Three-way decision-based conditional probabilities by opinion scores and Bayesian rules in circular-Pythagorean fuzzy sets for developing sustainable smart living framework.

• The study proposes a decision matrix for SSL frameworks, which are 37 SSL alternatives and 19 assessment criteria. • This paper focuses on the prioritisation of factors of SSL frameworks based on C-PFS-FWZIC. • This study develops TWD-based MCDM to rank and grade SSL frameworks using C-PFS-CPOS and C-PFVs. Sustainable smart living (SSL) is a crucial component in the emergence of smart cities. These cities offer potential solutions to address pressing urban challenges, including traffic congestion, energy consumption and environmental degradation. Recently, many SSL frameworks have been developed based on multiple factors. However, no framework can simultaneously address all these factors. Furthermore, no research has ranked and graded the identified SSL frameworks to select the most sustainable framework. These are considered challenging tasks. To address these challenges, three-way decisions (TWD) and multicriteria decision-making (MCDM) can serve as a valuable solution for city planners and decision-makers. This study introduces TWD-based MCDM as novel conditional probabilities by opinion scores (CPOS) within the context of circular-Pythagorean fuzzy sets (C-PFSs), namely, C-PFSs-CPOS method, to estimate the conditional probability of each alternative. Additionally, Bayesian decision theory within a C-PFS environment is employed to construct the decision thresholds for each alternative. Furthermore, the prioritisation of factors that impact the ranking and grading of SSL frameworks is achieved through the application of the fuzzy-weighted zero-inconsistency (FWZIC) method within a C-PFS environment, namely, C-PFS-FWZIC method. A total of 37 SSL frameworks (alternatives) are evaluated on the basis of 19 assessment factors (criteria) distributed in 4 layers. Results show that six alternatives exhibit a high level of sustainability, as evidenced by their position in the positive region, whereas two alternatives consistently fall within the negative region for all σ values. At σ = 0.05 , the remaining SSL framework alternatives are positioned within the boundary region. When σ value increases to a range of 0.55–0.59, TWD is transformed into a two-way decision-making. Sensitivity and correlation analyses are conducted to evaluate the stability and robustness of the proposed methods. [ABSTRACT FROM AUTHOR]