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Fixed Point Theorems of Fuzzy Integer Value Mappings and Optimization Management to Balance Problem

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Abstract

In this paper, the concepts of supremum and infimum of bounded Fuzzy integer set are given, their existence is proved, and their expressions formula in level set form are set up. Then some fixed point theorems for Fuzzy integer value mapping are obtained, and a balance problem is proposed. And then, using the new theories established by us about Fuzzy integers and Fuzzy integer value mappings, we give two examples (one is about the protection of some animal species whose surviving numbers are declining year by year, and the other one is about sustainable production problems to some kind of renewable energy) to show the optimal management method for the proposed balance problem.

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Acknowledgments

This work is partially supported by the Nature Science Foundation of China (Nos. 61433001 and 61273077).

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Authors and Affiliations

  1. Institute of Operations Research and Cybernetics, Hangzhou Dianzi University, Hangzhou, 310018, China

    Guixiang Wang & Yingying Han

  2. School of Management, Pudan University, Shanghai, 200433, China

    Xinkun Li

Authors
  1. Guixiang Wang
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  2. Yingying Han
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  3. Xinkun Li
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Correspondence to Guixiang Wang.

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Wang, G., Han, Y. & Li, X. Fixed Point Theorems of Fuzzy Integer Value Mappings and Optimization Management to Balance Problem. Int. J. Fuzzy Syst. 19, 829–837 (2017). https://doi.org/10.1007/s40815-016-0211-z

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  • DOI: https://doi.org/10.1007/s40815-016-0211-z

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