The Interaction between Fuzzy Subsets and Groupoids

Shin, Seung Joon; Kim, Hee Sik; Neggers, J.

The Interaction between Fuzzy Subsets and Groupoids

dc.contributor.author	Shin, Seung Joon
dc.contributor.author	Kim, Hee Sik
dc.contributor.author	Neggers, J.
dc.contributor.other	University of Michigan
dc.contributor.other	Hanyang University
dc.contributor.other	University of Alabama Tuscaloosa
dc.date.accessioned	2023-09-28T19:38:49Z
dc.date.available	2023-09-28T19:38:49Z
dc.date.issued	2014
dc.description.abstract	We discuss properties of a class of real-valued functions on a set X-2 constructed as finite (real) linear combinations of functions denoted as [(X, ); mu], where (X, ) is a groupoid (binary system) and mu is a fuzzy subset of X and where [(X., ); mu] (x, y) := mu (x y) - min {mu(x), mu(y)}. Many properties, for example, mu being a fuzzy subgroupoid of (X, ), can be restated as some properties of [(X, ); mu]. Thus, the context provided opens up ways to consider well-known concepts in a new light, with new ways to prove known results as well as to provide new questions and new results. Among these are identifications of many subsemigroups and left ideals of (Bin (X); square) for example.	en_US
dc.format.medium	electronic
dc.format.mimetype	application/pdf
dc.identifier.citation	Shin, S. J., Kim, H. S., & Neggers, J. (2014). The Interaction between Fuzzy Subsets and Groupoids. In The Scientific World Journal (Vol. 2014, pp. 1–6). Hindawi Limited. https://doi.org/10.1155/2014/246285
dc.identifier.doi	10.1155/2014/246285
dc.identifier.uri	https://ir.ua.edu/handle/123456789/11675
dc.language	English
dc.language.iso	en_US
dc.publisher	Hindawi
dc.rights.license	Attribution 4.0 International (CC BY 4.0)
dc.rights.uri	https://creativecommons.org/licenses/by/4.0/
dc.subject	Multidisciplinary Sciences
dc.title	The Interaction between Fuzzy Subsets and Groupoids	en_US
dc.type	Article
dc.type	text