Affiliations: [a] School of Mathematics and Computer, Wuyi University, Wuyishan, Fujian, China
| [b] Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul, Korea
| [c] Department of Mathematics, University of Alabama, Tuscaloosa, AL, USA
Correspondence:
[*]
Corresponding author. Hee Sik Kim, Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea. Tel.: +82 2 2290 0897; Fax: +82 2 2281 0019; E-mail: [email protected].
Note: [1] The first author is partly supported by the Fujian and Nanping Science and Technology Foundations (2016Y0077, 2013J01017, 2011Y0049, N2011WZ09).
Abstract: In this paper, the authors extend the theory of groupoids already developed for semigroups (Bin (X) , □) in a growing number of research papers with X a set and Bin (X) the set of groupoids (binary systems) defined on X to the generalizations: fuzzy (sub)groupoids (largely known as used here) and hyperfuzzy (sub)groupoids (largely novel as used here), showing (1) there are natural processes and (2) new results of interest can be obtained, including the existence of new parameters which on their collapse from hyperfuzzy (sub)groupoids to groupoids yield known results in some cases and new ones otherwise as well. Overall, the future for successful research in this area looks quite promising as noted in the paper itself.
