Abstract
Two different but related measurement problems are considered within the fuzzy set theory. The first problem is the membership measurement find the second is property ranking. These two measurement problems are combined and two axiomatizations of fuzzy set theory are obtained. In the first one, the indifference is transitive but in the second one this drawback is removed by utilizing interval orders.
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Bilgiç, T., Türkşen, I.B. (1997). Measurement-theoretic frameworks for fuzzy set theory. In: Martin, T.P., Ralescu, A.L. (eds) Fuzzy Logic in Artificial Intelligence Towards Intelligent Systems. FLAI 1995. Lecture Notes in Computer Science, vol 1188. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62474-0_19
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