Research Article
A way to obtain 2-uninorm on bounded lattice from uninorms defined on subintervals of bounded lattice
Abstract
In this paper, a way to obtain 2-uninorm on bounded lattice
from U1 disjunctive uninorm on [0, k] and U2 conjunctive uninorm on [k,1] is presented.
When the conditions disjunctive of U1
or conjunctive of U2 drop, it is showed that this method is
invalid. Additionally, some properties of this construction method are
investigated.
Keywords
References
- P. Akella, C-sets of n-uninorms, Fuzzy Sets and Systems, 160 (2009), 1-21.
- P. Akella, Structure of n-uninorms, Fuzzy Sets and Systems, 158 (2007), 1631-1651.
- G. Birkhoff, Lattice Theory, 3 rd edition, Providence, 1967.
- P. Dryga´s, E. Rak, Distributivity equation in the class of 2-uninorms, Fuzzy Sets and Systems, 2016 (291), 82-97.
- U. Ertu˘grul, F. Karac¸al, R. Mesiar, Modified ordinal sums o ¨ f triangular norms and triangular conorms on bounded lattices, International Journal of Intelligent Systems, 30 (2015) 807-817.
- U. Ertu˘grul, M. N. Kesicio˘glu, F. Karac¸al, Ordering base ¨ d on uninorms, Information Sciences, 330 (2016), 315-327.
- U. Ertu˘grul, M. N. Kesicio˘glu, F. Karac¸al, Ordering base ¨ d 2-uninorms on bounded lattices, New Trends in Mathematical Sciences, in press.
- J. Fodor, R. Yager, and A. Rybalov, Structure of uninorms, Internata. J. Uncertain. Fuzziness Knowledge-Based Systems, 5 (1997), 411-427.
- M. Grabisch, J.-L. Marichal, R. Mesiar, E. Pap, Aggregation Functions, Cambridge University Press, 2009.
- F. Karac¸al, M.A. ˙Ince, R. Mesiar, Nullnorms on bounded lattices, Information Sciences, 325 (2015), 227-236.
- F. Karac¸al, R. Mesiar, Uninorms on bounded lattices, Fuzzy Sets and Systems, 261 (2015), 33-43.
- R. R. Yager, A. Rybalov, Uninorm aggregation operators, Fuzzy Sets and Systems, 80 (1996), 111-120.
- R. R. Yager, Uninorms in fuzzy system modelling, Fuzzy Sets and Systems, 122 (2001), 167-175.
Year 2017,
Volume: 5 Issue: 2, 1 - 9, 30.03.2017
Abstract
References
- P. Akella, C-sets of n-uninorms, Fuzzy Sets and Systems, 160 (2009), 1-21.
- P. Akella, Structure of n-uninorms, Fuzzy Sets and Systems, 158 (2007), 1631-1651.
- G. Birkhoff, Lattice Theory, 3 rd edition, Providence, 1967.
- P. Dryga´s, E. Rak, Distributivity equation in the class of 2-uninorms, Fuzzy Sets and Systems, 2016 (291), 82-97.
- U. Ertu˘grul, F. Karac¸al, R. Mesiar, Modified ordinal sums o ¨ f triangular norms and triangular conorms on bounded lattices, International Journal of Intelligent Systems, 30 (2015) 807-817.
- U. Ertu˘grul, M. N. Kesicio˘glu, F. Karac¸al, Ordering base ¨ d on uninorms, Information Sciences, 330 (2016), 315-327.
- U. Ertu˘grul, M. N. Kesicio˘glu, F. Karac¸al, Ordering base ¨ d 2-uninorms on bounded lattices, New Trends in Mathematical Sciences, in press.
- J. Fodor, R. Yager, and A. Rybalov, Structure of uninorms, Internata. J. Uncertain. Fuzziness Knowledge-Based Systems, 5 (1997), 411-427.
- M. Grabisch, J.-L. Marichal, R. Mesiar, E. Pap, Aggregation Functions, Cambridge University Press, 2009.
- F. Karac¸al, M.A. ˙Ince, R. Mesiar, Nullnorms on bounded lattices, Information Sciences, 325 (2015), 227-236.
- F. Karac¸al, R. Mesiar, Uninorms on bounded lattices, Fuzzy Sets and Systems, 261 (2015), 33-43.
- R. R. Yager, A. Rybalov, Uninorm aggregation operators, Fuzzy Sets and Systems, 80 (1996), 111-120.
- R. R. Yager, Uninorms in fuzzy system modelling, Fuzzy Sets and Systems, 122 (2001), 167-175.
There are 13 citations in total.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Article |
| Authors | |
| Publication Date | March 30, 2017 |
| IZ | https://izlik.org/JA86JL42KW |
| Published in Issue | Year 2017 Volume: 5 Issue: 2 |