Operations for Real-Valued Bags and Bag Relations
Sadaaki Miyamoto · European Society for Fuzzy Logic and Technology Conference · 2009
A generalization of bags is proposed and fundamen- tal operations are described. That is, a real-valued bag is proposed which is a straightforward generalization of the traditional bags, but is necessary for complementation, and s-norm and t-norm opera- tions. We mainly describe how complementation and s-norms are related. As a result a duality theorem between s-norm and t-norm is obtained. R-bag relations with max-s norm composition and max- t norm composition are also proposed. Further generalization that includes fuzzy bags and real-valued bags having membership of a region in a plane is moreover discussed.