SELECTIVE GROUPOIDS AND FRAMEWORKS INDUCED BY FUZZY SUBSETS

Document Type: Research Paper

Authors

1 Department of Mathematics, Chungbuk National University, Cheongju, 28644, Korea

2 Research Institute for Natural Sci., Department of Mathematics, Hanyang University, Seoul, 04763, Korea

3 Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U. S. A.

Abstract

In this paper, we show that every selective groupoid induced by a fuzzy subset is a pogroupoid, and we discuss several properties in quasi ordered sets by introducing the notion of a framework.

Keywords


[1] R. K. Bandaru, K. P. Shum and N. Ra , Fuzzy ideals of implication groupoids, Italian J.
Pure and Appl. Math., 34 (2015), 277{290.
[2] G. Gratzer, General lattice theory, Springer, New York, 1978.
[3] J. S. Han, H. S. Kim and J. Neggers, Strong and ordinary d-algebras, J. Mult.-Valued Logic
& Soft Computing, 16 (2010), 331{339.
[4] D. Kelly and I. Rival, Planar lattices, Canad. J. Math., 27 (1975), 636{665.
[5] M. Khan, M. Shakeel, M. Gulistan and S. Rashid, Generalized fuzzy bi-ideals of order right
modular groupoids, Int. J. Algebra and Statistics, 4 (2015), 46{56.
[6] H. S. Kim and J. Neggers, The semigroups of binary systems and some perspectives, Bull.
Korean Math. Soc., 45 (2008), 651{661.
[7] J. Neggers, Partially ordered sets and groupoids, Kyungpook Math. J., 16 (1976), 7{20.
[8] J. Neggers and H. S. Kim, Modular posets and semigroups, Semigroup Forum, 53 (1996),
57{62.
[9] J. Neggers and H. S. Kim, On d-algebras, Math. Slovaca, 49 (1999), 19{26.
[10] J. Neggers and H. S. Kim, Algebras associated with posets, Demonstratio Math., 34 (2001),
13{23.
[11] J. Neggers and H. S. Kim, Fuzzy posets on sets, Fuzzy Sets and Sys., 117 (2001), 391{402.
[12] J. Neggers and H. S. Kim, Fuzzy pogroupoids, Information Sci., 175 (2005), 108{119.
[13] S. J. Shin, H. S. Kim and J. Neggers, On Abelian and related fuzzy subsets of groupoids, The
Scienti c World J., Article ID 476057, 2013 (2013), 5 pages.
[14] S. J. Shin, H. S. Kim and J. Neggers, The intersection between fuzzy subsets and groupoids,
The Scienti c World J., Article ID 246285, 2014 (2014), 6 pages.
[15] L. Zadeh, Fuzzy Sets, Inform. and Control, 8 (1965), 338{353.