Multiple attribute group decision-making based on novel probabilistic ordered weighted cosine similarity operators with Pythagorean fuzzy information

The cosine similarity measure has been widely studied under different information environments. Generally, average cosine similarity values are used to find the degree of similarity between two sets of elements. This paper proposes some new cosine similarity aggregation operators based on the ordered weighted averaging (OWA) and the probabilistic ordered weighted averaging (POWA) operators. First, we define the generalized Pythagorean fuzzy ordered weighted cosine similarity (GPFOWCS) operator using the generalized ordered weighted averaging (GOWA) operator in the normalization process of the cosine similarity measure. Several mathematical properties, particular cases, and families of the GPFOWCS operator are discussed. Next, the work defines the generalized Pythagorean fuzzy probabilistic ordered weighted cosine similarity (GPFPOWCS) operator that integrates probabilistic information, OWA weighting vector, and Pythagorean fuzzy cosine similarity values in a single formulation. The GPFPOWCS operator satisfies various desirable properties and includes a wide range of particular cases. The further generalizations of GPFOWCS and GPFPOWCS operators are also introduced utilizing the quasi-arithmetic means in the normalization process of the cosine similarity values. Next, a new multiple attribute group decision-making (MAGDM) approach based on the GPFPOWCS operator is formulated in the Pythagorean fuzzy context and illustrated with a numerical example regarding the selection of robots in the Aeronautics company. A comparative study with the existing approach is also presented to demonstrate the superiority and advantage of our formulated method. The experimental results suggest that the proposed cosine similarity aggregation operators provide an ability to the decision-makers for analyzing the final decision in a wide range of scenarios under real-world complex situations.