Narrow Results

In the present paper, the author introduces the notion of fuzzy IC-bags and does some characterizations of them. The concepts of fuzzy base sets, base equivalent fuzzy IC-Bags, cardinally equispaced fuzzy IC-Bags, and cardinally equivalent fuzzy IC-Bags have been developed. The types of peak elements, and the concerned types of peak membership grades have been discussed. It is observed that the collection of any particular type of peak elements together with their membership grades actually form fuzzy bags. A set of operations on fuzzy IC-Bags have been defined and some propositions have been proved. We note that under the conditions of uncertainty, where the counts of objects are not fixed, then the interval counts can occur with different fuzzy membership grades for each particular object in the collection, and the framework for fuzzy IC-Bags provides us with the opportunity to justify and model the organized complexity as a part of the associated intolerance embedded in the subjective patterns.

Many databases in real life involve pairs of the form (item,quantity). This kind of data can be characterized using the theory of bags. We present a general framework for extracting useful knowledge from bag databases using different types of patterns. Here we present different approaches for the task of discovering fuzzy association rules and gradual dependencies in bag databases.

The concept of IF-Bags was introduced by the author as a generalization of the notion of fuzzy bags. In case of IF-Bags, each element is associated with a crisp bag drawn from the Cartesian product I×I of the unit interval I = [0, 1]. This paper introduces a method for quantitatively measuring the similarity between two IF-Bags. As a consequence, the notions of a measure of coherence and a measure of hesitancy between two IF-Bags are also introduced. It is observed that the measure of coherence and the measure of hesitancy between the IF-Bags can be regarded as crucial factors in case of scenario evaluation as well as grading that relates to knowledge representation in soft decision analysis problems.