Solid waste management (SWM) protects public health, the environment, and limited resources in densely populated and urbanized countries such as Singapore. This work presents an advanced framework for optimizing SWM using advanced mathematical models and decision-making techniques, including the circular $q$-rung orthopair fuzzy set (C $q$-ROFS) for data, combined with the Choquet integral (CI) and logarithmic percentage change-driven objective weighting (LOPCOW) methods, enhanced by the aggregation operators (AOs) circular $q$-rung orthopair fuzzy Einstein Choquet integral weighted averaging (C $q$-ROFECIWA) and circular $q$-rung orthopair fuzzy Einstein Choquet integral weighted geometric (C $q$-ROFECIWG) aggregation operators. By conducting a systematic evaluation, these methods classified different alternatives to SWM, evaluating them according to criteria such as their environmental impact, cost-effectiveness, waste reduction efficiency, feasibility of implementation, health safety, and public acceptance. The operators C $q$-ROFECIWA and C $q$-ROFECIWG perform better than previous approaches in the effective management of multifaceted and dynamic SWM scenarios. The comparison study demonstrates that the integration of these operators with LOPCOW and the Choquet integral offers decision-making conclusions that are more reliable and sustainable. The study conducted in Singapore successfully finds the most feasible SWM alternatives and emphasizes the possibility of implementing more environmentally sustainable practices in the urban environment. This research offers practical insights for policymakers and emphasizes the need to improve and enhance these approaches to improve SWM in various urban environments.

Decision rules are effective tools for managing information and characterizing datasets. As a result, they contribute significantly to fuzzy rough-set theory-based decision-making procedures. Rough set theory (RS) is a robust method for analyzing ambiguity in data. Moreover, cubic bipolar fuzzy sets (CBFS), an extension of bipolar fuzzy sets, can discuss both uncertainty and bipolarity in numerous situations. This article presents the robust decision-making approach named cubic bipolar fuzzy soft rough sets (CBFSRSs) by integrating RS and cubic bipolar fuzzy soft sets. This study explores the construction and fundamental characteristics of a novel approach based on CBFSs. We introduce and examine the concept of rough sets based on CBFSs, develop level sets for CBFSs, and highlight their key properties through illustrative examples. Additionally, we propose a decision-making framework based on CBFSRS that is capable of effectively managing uncertain, conflicting, and imprecise information. This approach demonstrates the potential of CBFSs in enhancing decision-making processes in large data environments. To demonstrate the practical benefit of CBFSRSs in decision-making, we provide an example of how CBFSRS standards might be used in decision-making processes to help decision-makers make well-informed and reasoned decisions. The example shows that the proposed strategies are useful and effective by applying them to real-life problems. It proves that they can handle complex, uncertain, and conflicting information in real decision-making situations.

An $m$-polar fuzzy ( $m$F) model offers a practical framework for decision-making by providing higher flexibility in handling uncertainties and preferences. The ability of $m$F sets to tackle multiple reference points permits for a more nuanced analysis, leading to more accurate results in complex decision scenarios. This study was mainly devoted to introducing three novel aggregation operators (AGOs) for multi-criteria decision-making (MCDM) based on generalized geometric Heronian mean (GGHM) operations comprise the concept of $m$F sets. The presented operators consisted of the weighted $m$F power GGHM (W $m$FPGGHM), ordered weighted $m$F power GGHM averaging (OW $m$FPGGHM), and hybrid $m$F power GGHM (H $m$FPGGHM) operators. Some essential fundamental properties of the proposed AGOs were investigated: idempotency, monotonicity, boundedness, and Abelian property. Furthermore, an algorithm based on the initiated W $m$FPGGHM operators was developed to address diverse daily-life MCDM scenarios. Next, to validate the efficiency of the established algorithm, it was implemented in a daily-life MCDM problem involving urban transportation management. At last, a sensitivity analysis of the initiated AGOs was provided with existing $m$F set-based operators involving Dombi, Yager, and Aczel-Alsina's operations-based AGOs.

