Fuzzy Gamma Modules Based on Fuzzy Binary Operations
Min Zhou, Daijing Xiang and Jianming Zhan
By different way from Rosenfeld’s approach (J. Math. Anal. Appl. 35 (1971) 512–517), we investigate the fuzziness of the gamma module operations by fuzzy binary operations, and establish a new kind of gamma modules structure on a crisp set. To establish the theories of fuzzy gamma modules based on fuzzy binary operations, the concepts, as well as some related properties, of fuzzy gamma submodules, fuzzy gamma quotient modules and gamma homomorphisms are investigated. In particular, by constructing proper fuzzy gamma modules, we prove three isomorphism theorems about fuzzy gamma modules.
Keywords: Fuzzy binary operation, Fuzzy gamma module, Fuzzy gamma submodule, Fuzzy gamma quotient module, Fuzzy gamma homomorphism (isomorphism).
2000 Mathematics Subject Classification: 16Y60; 13E05; 03G25.