A granulation-interpolation computing approach for constructing a collection of fuzzy sets

Interval interpretation and membership elicitation are still two uncertain issues in fuzzy set theory, although there have been some studies proposed. In this paper, a granulation-interpolation (GrIp) computing approach which constructs a population of fuzzy sets is proposed in an attempt to address these issues. Granulation is a function for producing a collection of support intervals of fuzzy sets, and the representative data points or knots are determined in these intervals. Interpolation, a curve fitting technique, elicits the membership functions crossing these knots within the support intervals. The numerical results show how different parameters form different distribution patterns in the fuzzy sets collections. Different patterns can satisfy different requirements in the applications. The advantage of this new model is the small number of parameters required for two straightforward algorithms to efficiently construct a series of ordinal fuzzy sets for a linguistic variable. A particular application shows the usability and flexibility, where the patterns of the distribution are describable and scalable by only a few parameters. The proposed model is an ideal tool for specialists to develop a class of fuzzy sets from the group view rather than the classical approaches from the individual view.