learning from Examples. IEEE Transactions on Systems, Man, and Cybernetics, 22(6), 1414–1427.
Weisstein, E. W. (2010a). Conditional probability. Retrieved from MathWorld—A Wolfram Web Resource http://mathworld.wolfram.com/ConditionalProbability.html
Weisstein, E. W. (2010b). Correlation coefficient. Retrieved from MathWorld—A Wolfram Web Resource http://mathworld.wolfram.com/CorrelationCoefficient.html
Witten, I. H., & Frank, E. (2005). Data mining, practical machine learning tools and techniques (2nd ed.). San Francisco: Morgan Kaufmann.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.
Zadeh, L. A. (1975a). Calculus of fuzzy restrictions. In L. A. Zadeh, K.-S. Fu, K. Tanaka, & M. Shimura (Eds.), Fuzzy sets and their applications to cognitive and decision processes. New York: Academic Press.
Zadeh, L. A. (1975b). The concept of a linguistic variable and its application to approximate reasoning. Information Sciences, I(8), 199–251.
Zadeh, L. A. (2008). Is there a need for fuzzy logic. Information Sciences, 178(13), 2751–2779.
Zimmermann, H. J. (1997). Fuzzy data analysis. In O. Kaynak, L. A. Zadeh, B. Turksen, & I. J. Rudas (Eds.), Computational intelligence: Soft computing and fuzzy-neuro integration with applications. Berlin: Springer.
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Kaufmann, M. (2014). Fuzziness and Induction. In: Inductive Fuzzy Classification in Marketing Analytics. Fuzzy Management Methods. Springer, Cham. https://doi.org/10.1007/978-3-319-05861-0_2
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