Buradasınız

Bulanõk ve Yaklaşõmlõ Kümeler (series C)

Bulanõk and Yaklaşõmlõ Sets (series C)

Journal Name:

Publication Year:

Abstract (2. Language): 
In this study, fuzzy set theory proposed by Zadeh and rough set theory proposed by Pawlak are introduced. These set theories deal with several fundamentally different type of uncertainty which can not be properly characterized and investigated mathematically by the classical logic. After given the fundamental concept of these two theories we investigate some important relationships between them. We then define the upper approximations of fuzzy sets with respect to a direct product of fuzzy normal subgroups and studied their properties.
Abstract (Original Language): 
Bu çalõşmada, klasik mantõğõn tanõmlayamadõğõ belirsiz kavramlarõn matematiksel olarak ifade edilebilmesine olanak sağlayan Zadeh’in bulanõk kümeler (fuzzy sets) teorisi ve Pawlak’õn yaklaşõml õ kümeler (rough sets) teorisi üzerinde durulmuştur. Bu iki teoriyle ilgili temel kavramlar verildikten sonra aralarõndaki bazõ önemli ilişkiler incelenmiştir. Daha sonra bulanõk normal altgruplarõn direkt çarpõmõna göre bulanõk kümelerin üst yaklaşõmõ tanõmlanarak bazõ özellikleri verilmiştir.
13-25

REFERENCES

References: 

[1] Bonikowaski, Z., Algebraic structures of rough sets, Rough sets, Fuzzy sets and Knowledge
Discovery, Springer-Verlag, Berlin(1995)
[2] Bismas B., Nanda S., Rough groups and rough subgroups, Bull. Polish Acad. Sci. Math.
42(1994) 251-254.
[3] Dubois, D. and Prade H., Editorial, Fuzzy Sets and Syst. 122 (2001) 1-3.
[4] Dubois, D. and Prade, H., Fuzzy Sets and Systems: Theory and Applications, Academic Press,
New York. (1980).
[5] Iwinski, T., Algebraic approach to rough sets, Bull. Polish Acad. Sci. Math. 35 (1987) 673-
683.
[6] Jiashang, J., Congxin, W. and Degang, C., The product structure of fuzzy rough sets on a
group and the rough T- fuzzy group, Information Science,(Baskõda)(2004)
[7] Kaufmann, A. and Gupta, M.M., Introduction to Fuzzy Arithmetic Theory and Applications,
Van Nostrand Rienhold, New York(1991).
[8] Klir, J. G, and Folger, T. A., Fuzzy Sets, And Information, New Jersey(1988).
[9] Kumar, R., Fuzzy Algebra I, University of Delhi, Publ. Division(1993).
[10] Kuroki, N., Rough ideals in semigroups, Inform. Sci. 100 (1997) 139-163.
[11] Kuroki, N., Nang P. P., The lower and upper approximations in fuzzy group, Inform. Sci.,
90(1996) 203-220.
[12] Kuroki, N., Mordeson J. N., Structure of rough sets and rough groups, J. Fuzzy Math., 5(1)
(1997) 183-191.
[13] Maji P.K., Biswas R. and Roy A.R., Soft set theory, Computers and Mathematics with
Applications 45(2003) 555-562.
[14] Molodtsov, D., Soft set theory-first results, Computers Malath. Applic. 37 (1999) 19-31.
[15] Morsi, N.N. and Yakout, M.M., Axiomatics for fuzzy rough sets, Fuzzy Sets and Systems, 100,
327-342(1998).
[16] Pawlak, Z., Rough sets, Int. J. of Information and Computer Sciences, 11, 5, 341-356 (1982).
[17] Pomykala, J. and Pomykala, J.A., The stone algebra of rough sets, Bull. Polish Acad. Sci.
Math. 36 (1988) 495-508.
[18] Wakczak B., Massart D. L., Rough set theory, Chemometrics and Intelligent Laboratory
Systems, 47(1999) 1-16.
[19] Zadeh, L., Fuzzy sets, Information and Control, 8, 338-353(1965).
[20] Zimmermann, H.J., Fuzzy Set Theory and Its Applications, Kluwer (1991).

Thank you for copying data from http://www.arastirmax.com