The problem of delay-range-dependent (DRD) stability analysis for continuous time Takagi–Sugeno (T–S) fuzzy time-delay systems (TDSs) is addressed in this paper. An improved DRD stability criterion is proposed in an linear matrix inequality (LMI) framework by constructing an appropriate delay-product-type (DPT) Lyapunov–Krasovskii functional (LKF) to make use of Bessel-Legendre polynomial based relaxed integral inequality. The modification in the proposed LKF along with the judicious choice of integral inequalities helps to obtain a less conservative delay upper bound for a given lower bound. The efficacy of the obtained stability conditions is validated through the solution of three numerical examples.