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This paper aims to present Bipolar valued probabilistic hesitant fuzzy sets (BVPHFSs) by combining bipolar fuzzy sets and probabilistic hesitant fuzzy sets (PHFSs). PHFSs are a strong version of hesitant fuzzy sets (HFSs) in terms of evaluated as probabilistic of each element. Probabilistic hesitant fuzzy sets (PHFSs) are a set structure that argues that each alternative should be evaluated probabilistically. In this framework, the proposed cluster allows probabilistic evaluation of decision- makers' opinions as negative. Thus, this case proposes flexibility about selection of an element and aids to overcome with noise channels. Furthermore, some new aggregation operators are discussed called bipolar valued probabilistic hesitant fuzzy weighted average operator (BVPHFWA), Generalized bipolar valued probabilistic hesitant fuzzy weighted average operator (GBVPHFWA), bipolar valued probabilistic hesitant fuzzy weighted geometric operator (BVPHFWG), Generalized bipolar valued probabilistic hesitant fuzzy weighted geometric operator (GBVPHFWG), bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric operator (BVPHFHWAG) and Generalized bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric (GBVPHFHWAG) and some basic properties are presented. A score function is defined ranking alternatives. Moreover, two different algorithms are put forward with helping to TOPSIS method and by using aggregation operators over BVPHFSs. The validity of proposed operators are analyzed with an example and results are compared in their own. [ABSTRACT FROM AUTHOR]

This research work proposes a novel approach for multi stage decision analysis (MSDA) using innovative concepts of cubic intuitionistic fuzzy set (CIFS) theory. The paper introduces CIF-technique for order preference by similarity to ideal solution (TOPSIS) as a robust method for MSDA problems, particularly for the diagnosis of epilepsy disorders. To achieve this goal, new similarity measures (SMs) are developed for CIFS, including the Cosine angle between two vectors, a new distance measure, and the Cosine function, presented as three different types of Cosine similarity measures. The proposed CIF-TOPSIS approach is found to be suitable for precise value performance ratings and is expected to be a viable approach for case studies in the diagnosis of epilepsy disorders. The efficiency and reliability of the proposed MSDA methods is efficiently carried through numerical examples and comparative analysis. [ABSTRACT FROM AUTHOR]