Weighted interval-valued dual-hesitant fuzzy sets and its application in teaching quality assessment

Abstract

As a robust generalization to fuzzy set, the interval-valued dual-hesitant fuzzy set (IVDHFS) was put forward, which provided several possible membership and non-membership interval values to be associated with a specific substance. But IVDHFS does not couple the membership and non-membership values with their corresponding weights/importance degrees to assess a variable, which is irrational. To circumvent this issue, this study introduces the weighted interval-valued dual-hesitant fuzzy set (WIVDHFS) which describe the membership and non-membership values in the form of interval along with their weights. These assigned weights give more detail about the level of agreeness and disagreeness and thereby can help the decision makers (DMs) to obtain precise, rational, and consistent decision consequences. After introducing the pioneer notion of WIVDHFS, several related terms, viz. connected weighted interval-valued dual-hesitant element (WIVDHFE), score function, and accuracy function are defined. Using Archimedean t-norm and t-conorm, some basic operational laws for WIVDHFEs are constructed. Next, to aggregate WIVDHFEs, two types of aggregation operators based on Archimedean t-norm and t-conorm, namely the generalized weighted interval-valued dual-hesitant fuzzy-weighted averaging operator and the generalized weighted interval-valued dual-hesitant fuzzy-weighted geometric operator are designed along with their relevant properties. Meanwhile, some of their special cases and relationships are also explored. On the basis of special cases, a novel multi-criteria group decision-making approach under weighted interval-valued dual-hesitant fuzzy environment is then constructed. Finally, an application case about teaching quality assessment is presented, and some analyses and comparisons are provided to validate the proposed approach.