ON ( FUZZY ) ISOMORPHISM THEOREMS OF SOFT Γ-HYPERMODULES

To solve complicated problems in economics, engineering, and environment, we cannot successfully use classical methods because of various uncertainties typical for those problems. There are three theories: theory of probability, theory of fuzzy sets, and the interval mathematics which we can consider as mathematical tools for dealing with uncertainties. Uncertainties cannot be handled using traditional mathematical tools but may be dealt with using a wide range of existing theories such as the probability theory, the theory of (intuitionistic) fuzzy sets, the theory of vague sets, the theory of interval mathematics, and the theory of rough sets. One major problem shared by those theories is their incompatibility with the parameterization tools. To overcome these difficulties, Molodtsov [34] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. Molodtsov pointed out several directions for the applications of soft sets. At present, works on the soft set theory are progressing rapidly. Ali et al. [2] proposed some new operations on soft sets. Moreover, Cagman et al. [8] considered soft matrix theory and its decision making. Chen et al. [9] presented a new definition of soft set parametrization reduction, and compared this definition to the related concept of attribute reduction