Affiliations: [a] School of Mathematics and Computer Science, Changsha University of Science and Technology, Changsha, Hunan 410114, P.R. China. langguangming1984@126.com | [b] College of Science, Central South University of Forestry and Technology, Changsha, Hunan 410004, P.R. China and College of Information System and Management, National University of Defense Technology, Changsha, Hunan 410073, P.R. China
Correspondence:
[†]
Address for correspondence: Changsha University of Science and Technology, Changsha, Hunan 410114, P.R. China
Note: [*] The authors thank the anonymous reviewers for their professional comments and valuable suggestions.
Abstract: In practical situations, interval-valued fuzzy sets are of interest because fuzzy sets of this kind are frequently encountered. In this paper, motivated by the needs for solving imprecise problems, we generalize the concept of shadowed sets for understanding interval-valued fuzzy sets and provide a solution to compute a pair of thresholds by searching for a balance of uncertainty. Then we present three-way approximations of interval-valued fuzzy sets and a formulation for calculating the pair of thresholds using single-valued loss functions. We also compute three-way approximations of interval-valued fuzzy sets using interval-valued loss functions. Afterwards, we employ several examples to illustrate that how to take an action for an object with an interval-valued membership grade using an interval-valued loss function.
