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Association Measures on Sets with Involution and Similarity Measure

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Recent Developments and New Direction in Soft-Computing Foundations and Applications

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 342))

Abstract

The methods of construction of non-statistical association measures on the sets with involution operation and similarity measure are proposed. The Pearson’s correlation coefficient is obtained as a particular case of the class of association measures associated with Lukasiewicz t-conorm. Examples of association measures on [0, 1] and on the set of fuzzy sets are considered.

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Acknowledgment

The results have been partially supported by the projects SIP 20151589 and 20162204 of Instituto Politécnico Nacional, Mexico.

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Authors and Affiliations

  1. Centro de Investigación en Computación (CIC-IPN), Instituto Politécnico Nacional, DF, Mexico

    I. Batyrshin

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  1. I. Batyrshin
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Correspondence to I. Batyrshin .

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Editors and Affiliations

  1. University of California, Berkeley, USA

    Lotfi A. Zadeh

  2. Tech. of the Republic of Azerbaijan, Ministry of Communications Info., Baku, Azerbaijan

    Ali M. Abbasov

  3. Machine Intelligence Institute, New Rochelle, New York, USA

    Ronald R. Yager

  4. Azerbaijan Technical University, Baku, Azerbaijan

    Shahnaz N. Shahbazova

  5. University of Alberta, Edmonton, Alberta, Canada

    Marek Z. Reformat

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Batyrshin, I. (2016). Association Measures on Sets with Involution and Similarity Measure. In: Zadeh, L., Abbasov, A., Yager, R., Shahbazova, S., Reformat, M. (eds) Recent Developments and New Direction in Soft-Computing Foundations and Applications. Studies in Fuzziness and Soft Computing, vol 342. Springer, Cham. https://doi.org/10.1007/978-3-319-32229-2_16

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  • DOI: https://doi.org/10.1007/978-3-319-32229-2_16

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32227-8

  • Online ISBN: 978-3-319-32229-2

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