Decision-theoretic rough sets-based three-way approximations of interval-valued fuzzy sets
This work addresses uncertainty handling in fuzzy set theory for applications like data analysis, but it appears incremental as it extends existing rough set methods to interval-valued contexts.
The paper tackles the problem of approximating interval-valued fuzzy sets by developing three-way approximations using decision-theoretic rough sets, with methods including shadowed sets and error-based formulations to compute thresholds for decision-making.
In practical situations, interval-valued fuzzy sets are frequently encountered. In this paper, firstly, we present shadowed sets for interpreting and understanding interval fuzzy sets. We also provide an analytic solution to computing the pair of thresholds by searching for a balance of uncertainty in the framework of shadowed sets. Secondly, we construct errors-based three-way approximations of interval-valued fuzzy sets. We also provide an alternative decision-theoretic formulation for calculating the pair of thresholds by transforming interval-valued loss functions into single-valued loss functions, in which the required thresholds are computed by minimizing decision costs. Thirdly, we compute errors-based three-way approximations of interval-valued fuzzy sets by using interval-valued loss functions. Finally, we employ several examples to illustrate that how to take an action for an object with interval-valued membership grade by using interval-valued loss functions.