Some generalized q‐rung orthopair fuzzy Einstein interactive geometric aggregation operators with improved operational laws

Abstract

The q-rung orthopair sets (q-ROFSs) is an extended version of conventional orthopair fuzzy sets, such as intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs). The most appealing feature of q-ROFSs is that they provide a wider range of reasonable membership grades and offer decision makers (DMs) more leeway in expressing their legitimate perceptions. The q-rung orthopair fuzzy numbers (q-ROFNs) play a vital role in computational intelligence, machine learning, neural network, and artificial intelligence. We develop numerous generalized aggregation operators (AOs) for information fusion of q-ROFNs to address some drawbacks of existing AOs. For this objective, we enhance the existing AOs by adding pairs of hesitation within the membership functions, and as a result, we introduce new operational rules for q-ROFNs utilizing Einstein norm operations. Based on suggested operational laws, we introduce new AOs namely “q-rung orthopair fuzzy Einstein interactive weighted geometric operator,” “q-rung orthopair fuzzy Einstein interactive ordered weighted geometric operator,” “generalized q-rung orthopair fuzzy Einstein interactive weighted geometric operator,” “generalized q-rung orthopair fuzzy Einstein interactive ordered weighted geometric operator,” and “generalized q-rung orthopair fuzzy Einstein interactive hybrid geometric operator.” Then, certain special cases of proposed AOs are explored and their some essential characteristics are described. A new multicriteria decision-making (MCDM) approach is devised with the help of suggested AOs for modeling uncertainties in the real-life problems. Additionally, a practical application of proposed MCDM approach is presented. Moreover, the comparison analysis, sensitivity analysis and authenticity analysis of proposed MCDM approach with existing approaches is also presented to discuss the feasibility, authenticity, and superiority of the proposed method.