This research introduced cubic bipolar neutrosophic sets (CBNSs), a novel framework that significantly enhanced the capabilities of bipolar neutrosophic sets (BNSs) in handling uncertainty and vagueness within data analysis. By integrating bipolarity and cubic sets, CBNSs provide a more comprehensive and accurate representation of information. We have defined key operations for CBNSs and thoroughly investigated their structural properties. Additionally, we have introduced cubic bipolar neutrosophic soft sets (CBNSSs) as a flexible parameterization tool for CBNSs. To validate the practical utility of CBNSs, we conducted a case study in decision-making. Our algorithmic approach effectively addressed the challenges posed by uncertainty and vagueness in the decision-making process. The results of our research unequivocally demonstrated the superiority of CBNSs over existing methods in terms of accuracy, flexibility, and applicability. By offering a more nuanced representation of information, CBNSs provide a valuable tool for researchers and practitioners tackling complex decision problems.

In this paper, we proposed a hybrid $\mathfrak{M}$-polar 3-spherical $\mathcal{Q}$-fuzzy soft set model by integrating $\mathfrak{M}$-polar, 3-spherical, and $\mathcal{Q}$-fuzzy soft sets. The model handles three-dimensional, $\mathfrak{M}$-polar parametrized data. Fundamental operations such as union, intersection, complement, maximum, minimum, direct sum, direct product, and a weighted geometric aggregation operator were defined within the proposed $\mathfrak{M}$-polar 3-spherical $\mathcal{Q}$-fuzzy soft set framework. The new model enhanced flexibility and effectiveness in managing vagueness and uncertainty in complex decision-making problems. An application to artificial intelligence (AI) model selection and multi-criteria decision-making (MCDM) demonstrated the advantages of the proposed framework.

In this work, we introduce the concept of new approximate fuzzy structures, specifically Fermatean $m$-polar fuzzy soft rough sets (FMPFSRSs), a novel hybrid structure that combines soft sets, rough sets, Fermatean fuzzy sets, and $m$-polar fuzzy sets. The proposed FMPFSRS model effectively captures data uncertainty and imprecision through crisp soft and Fermatean $m$-polar fuzzy soft approximation spaces. We establish the fundamental properties of these approximation spaces (demonstrating 92% uncertainty reduction in test cases) and provide illustrative examples. Our medical case study on coronary artery disease diagnosis achieves 89.2% diagnostic accuracy, significantly outperforming traditional fuzzy set approaches (76.5% accuracy) while reducing decision time by 44% (2.3 sec vs 4.1 sec). The methodology classifies patients using multidimensional data analysis with score ( $S=0.725$ for severe cases), precision ( $H=0.650$), and certainty ( $C=0.504$) functions. Clinical validation shows strong parameter sensitivity (cholesterol $\beta =0.42$, $p<0.001$; blood pressure $\beta =0.38$, $p<0.001$), confirming the model's reliability. The framework's versatility is demonstrated through successful application to complex multi-criteria decision-making scenarios in healthcare, with particular effectiveness in handling cases showing 62% inherent data uncertainty.

In this article, we presented two novel approaches for group decision-making (GDM) that were derived from the initiated linguistic $q$-rung orthopair fuzzy Aczel-Alsina weighted arithmetic (L $q$-ROFAAWA) aggregation operator (AgOp) using linguistic $q$-rung orthopair fuzzy numbers (L $q$-ROFNs). To introduce these GDM techniques, we first defined new operational laws for L $q$-ROFNs based on Aczel-Alsina $t$-norm and $t$-conorm. The developed scalar multiplication and addition operations of L $q$-ROFNs addressed the limitations of operations when $q=1$. The first proposed GDM methodology assumed that both experts' weights and attribute weights were fully known, while the second technique assumed that both sets of weights were entirely unknown. We also discussed properties of L $q$-ROFNs under the L $q$-ROFAAWA operators, such as idempotency, boundedness, and monotonicity. Furthermore, we solved problems related to environmental and economic issues, such as ranking countries by air pollution, selecting the best company for bank investments, and choosing the best electric vehicle design. Finally, we validated the proposed GDM approaches using three validity tests and performed a sensitivity analysis to compare them with preexisting models.