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Refined Neutrosophy and Lattices vs. Pair Structures and YinYang Bipolar Fuzzy Set

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  • Florentin Smarandache

    (Mathematics Department, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA)

Abstract

In this paper, we present the lattice structures of neutrosophic theories. We prove that Zhang-Zhang’s YinYang bipolar fuzzy set is a subclass of the Single-Valued bipolar neutrosophic set. Then we show that the pair structure is a particular case of refined neutrosophy, and the number of types of neutralities (sub-indeterminacies) may be any finite or infinite number.

Suggested Citation

  • Florentin Smarandache, 2019. "Refined Neutrosophy and Lattices vs. Pair Structures and YinYang Bipolar Fuzzy Set," Mathematics, MDPI, vol. 7(4), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:353-:d:223179
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    References listed on IDEAS

    as
    1. Javier Montero & Humberto Bustince & Camilo Franco & J. Tinguaro Rodríguez & Daniel Gómez & Miguel Pagola & Javier Fernandez & Edurne Barrenechea, 2014. "Paired structures and bipolar knowledge representation," MSAP Working Paper Series 06_2014, University of Copenhagen, Department of Food and Resource Economics.
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    Cited by:

    1. Chao Zhang & Deyu Li & Xiangping Kang & Yudong Liang & Said Broumi & Arun Kumar Sangaiah, 2020. "Multi-Attribute Group Decision Making Based on Multigranulation Probabilistic Models with Interval-Valued Neutrosophic Information," Mathematics, MDPI, vol. 8(2), pages 1-21, February.

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