Interval-valued T-spherical fuzzy set (IVTSFS) handles uncertain and vague information by discussing their membership degree (MD), abstinence (AD), non-membership (NMD), refusal (RD). MD, AD, NMD, RD are defined in terms of closed subintervals [0, 1] that reduce loss compared to the (TSFS), which takes crisp values from intervals; hence, some may be lost. The purpose this manuscript is develop ...