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Interpretability of linguistic variables: a formal account. (English) Zbl 1249.94093

Summary: This contribution is concerned with the interpretability of fuzzy rule-based systems. While this property is widely considered to be a crucial one in fuzzy rule-based modeling, a more detailed formal investigation of what “interpretability” actually means is not available. So far, interpretability has most often been associated with rather heuristic assumptions about shape and mutual overlapping of fuzzy membership functions. In this paper, we attempt to approach this problem from a more general and formal point of view. First, we clarify what the different aspects of interpretability are in our opinion. Consequently, we propose an axiomatic framework for dealing with the interpretability of linguistic variables (in Zadeh’s original sense) which is underlined by examples and application aspects, such as, fuzzy systems design aid, data-driven learning and tuning, and rule base simplification.

MSC:

94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)
68T05 Learning and adaptive systems in artificial intelligence
68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
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