Lattice valued intuitionistic fuzzy sets
Tadeusz Gerstenkorn ; Andreja Tepavĉević
Open Mathematics, Tome 2 (2004), p. 388-398 / Harvested from The Polish Digital Mathematics Library

In this paper a new definition of a lattice valued intuitionistic fuzzy set (LIFS) is introduced, in an attempt to overcome the disadvantages of earlier definitions. Some properties of this kind of fuzzy sets and their basic operations are given. The theorem of synthesis is proved: For every two families of subsets of a set satisfying certain conditions, there is an lattice valued intuitionistic fuzzy set for which these are families of level sets.

Publié le : 2004-01-01
EUDML-ID : urn:eudml:doc:268799
@article{bwmeta1.element.doi-10_2478_BF02475236,
     author = {Tadeusz Gerstenkorn and Andreja Tepav\^cevi\'c},
     title = {Lattice valued intuitionistic fuzzy sets},
     journal = {Open Mathematics},
     volume = {2},
     year = {2004},
     pages = {388-398},
     zbl = {1060.03074},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475236}
}
Tadeusz Gerstenkorn; Andreja Tepavĉević. Lattice valued intuitionistic fuzzy sets. Open Mathematics, Tome 2 (2004) pp. 388-398. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475236/

[1] K. Atanassov: “Intuitionistic fuzzy sets”,Fuzzy Sets and Systems, Vol.20, (1986),pp.87–96. http://dx.doi.org/10.1016/S0165-0114(86)80034-3 | Zbl 0631.03040

[2] K. Atanassov, S. Stoeva: “IntuitionisticL-fuzzy sets”,Cybernetics and Systems Research, Vol. 2, R. Trappl (ed.) Etsevier Science Publishers B.V., North-Holland, (1984), pp. 539–540.

[3] K. Atanassov:Intuitionistic fuzzy sets, Theory and Applications, Physica-Verlag, Springer Company, Heilderberg, New York, 1999.

[4] B. A. Davey, H.A. Priestly.Introduction to lattices and order, Cambridge University Press, 1990.

[5] T. Gerstenkorn, J. Mańko: “Bifuzzy probabilistic sets”Fuzzy Sets and Systems,Vol.71, (1995),pp.207–214. http://dx.doi.org/10.1016/0165-0114(94)00254-5 | Zbl 0845.60004

[6] T. Gerstenkorn, J. Mańko: “Bifuzzy probability of intuitionistic fuzzy sets”,Notes on Intuitionistic Fuzzy Sets, Vol. 4 (1998), pp. 8–14.

[7] T. Gerstenkorn, J. Mańko: “On probability and independence in intuitionistic fuzzy set theory”,Notes on Intuitionistic Fuzzy Sets, Vol. 1, (1995), pp. 36–39. | Zbl 0850.60002

[8] T. Gerstenkorn, A. Tepavĉević: “Lattice valued bifuzzy sets, New Logic for the New Economy”, VIII SIGEF Congress Proceedings, ed. by G. Zollo, pp. 65–68.

[9] B. Ŝeŝelja, A. Tepavĉević: “Representation of lattices by fuzzy sets”,Information Sciences, Vol. 79, (1993), pp. 171–180. | Zbl 0798.06013

[10] B. Ŝeŝelja, A. Tepavĉević, G. Vojvodić: “L-fuzzy sets and codes”,Fuzzy sets and systems, Vol. 53, (1993), pp. 217–222. http://dx.doi.org/10.1016/0165-0114(93)90175-H | Zbl 0782.94012

[11] B. Ŝeŝelja, A. Tepavĉević: “Completion of ordered structures by cuts of fuzzy sets, an overview”,Fuzzy Sets and Systems,Vol.136 (2003),pp.1–19. http://dx.doi.org/10.1016/S0165-0114(02)00365-2 | Zbl 1020.06005

[12] B. Ŝeŝelja, A. Tepavĉević: “Representing ordered structures by fuzzy sets, an overview”,Fuzzy Sets and Systems,Vol.136, (2003),pp.21–39. http://dx.doi.org/10.1016/S0165-0114(02)00366-4 | Zbl 1026.03039