Shadowed sets of type‐II: Representing and computing shadowiness in shadowed sets

Shadowed sets were developed to interpret and determine the required pair of thresholds, which resolves the issue with Zadeh's proposal about a three‐way approximation of fuzzy sets. However, a serious shortcoming of shadowed sets is that they are not capable of coming to grips with the degree of shadowiness (or doubt) associated with the elements of a shadowed set, especially the elements in the doubtful zone (i.e., shadow region) and as a result, all the elements in the shadow region are shown no commitment during the process of decision making. This paper proposes an alternative construct that keeps record of the degree of doubt associated with the elements in a shadowed set. It aims at introducing, discussing the concepts of shadowed sets of type‐II, and studying their related operations. Shadowed sets of type‐II provide a capable framework that despite localizing the uncertainty associated with fuzzy sets; adheres to the gradual transition of membership grades of the elements in the doubtful zone.