DefinePK

Abstract

To cope with human opinion in real-life problems with the help of the truth degree (TD), abstinence degree (AD), falsity degree (FD), and refusal degree (RD), the notion of T-spherical fuzzy set (TSFS) is developed as a replacement of the picture fuzzy set (PFS) which fails to handle information due to the strict condition on the TD, AD, FD, and RD. TSFS allows any value for TD, AD, FD, and RD from the with a parameter. Several aggregation operators (AOs) exist for the aggregation of the information among which the Heronian mean (HM) operator (HMO) is the significant one. This manuscript aims to discuss the theory of HMOs in a T-spherical fuzzy (TSF) environment that will allow us to model human opinion based on complex information in several practical scenarios. We develop the generalized TSF (GTSFHM) operator, generalized TSF weighted HM (GTSFWHM) operator, TSF geometric HM (TSFGHM) operator, and TSF weighted geometric HM (TSFWGHM) operator. Further, the basic properties of the aggregation of the HMOs in the TSF environment are also discussed. Moreover, an enterprise resource planning problem based on the multi-attribute decision-making (MADM) procedure is investigated given the TSF HMOs followed by a comprehensive example showing the applicability of the proposed HMOs. Some exceptional cases of the proposed HMOs are investigated and a comparison of the newly developed TSF HMOs with previously developed HMOs is examined where the advantages of the new HMOs are discussed.