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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]

Intuitionistic fuzzy (IF) information aggregation in multi-criteria decision making (MCDM) is a substantial stream that has attracted significant research attention. There are various IF aggregation operators have been suggested for extracting more informative data from imprecise and redundant raw information. However, some of the aggregation techniques that are currently being applied in IF environments are non-monotonic with respect to the total order, and suffer from high computational complexity and inflexibility. It is necessary to develop some novel IF aggregation operators that can surpass these imperfections. This paper aims to construct some IF aggregation operators based on Yager's triangular norms to shed light on decision-making issues. At first, we present some novel IF operations such as Yager sum, Yager product and Yager scalar multiplication on IF sets. Based on these new operations, we propose the IF Yaeger weighted geometric operator and the IF Yaeger ordered weighted geometric operator, and prove that they are monotone with respect to the total order. Then, the focus on IF MCDM have motivated the creation of a new MCDM model that relies on suggested operators. We show the applicability and validity of the model by using it to select the most influential worldwide supplier for a manufacturing company and evaluate the most efficient method of health-care disposal. In addition, we discuss the sensitivity of the proposed operator to decision findings and criterion weights, and also analyze it in comparison with some existing aggregation operators. The final results show that the proposed operator is suitable for aggregating both IF information on "non-empty lattice" and IF data on total orders. [ABSTRACT FROM AUTHOR]

Linguistic q-rung orthpair fuzzy sets (Lq-ROFSs) can facilitate describing the uncertainty and the vagueness information existing in the real world. Based on the advantages of Lq-ROFSs, this paper innovatively puts forward a new method to solve the multi-attribute group decision-making (MAGDM) problems when the attribute weight is completely unknown, and proves the feasibility and effectiveness of this method through illustrative examples. Firstly, we propose the linguistic q-rung orthopair fuzzy generalized power average (Lq-ROFGPA) operator, which considers not only the importance of the data itself, but also the interaction between the data, and prove its properties. In particular, the linguistic q-rung orthopair fuzzy weighted generalized power average (Lq-ROFWGPA) operator takes into account the weight between data, which can better aggregate evaluation information. Then, we introduce decision making trial and evaluation laboratory (DEMATEL) method of the linguistic q-rung orthpair fuzzy numbers (Lq-ROFNs) to analyze the causal relationship and key elements of complex systems. Based on DEMATEL method, we further develop a weight model to calculate the attribute weights, which can make up for the deficiency which is the influence of the interaction between attributes that the existing weight determination method for Lq-ROFNs does not consider. Finally, we present a new MAGDM method based on the Lq-ROFWGPA operator and DEMATEL method. Further, several practical examples are given to illustrate the effectiveness and superiority of this new method in comparison with other existing MAGDM methods. [ABSTRACT FROM AUTHOR]