Fuzzy bags and application to construction of measures of association between data items in information systems

A bag is a collection of elements in which a symbol can be repeated, and hence diferent from an ordinary set. Fuzzy bags have been proposed by Yager, but the relations and operations therein should be modified so that they are compatible with those for ordinary fuzzy sets. Modified bag relations and basic operations are defined, a number of theoretical properties are shown, and an application to construction of association measures for information items is considered here. An appropriate data structure and an efficient algorithm are discussed.