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Fuzzy modifiers at the core of interpretable fuzzy systems

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Abstract

Fuzzy modifiers associated with linguistic hedges have been introduced by L.A. Zadeh at the early stage of approximate reasoning and they are fundamental elements in the management of interpretable systems. They can be regarded as a solution to the construction of fuzzy sets slightly different from original ones. We first present the main definitions of modifiers based on mathematical transformations of membership functions, mainly focusing on so-called post-modifiers and pre-modifiers, as well as definitions based on fuzzy relations. We show that measures of similarity are useful to evaluate the proximity between the original fuzzy sets and their modified form and we point out links between modifiers and similarities. We then propose an overview of application domains which can take advantage of fuzzy modifiers, for instance analogy-based reasoning, rule-based systems, gradual systems, databases, machine learning, image processing, and description logic. It can be observed that fuzzy modifiers are either constructed in a prior way by means of formal definitions or automatically learnt or tuned, for instance in hybrid systems involving genetic algorithm-based methods.
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hal-01221751 , version 1 (28-10-2015)

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Bernadette Bouchon-Meunier, Christophe Marsala. Fuzzy modifiers at the core of interpretable fuzzy systems. Fifty Years of Fuzzy Logic and its Applications, 326, Springer, pp.51-63, 2015, Studies in Fuzziness and Soft Computing, ⟨10.1007/978-3-319-19683-1_4⟩. ⟨hal-01221751⟩
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