Affiliations: [a] School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong, P.R. China | [b] Department of Mathematics, South China University of Technology, Guangzhou, Guangdong, P.R. China
Correspondence:
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Corresponding author. Ze Gu, School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong, P.R. China. Tel.: +86 18027805050; Fax: +86 07582716503;E-mail: guze528@sina.com.
Note: [1] Supported in part by the NNSF of China (No. 11571119). E-mail: xilintang@21cn.com.
Abstract: In this paper, we study the least strongly regular equivalence relation containing a given binary relation on a semihypergroup. Also, we discuss the least fuzzy strongly regular equivalence relation greater than or equal to a given fuzzy relation on a semihypergroup. As an application of the results of this paper, the fundamental relation β∗ and the least fuzzy strongly regular equivalence relation βf∗ on a semihypergroup are obtained. Furthermore, we respectively give descriptions of the greatest strongly regular equivalence relation contained in a given equivalence relation containing β∗ and the greatest fuzzy strongly regular equivalence relation less than or equal to a given fuzzy equivalence relation greater than or equal to βf∗ on a semihypergroup.
