A novel MADM technique based on extended power generalized Maclaurin symmetric mean operators under probabilistic dual hesitant fuzzy setting and its application to sustainable suppliers selection

• A novel probabilistic dual hesitant fuzzy entropy is proposed. • Some novel probabilistic dual hesitant fuzzy distance measures are proposed. • The PDHFEPGMSM and PDHFWEPGMSM operators are proposed. • A novel MADM technique is proposed based on the PDHFWEPGMSM operator. • Case study of a SSS is presented to show the potentiality of the proposed technique. Sustainable suppliers selection is a typical multi-attribute decision-making (MADM) problem. MADM is a common problem in the field of decision-making, which is full of uncertainty and fuzziness. As a novel extension of fuzzy set (FS), probabilistic dual hesitant fuzzy set (PDHFS) can more fully and comprehensively express the uncertain and fuzzy information in MADM problems. In order to more effectively integrate the information of PDHFS, in this study, depend on extended power average (EPA) and generalized Maclaurin symmetric mean (GMSM) operators, probabilistic dual hesitant fuzzy extended power average generalized Maclaurin symmetric mean (PDHFEPMSM) operator and its weighted form (PDHFWEPMSM) which can consider the extremely data and the interrelationship among all decision attributes are defined and studied. Evidently, the novel proposed operators can obtain more accurate results than other existing methods. In addition, some precious properties and some special cases of these operators are discussed and studied. Afterwards, a novel PDHF MADM technique is developed based on the PDHFWEPGMSM and applied to MADM problem with probabilistic dual hesitant fuzzy elements (PDHFEs). Finally, a numerical example of sustainable suppliers selection is built to illustrate the practicality of the proposed MADM technique. Sensitivity analysis of parameters and further comparative analysis attest the flexibility and validity of the proposed MADM technique. The method presented in this paper can effectually solve the MADM problems which the decision-making information is expressed by PDHFEs and the attributes are interactive.