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Emergency decision making is critically important for countries or communities to enhance the effectiveness and validity of the emergency response, which can greatly lower environmental damage, casualties, and economic loss. In the case of emergency decision evaluation, the essential problems that arise serious inexactness, fuzziness, and ambiguity. Interval-valued Pythagorean fuzzy set (IVPFS), portrayed by membership and non-membership with the interval form, is an effective and flexible way to seize indeterminacy. In this paper, primarily, a novel score function for an interval-valued Pythagorean fuzzy number is initiated for managing some comparative issues. Then, a new distance measure for IVPFSs with multiple parameters is studied for solving the counter-intuitive situations. The interesting properties among the developed similarity measures, distance measures, and entropy have also been derived. Then, the objective weights of diverse attributes are ascertained by a novel entropy approach. Also, we explore the combination weight, which can reveal both objective preference and subjective preference. In addition, two interval-valued Pythagorean fuzzy decision making methods based on weighted distance-based approximation and multiparametric similarity measure are presented. Later, the validity of the algorithms is illustrated by a mine emergency decision making issue with the influence of diverse parameters on the ordering. Finally, a comparison with some existing decision making methods has been executed by the counter-intuitive phenomena and discrimination problems for verifying their effectiveness.
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