Publication Date



Technical Report: UTEP-CS-23-18a

To appear in Proceedings of the 20th World Congress of the International Fuzzy Systems Association IFSA'2023,, Daegu, South Korea, August 20-24, 2023.


Intuitively, interval-values fuzzy degrees are more adequate for representing expert uncertainty than the traditional [0,1]-based ones. Indeed, the very need for fuzzy degrees comes from the fact that experts often cannot describe their opinion not in terms of precise numbers, but by using imprecise ("fuzzy") words from natural language like "small". In such situations, it is strange to expect the same expert to be able to provide an exact number describing his/her degree of certainty; it is more natural to ask this expert to mark the whole interval (or even, more generally, a fuzzy set of possible degrees). In spite of this intuitive adequacy, and in spite of several successful applications of interval-valued degrees, most applications of fuzzy techniques are still based on the traditional [0,1]-based degrees. According to researcher who studied this puzzling phenomenon, the problem is that while people are accustomed to marking their opinion on a numerical scale, most people do not have any experience of using interval. To ease people's use of interval-valued degrees, we propose to take into account that the set of all interval-valued degrees is, in some reasonable sense, equivalent to the set of colors -- thus, we can represent degrees as appropriate colors. This idea can be naturally extended to Z-numbers -- and it also provides an additional argument why interval-valued degrees are more adequate, at least more adequate in the analysis of complex phenomena.

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