- Volume 34 Issue 3
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THE LATTICE OF INTERVAL-VALUED FUZZY IDEALS OF A RING
- Lee, Keon-Chang (Department of Computer Science, Dongshin University) ;
- Hur, Kul (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University) ;
- Lim, Pyung-Ki (Division of Mathematics and Informational Statistics, and Nanoscale Science and Technology Institute, Wonkwang University)
- Received : 2012.05.24
- Accepted : 2012.08.01
- Published : 2012.09.25
We investigate the lattice structure of various sublattices of the lattice of interval-valued fuzzy subrings of a given ring. We prove that a special class of interval-valued fuzzy ideals of a ring. Finally, we show that the lattice of interval-valued fuzzy ideals of R is not complemented[resp. has no atoms(dual atoms)].
Supported by : Wonkwang University
- G.Birkoff, Lattice Theory, A.M.S. Colliquium Publication Vol.XXV(1967).
- R.Biswas, Rosenfeld's fuzzy subgroups with interval-valued membership functions, Fuzzy set and systems 63(1995) 87-90.
- M.Cheong and K.Hur, Interval-valued fuzzy ideals and bi-ideals of a semigroup, Honam Math.J.33(4)(2011).
- J.Y.Choi, S.R.Kim and K.Hur, Interval-valued smooth topological spaces, Honam Math.J.32(4)(2010), 711-738. https://doi.org/10.5831/HMJ.2010.32.4.711
- H.W.Kang and K.Hur, Interval-valued fuzzy subgroups and rings, Honam. Math. J. 32.(4)(2010), 593-617 https://doi.org/10.5831/HMJ.2010.32.4.593
- T.K.Mondal and S.K.Samanta, Topology of interval-valued fuzzy sets, Indian J.Pure Appl.Math.30(1)(1999)20-38
- L.A.Zadeh, Fuzzy sets, Inform and Control 8, 338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X
- L.A.Zadeh, The concept of a linguistic variable and its application to approximate reasoning I, Inform.Sci 8(1975) 199-249 https://doi.org/10.1016/0020-0255(75)90036-5