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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]

Traffic on highways has increased significantly in the past few years. Consequently, this has caused delays for the drivers in reaching their final destination and increased the highway's congestion level. Many options have been proposed to ease these issues. In this paper, a model of the highway drivers' population was built based on several factors, including the behavioral patterns of the drivers, like drivers' time flexibility to reach the destination, their carpool eligibility, and their tolerance to pay the toll price, in addition to the traffic information from the system. A fuzzy logic decision-making model is presented to emulate how drivers would choose the lane to use based on the aforementioned factors and the current congestion levels of all the lanes on the highway. The presented model, along with the simulation results from applying the model to different simulation scenarios, show the usefulness of such a model in predicting an optimal toll value. Such optimal value would reduce congestion on the highway at one end while maximizing the revenue for the toll company. [ABSTRACT FROM AUTHOR]