The Interaction between Fuzzy Subsets and Groupoids
We discuss properties of a class of real-valued functions on a set X2 constructed as finite (real) linear combinations of functions denoted as X,*;μ, where X,* is a groupoid (binary system) and μ is a fuzzy subset of X and where X,*;μx,y≔μx*y-minμx,μy. Many properties, for example, μ being a fuzzy s...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/246285 |
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doaj-90e128ad70de4b948700104123d77d9a2020-11-24T21:52:57ZengHindawi LimitedThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/246285246285The Interaction between Fuzzy Subsets and GroupoidsSeung Joon Shin0Hee Sik Kim1J. Neggers2Department of Physics, University of Michigan, Ann Arbor, MI 48109, USADepartment of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Republic of KoreaDepartment of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, USAWe discuss properties of a class of real-valued functions on a set X2 constructed as finite (real) linear combinations of functions denoted as X,*;μ, where X,* is a groupoid (binary system) and μ is a fuzzy subset of X and where X,*;μx,y≔μx*y-minμx,μy. Many properties, for example, μ being a fuzzy subgroupoid of X,*, can be restated as some properties of X,*;μ. 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 BinX;□ for example.http://dx.doi.org/10.1155/2014/246285 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Seung Joon Shin Hee Sik Kim J. Neggers |
| spellingShingle |
Seung Joon Shin Hee Sik Kim J. Neggers The Interaction between Fuzzy Subsets and Groupoids The Scientific World Journal |
| author_facet |
Seung Joon Shin Hee Sik Kim J. Neggers |
| author_sort |
Seung Joon Shin |
| title |
The Interaction between Fuzzy Subsets and Groupoids |
| title_short |
The Interaction between Fuzzy Subsets and Groupoids |
| title_full |
The Interaction between Fuzzy Subsets and Groupoids |
| title_fullStr |
The Interaction between Fuzzy Subsets and Groupoids |
| title_full_unstemmed |
The Interaction between Fuzzy Subsets and Groupoids |
| title_sort |
interaction between fuzzy subsets and groupoids |
| publisher |
Hindawi Limited |
| series |
The Scientific World Journal |
| issn |
2356-6140 1537-744X |
| publishDate |
2014-01-01 |
| description |
We discuss properties of a class of real-valued functions on a set X2 constructed as finite (real) linear combinations of functions denoted as X,*;μ, where X,* is a groupoid (binary system) and μ is a fuzzy subset of X and where X,*;μx,y≔μx*y-minμx,μy. Many properties, for example, μ being a fuzzy subgroupoid of X,*, can be restated as some properties of X,*;μ. 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 BinX;□ for example. |
| url |
http://dx.doi.org/10.1155/2014/246285 |
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