Approximations of π

Computer science

Mathematical optimization

Mathematics

Applied mathematics

Fuzzy logic

Algorithm

Heuristic

Artificial intelligence

Information Sciences

A model of decision-theoretic three-way approximations of fuzzy sets that can calculate a pair of interpretable thresholds (α, β) by combining shadowed sets with three-way decisions was established by Deng. In that model, the significant contribution is that the value 0.5, which denotes a membership grade with the highest uncertainty, is used to replace the uncertain region with the interval [0,1] in shadowed sets. From the principle of the minimum decision cost, although the lowest overall cost can be achieved precisely in some data distributions based on the value 0.5, there is a difference between the obtained overall cost and the least cost in some cases. Therefore, in this paper, based on Deng’s model, the concept of a general three-way approximation of a fuzzy set is proposed to replace 0.5 with a variable value c(0 < c < 1). Then, the loss function composed of the elevation and reduction operations in shadowed sets is established. In addition, the relationship between the required thresholds (α, β) wit...

A general model of decision-theoretic three-way approximations of fuzzy sets based on a heuristic algorithm