The Interaction between Fuzzy Subsets and Groupoids
- Title
- The Interaction between Fuzzy Subsets and Groupoids
- Author
- 김희식
- Issue Date
- 2014-04
- Publisher
- HINDAWI PUBLISHING CORPORATION, 410 PARK AVENUE, 15TH FLOOR, #287 PMB, NEW YORK, NY 10022 USA
- Citation
- ?e Scientific World Journal, Volume 2014, Article ID 246285, 6 pages
- 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.
- URI
- https://www.hindawi.com/journals/tswj/2014/246285/abs/http://hdl.handle.net/20.500.11754/51682
- ISSN
- 1537-744X
- DOI
- 10.1155/2014/246285
- Appears in Collections:
- COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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