On axiomatic characterization of fuzzy approximation operators. III. The fuzzy diamond and fuzzy box based cases

For pt.II, 31st IEEE International Symposium on Multiple-Valued Logic (2001). In three previous papers we have developed axiomatic characterizations of approximation operators which: firstly, are defined by classical diamond and box operator of the modal logic (Thiele, 2000); secondly, are defined by the "fuzzified" diamond and box operator applied to crisp sets, i.e. by using the concept of fuzzy rough set (Thiele, 2000); thirdly, are defined by the classical diamond and box operator applied to fuzzy sets, i.e. by using the concepts of rough fuzzy sets (Thiele, 2001). The paper presented is the last one concerning these ideas, i.e. we take the "fuzzified" diamond and box operator and apply these to fuzzy sets. So we define a further type of fuzzy approximation operators and develop an axiomatic characterization of such operators.