m-Polar Fuzzy Sets: An Extension of Bipolar Fuzzy Sets

Recently, bipolar fuzzy sets have been studied and applied a bit enthusiastically and a bit increasingly. In this paper we prove that bipolar fuzzy sets and [0,1](2)-sets (which have been deeply studied) are actually cryptomorphic mathematical notions. Since researches or modelings on real world problems often involve multi-agent, multi-attribute, multi-object, multi-index, multi-polar information, uncertainty, or/and limit process, we put forward (or highlight) the notion of m-polar fuzzy set (actually, [0,1](m)-set which can be seen as a generalization of bipolar fuzzy set, where m is an arbitrary ordinal number) and illustrate how many concepts have been defined based on bipolar fuzzy sets and many results which are related to these concepts can be generalized to the case of m-polar fuzzy sets. We also give examples to show how to apply m-polar fuzzy sets in real world problems.