Abstract
In Wu Fuzzy Systems and Mathematics 3:94–99, 2012, the author introduced concepts of \(\alpha \)-remote neighborhood mapping and \(\alpha \)-quasi uniform, and obtained many good results in \(\alpha \)-quasi uniform spaces. This chapter will further investigate properties of \(\alpha \)-remote neighborhood mapping, and give some characterizations of \(\alpha \)-quasi uniforms. Based on this, this chapter also introduces concept of \(\alpha \)-P.Q. metric, and establishes the relations between \(\alpha \)-quasi uniforms and \(\alpha \)-P.Q. metrics.
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Acknowledgments
Thanks to the support by: 1. National Science Foundation (No.10971125). 2. Science Foundation of Guangdong Province (No. 01000004) 3. The construct program of the key discipline in Hunan University of Science and Engineering.
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Wu, XY., Xie, LL., Bai, SZ. (2014). Characterizations of \(\alpha \)-Quasi Uniformity and Theory of \(\alpha \)-P.Q. Metrics. In: Cao, BY., Nasseri, H. (eds) Fuzzy Information & Engineering and Operations Research & Management. Advances in Intelligent Systems and Computing, vol 211. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38667-1_14
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DOI: https://doi.org/10.1007/978-3-642-38667-1_14
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