| Decision makers can use different fuzzy sets to describe complex decision information.In some cases,probabilistic hesitant fuzzy information can avoid the loss of data and information,and describe the uncertainty of the problem more reasonably.This thesis proposes several decision-making methods for the multi-attribute decision-making problem under probabilistic hesitation and fuzzy information.Aiming at the multi-attribute decision-making problem where the attribute value is the probability hesitant fuzzy element and the attribute weight is unknown,a multi-attribute decision-making method based on the probability hesitant fuzzy Einstein weighted geometric average operator is proposed.Combining the Einstein operation and the probability hesitation fuzzy element,defines the probability hesitation fuzzy Einstein sum,product,and idempotent algorithm,and proposes four probability hesitation fuzzy Einstein geometric mean operators.Calculate attribute weights by establishing an optimization model.A multi-attribute decision-making method based on probability hesitant fuzzy Einstein weighted geometric average operator is proposed,and the rationality of the method is illustrated by an example of coal mine rescue decision-making.Aiming at the multi-attribute decision-making problem where the attribute value is the probabilistic hesitant fuzzy element,a probabilistic hesitant fuzzy multi-attribute decision-making method based on the ELECTRE method is proposed.Define the fuzzy entropy,hesitation entropy and total entropy of the probabilistic hesitation fuzzy element.Under the condition that the attribute weight is unknown,a method for calculating the attribute weight is given.A probabilistic hesitation fuzzy ELECTRE multi-attribute decision-making method is proposed,and the rationality of the method is illustrated through an example of urban planning decision-making.Aiming at the multi-attribute decision-making problem whose attribute value is the Pythagorean probability hesitant fuzzy element,a Pythagorean probabilistic hesitant fuzzy multi-attribute decision-making method based on TODIM method is proposed.Define the Pythagorean probability hesitation fuzzy set,and give the algorithm of the Pythagorean probability hesitation fuzzy element.Define the distance measure and measurement function of the Pythagorean probability hesitation fuzzy element.According to the maximum deviation method,the attribute weight is calculated by establishing an optimization model.A Pythagorean probabilistic hesitant fuzzy TODIM multi-attribute decision-making method with unknown attribute weights is proposed,and the rationality of the method is illustrated by an example of the decision-making of sewage treatment plan. |
