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International Fuzzy Systems Association World Congress

IFSA/NAFIPS 2019 2019: Fuzzy Techniques: Theory and Applications pp 33–43Cite as

Local Properties of Strengthened Ordered Directional and Other Forms of Monotonicity

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1000))

Abstract

In this study we discuss some of the recent generalized forms of monotonicity, introduced in the attempt of relaxing the monotonicity condition of aggregation functions. Specifically, we deal with weak, directional, ordered directional and strengthened ordered directional monotonicity. We present some of the most relevant properties of the functions that satisfy each of these monotonicity conditions and, using the concept of pointwise directional monotonicity, we carry out a local study of the discussed relaxations of monotonicity. This local study enables to highlight the differences between each notion of monotonicity. We illustrate such differences with an example of a restricted equivalence function.

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Acknowledgments

This work is supported by the project TIN2016-77356-P (AEI/FEDER, UE), by the Public University of Navarra under the project PJUPNA13 and by Slovak grant APVV-14-0013.

Author information

Authors and Affiliations

  1. Public University of Navarra, Pamplona, Spain

    Mikel Sesma-Sara, Laura De Miguel, Javier Fernandez & Humberto Bustince

  2. Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

Authors
  1. Mikel Sesma-Sara
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  2. Laura De Miguel
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  3. Radko Mesiar
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  4. Javier Fernandez
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  5. Humberto Bustince
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Corresponding author

Correspondence to Mikel Sesma-Sara .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, USA

    Ralph Baker Kearfott

  2. Center for Computing Research (CIC), Instituto Politecnico Nacional, Ciudad de Mexico, Mexico

    Ildar Batyrshin

  3. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, AB, Canada

    Marek Reformat

  4. Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA

    Martine Ceberio

  5. Department of Computer Science, University of Texas at El Paso , El Paso, TX, USA

    Vladik Kreinovich

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Sesma-Sara, M., De Miguel, L., Mesiar, R., Fernandez, J., Bustince, H. (2019). Local Properties of Strengthened Ordered Directional and Other Forms of Monotonicity. In: Kearfott, R., Batyrshin, I., Reformat, M., Ceberio, M., Kreinovich, V. (eds) Fuzzy Techniques: Theory and Applications. IFSA/NAFIPS 2019 2019. Advances in Intelligent Systems and Computing, vol 1000. Springer, Cham. https://doi.org/10.1007/978-3-030-21920-8_4

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