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Fuzziness and Induction

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Book cover Inductive Fuzzy Classification in Marketing Analytics

Part of the book series: Fuzzy Management Methods ((FMM))

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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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Authors and Affiliations

  1. Lucerne University of Applied Sciences and Arts Engineering and Architecture, Horw, Switzerland

    Michael Kaufmann

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  1. Michael Kaufmann
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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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