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Generalized Fuzzy Sets and Fuzzy Relations

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International Conference on Oriental Thinking and Fuzzy Logic

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 443))

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Abstract

In classical fuzzy set theory, a fuzzy set is a membership function which associates with each element a real number in [0, 1], a fuzzy relation is a function which associates with each pair of elements a real number in [0, 1]. In the present paper, we generalize the above two concepts by associating with each set a real number in [0, 1], and associating with each pair of sets a real number in [0, 1], respectively. We then give a series of properties for these two types of generalized concepts. We also show that a generalized fuzzy relation can be induced by a classical fuzzy relation, which shows the communication of our generalized fuzzy concepts with the classical fuzzy theory.

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Acknowledgments

This article is completed during the first author being a visiting scholar in Jiangnan University. Research was partially supported by the domestic senior visiting scholar program in higher occupation colleges in Jiangsu province (2014FX075).

The authors are grateful to the referees for their valuable suggestions, which result in the present version of the paper. This paper was also supported by the Natural Science Foundation of Jiangsu Province (No. BK20151117).

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Authors and Affiliations

  1. Wuxi City College of Vocational Technology, 214153, Jiangsu, China

    Yan-cai Zhao

  2. School of Science, Jiangnan University, 214122, Jiangsu, China

    Yan-cai Zhao, Zu-hua Liao, Teng Lu & Juan Tong

Authors
  1. Yan-cai Zhao
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  2. Zu-hua Liao
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  3. Teng Lu
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  4. Juan Tong
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Corresponding authors

Correspondence to Yan-cai Zhao or Zu-hua Liao .

Editor information

Editors and Affiliations

  1. Guangzhou Vocational Collg. Sci. & Tech., Guangzhou, China

    Bing-Yuan Cao

  2. West Texas A&M University, Canyon,TX,USA, Liaoning Technical University, Fuxin, China

    Pei-Zhuang Wang

  3. Foreign Affairs Office, National Defense University, Beijing, China

    Zeng-Liang Liu

  4. School of Math and Info. Science, Guangzhou University, Guangzhou, China

    Yu-Bin Zhong

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Zhao, Yc., Liao, Zh., Lu, T., Tong, J. (2016). Generalized Fuzzy Sets and Fuzzy Relations. In: Cao, BY., Wang, PZ., Liu, ZL., Zhong, YB. (eds) International Conference on Oriental Thinking and Fuzzy Logic. Advances in Intelligent Systems and Computing, vol 443. Springer, Cham. https://doi.org/10.1007/978-3-319-30874-6_2

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  • DOI: https://doi.org/10.1007/978-3-319-30874-6_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30873-9

  • Online ISBN: 978-3-319-30874-6

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