TY  - JOUR
AU  - Coroianu, Lucian
AU  - Fullér, Róbert
TI  - Nguyen type theorem for extension principle based on a joint possibility distribution
JF  - INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
J2  - INT J APPROX REASON
VL  - 95
PY  - 2018
SP  - 22
EP  - 35
PG  - 14
SN  - 0888-613X
DO  - 10.1016/j.ijar.2018.01.007
UR  - https://m2.mtmt.hu/api/publication/3329725
ID  - 3329725
N1  - Department of Mathematics and Computer Science, University of Oradea, Romania            
            Department of Informatics, Széchenyi István University, Győr, Hungary            
            Institute of Applied Mathematics Óbuda University, Budapest, Hungary            
            Cited By :8            
            Export Date: 22 June 2022            
            CODEN: IJARE            
            Correspondence Address: Coroianu, L.; Department of Mathematics and Computer Science, Romania; email: lcoroianu@uoradea.ro
AB  - In this paper, first we prove that making abstraction of the output obtained from the interactive extension principle based on a joint possibility distribution, in the case of unimodal fuzzy numbers and when the function that generates the operation is continuous and strictly increasing in each argument restricted to the support of each fuzzy number used in the process, then we can use joint possibility distributions with the property that the left/right side of the output is obtained from the convolution of the values in the left/right side of these fuzzy numbers. Then, considering joint possibility distributions with the aforementioned property, we find an Nguyen type characterization of the level sets of the output based on interactive extension principle, in terms of the level sets of the fuzzy numbers used in the process. These two key results complete well-known results obtained in the case of Zadeh's extension principle and also in the case of triangular norm-based extension principle. As an interesting corollary, in the special case of unimodal fuzzy numbers, the Nguyen theorem can be used to present a new proof concerning necessary and sufficient conditions on the equality of the outputs based on joint possibility distributions, respectively based on Zadeh's extension principle.
LA  - English
DB  - MTMT
ER  - 

TY  - JOUR
AU  - Fullér, Róbert
AU  - Tibor, Keresztfalvi
TI  - On generalization of Nguyen's theorem
JF  - FUZZY SETS AND SYSTEMS
J2  - FUZZY SET SYST
VL  - 41
PY  - 1991
IS  - 3
SP  - 371
EP  - 374
PG  - 4
SN  - 0165-0114
DO  - 10.1016/0165-0114(91)90139-H
UR  - https://m2.mtmt.hu/api/publication/1114689
ID  - 1114689
AB  - The goal of this paper is to generalize certain results of Nguyen [1] (concerning the α-cuts of two-place functions defined by the Zadeh’s extension principle) to the case of extended two-place functions defined via a sup-t-norm convolution.
LA  - English
DB  - MTMT
ER  -