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A Natural Formalization of Changing-One’s-Mind Leads to Square Root of “Not” and to Complex-Valued Fuzzy Logic

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Explainable AI and Other Applications of Fuzzy Techniques (NAFIPS 2021)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 258))

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Abstract

We show that a natural formalization of the process of changing one’s mind leads to such seemingly non-intuitive ideas as square root of “not” and complex-valued fuzzy degrees.

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Acknowledgments

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). 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.

The authors are greatly thankful to Scott Dick for his encouragement, and to the anonymous referees for their valuable suggestions.

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Authors and Affiliations

  1. University of Texas at El Paso, 500 W. University, El Paso, TX, 79968, USA

    Olga Kosheleva & Vladik Kreinovich

Authors
  1. Olga Kosheleva
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  2. Vladik Kreinovich
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Corresponding author

Correspondence to Vladik Kreinovich .

Editor information

Editors and Affiliations

  1. Purdue University, West Lafayette, IN, USA

    Julia Rayz

  2. Purdue University, West Lafayette, IN, USA

    Victor Raskin

  3. University of Alberta, Edmonton, AB, Canada

    Scott Dick

  4. University of Texas at El Paso, El Paso, TX, USA

    Vladik Kreinovich

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Kosheleva, O., Kreinovich, V. (2022). A Natural Formalization of Changing-One’s-Mind Leads to Square Root of “Not” and to Complex-Valued Fuzzy Logic. In: Rayz, J., Raskin, V., Dick, S., Kreinovich, V. (eds) Explainable AI and Other Applications of Fuzzy Techniques. NAFIPS 2021. Lecture Notes in Networks and Systems, vol 258. Springer, Cham. https://doi.org/10.1007/978-3-030-82099-2_17

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