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A note on the correlation and information energy of interval-valued fuzzy numbers. (English)
Fuzzy Sets Syst. 123, No.1, 89-92 (2001).
This short, technical note shows that several results given in [{\it G. Wang} and {\it X. Li}, Fuzzy Sets Syst. 103, 169-175 (1999; Zbl 1017.94034)] concerning parameters of interval-valued fuzzy numbers are not valid in their necessity parts. All these errors are caused by a false claim of Wang and Li that an upper semicontinuous non-negative function $f$ defined on $[a,b]$ with zero Riemann integral over $[a,b]$ is necessarily the zero function on $[a,b]$. The present paper brings several counterexamples violating original results of Wang and Li. Moreover, it indicates the way for correcting all violated results, restricting all considerations to the interval-valued fuzzy numbers with continuous lower and upper fuzzy sets.
Reviewer: R.Mesiar (Bratislava)