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An Ontological and Epistemological Perspective of Fuzzy Set Theory by I. Burhan Türksen

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Chapter 3

MEASUREMENT OF MEMBERSHIP

In this section, assignment and/or acquisition of membership values and hence membership functions are reviewed in order to show that there is an implicit verification of these assignments, i.e., truth qualifications associated with such assignments. Ever science Zadeh (1965) introduced the fuzzy sets one of the main controversies has been on the meaning, i.e., semantics, and measurement of membership functions. In particular, a lack of a consensus on the meaning of membership functions has created confusion. In order to diffuse this cloud of confusion and form a foundation for a sound theory of fuzzy sets and its linkage with truth assignments, a rigorous semantics together with practical elicitation methods ...

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