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

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Chapter 12

BELIEF, PLAUSIBILITY AND PROBABILITY MEASURES ON INTERVAL-VALUED TYPE 2 FUZZY SETS

Within last fourty years, Zadeh (1965-2004) has proposed seminal concepts for fuzzy sets, approximate reasoning, Type 2 fuzzy sets, CWW, Computing With Words, and CWP, Computing With Perceptions.

For about twenty years or so, we have shown that the combination of two or more Type 1 fuzzy sets with linguistic connectives, i.e., “AND”, “OR”, etc., generate interval-valued Type 2 fuzzy sets (Türkimageen, 1982-2002) due to the break down of classical equivalences in fuzzy theory.

Shortly after the introduction of fuzzy sets Dempster (1967) proposed upper and lower ...

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