A fuzzy set based framework for concept of affinity
Moussa Larbani, Chen Yuh-Weh · 2009
The traditional set theory is constructed on the steady state, the bivalent logic and the fixed set boundary. However, the development of fuzzy set or rough set inspires us that an element, which membership degree to a specified set could be multivalent (fuzzy set) and the set boundary could also be undetermined (rough set). No mattering from the scope of traditional set, fuzzy set or rough set, the element is belonged to a specified set or not is assumed as a steady (time-independent) behavior. Thus, we may regard these aforementioned set theories as the time-independent set theories. In this study, we explore the possibility of proposing a time-dependent set theory, which means the relation between two objects we consider it should be time- dependent: we name it the affinity set theory. We present a simple framework for the concept of affinity based on fuzzy set theory. The notion of affinity set is introduced. A new forecasting method based on game theory and affinity set is also presented.