论文信息 - On Fuzzy Spaces and Fuzzy Group Theory

On Fuzzy Spaces and Fuzzy Group Theory

Abstract The concept of fuzzy space is introduced. This concept corresponds to the concept of the universal set in the ordinary case. The algebra of fuzzy spaces and fuzzy subspaces is studied. Using the concept of fuzzy space and fuzzy binary operation, a new approach to study fuzzy group theory is given. This approach can be considered as a generalization and reformulation of the Rosenfeld theory of fuzzy subgroups. Therefore, it is an active tool to develop the theory of fuzzy groups.

K. A. Dib

[1] J. M Anthony,et al. Fuzzy groups redefined , 1979 .

[2] Chris J. Hinde,et al. Inference of fuzzy relational tableaux from fuzzy exemplifications , 1983 .

[3] Salvatore Sessa,et al. On fuzzy subgroups and fuzzy ideals under triangular norms , 1984 .

[4] Ladislav J. Kohout,et al. Applications of Fuzzy sets to Systems Analysis, C.V. Negoita, D.A. Ralescu, in: Interdisciplinary Systems Research, 11. Birkhäuser Verlag, Basel and Stuttgart (1975), 191, Sons, Inc., New York.) , 1976 .

[5] P. Das. Fuzzy groups and level subgroups , 1981 .

[6] B. Schweizer,et al. Statistical metric spaces. , 1960 .

[7] Howard Sherwood,et al. A characterization of fuzzy subgroups , 1982 .

[8] Nabil L. Youssef,et al. A new approach to fuzzy groupoids , 1992 .

[9] Wang-jin Liu,et al. Fuzzy invariant subgroups and fuzzy ideals , 1982 .

[10] Nabil L. Youssef,et al. Fuzzy Cartesian product, fuzzy relations and fuzzy functions , 1991 .

[11] Mustafa Akgül,et al. Some properties of fuzzy groups , 1988 .

[12] Howard Sherwood,et al. Products of fuzzy subgroups , 1983 .