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How to Elicit Complex-Valued Fuzzy Degrees

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Applications of Fuzzy Techniques (NAFIPS 2022)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 500))

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Abstract

In traditional fuzzy logic, an expert’s degree of certainty in a statement is described by a single number from the interval [0, 1]. However, there are situations when a single number is not sufficient: e.g., a situation when we know nothing and a situation in which we have a lot of arguments for a given statement and an equal number of arguments against it are both described by the same number 0.5. Several techniques have been proposed to distinguish between such situations. The most widely used are interval-valued techniques, where we allow the expert to describe his/her degree of certainty by a subinterval of the interval [0, 1]. Eliciting an interval-valued degree is straightforward. On the other hand, in many practical applications, another technique has been useful: complex-valued fuzzy degrees. Unfortunately, in the complex-valued case, there is no direct way to elicit such degrees. In this paper, we explain a reasonable natural way to elicit these degrees indirectly.

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Acknowledgement

This work was supported in part by the National Science Foundation grants 1623190 (A Model of Change for Preparing a New Generation for Professional Practice in Computer Science), and HRD-1834620 and HRD-2034030 (CAHSI Includes), and by the AT &T Fellowship in Information Technology.

It was also supported by the program of the development of the Scientific-Educational Mathematical Center of Volga Federal District No. 075-02-2020-1478, and by a grant from the Hungarian National Research, Development and Innovation Office (NRDI).

The authors are thankful to the anonymous referees for valuable suggestions.

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Correspondence to Vladik Kreinovich .

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Bokati, L., Kosheleva, O., Kreinovich, V. (2023). How to Elicit Complex-Valued Fuzzy Degrees. In: Dick, S., Kreinovich, V., Lingras, P. (eds) Applications of Fuzzy Techniques. NAFIPS 2022. Lecture Notes in Networks and Systems, vol 500. Springer, Cham. https://doi.org/10.1007/978-3-031-16038-7_1

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