Artificial intelligence (AI) stands out as a significant technological innovation, driving progress in diverse areas such as big data analysis, supply chain management, energy efficiency, sustainable development, etc. The present study investigates how AI could contribute to the sustainability of the healthcare supply chain (HSC) and managing medical needs. Medical organizations can boost the logistics of their tasks, reduce pharmaceutical trash, and strengthen revenue projections through the adoption of AI tools. This study aims to provide a structured evaluation of AI-driven solutions for enhancing healthcare supply chain robustness, especially under conditions of uncertainty and complex logistics demands. To determine the investment value of AI applications in HSC management, the current research adopted a revolutionary multi-criteria decision-making (MCDM) methodology tailored to the healthcare sector’s unique demands, including six critical factors. In light of these criteria, six highly technologically advanced AI-based solutions are examined. The implementation of a circular intuitionistic fuzzy set (CIFS) in the instance discussed provides a versatile and expressive way to describe vague and uncertain information. This study leverages the CIF topology to address data complexities and uncover the underlying structural features of a large dataset. At the outset, we adopted the LOPCOW approach, which includes logarithmic variation to assign weights to criteria, whereas the AROMAN method utilizes a powerful two-step normalization technique to rank alternatives, hence guaranteeing a trustworthy and accurate appraisal. A substantial degree of robustness was confirmed by the technique following a comparison of the operators as well as sensitivity testing.

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.

The concept of complex fuzzy sets, where the unit disk of the complex plane acts as the codomain of the membership function, as an extension of fuzzy sets. The objective of this article is to use complex fuzzy sets in BCK/BCI-algebras. We present the concept of a complex fuzzy subalgebra in a BCK/BCI-algebra and explore their properties. Furthermore, we discuss the modal and level operators of these complex fuzzy subalgebras, highlighting their importance in BCK/BCI-algebras. We study various operations, and the laws of a complex fuzzy system, including union, intersection, complement, simple differences, and bounded differences of complex fuzzy ideals within BCK/BCI-algebras. Finally, we generate a computer programming algorithm that implements our complex fuzzy subalgebras/ideals in BCK/BCI-algebras procedure for ease of lengthy calculations.

In this paper, we propose a new hybrid model, multi Q-hesitant fuzzy soft multi-granulation rough set model, by combining a multi Q-hesitant fuzzy soft set and multi-granulation rough set. We demonstrate some useful properties of these multi Q-hesitant fuzzy soft multi-granulation rough sets. Furthermore, we define multi Q-hesitant fuzzy soft ( $M^{k}QHFS$ ) rough approximation operators in terms of $M^{k}QHFS$ relations and $M^{k}QHFS$ multi-granulation rough approximation operators in terms of $M^{k}QHFS$ relations. We study the main properties of lower and upper $M^{k}QHFS$ rough approximation operators and lower and upper $M^{k}QHFS$ multi-granulation rough approximation operators. Moreover, we develop a general framework for dealing with uncertainty in decision-making by using the multi Q-hesitant fuzzy soft multi-granulation rough sets. We analyze the photovoltaic systems fault detection to show the proposed decision methodology.

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.

An interval-valued fuzziness structure is an effective approach addressing ambiguity and for expressing people's hesitation in everyday situations. An $ \mathcal{N} $-structure is a novel technique for solving practical problems. This is beneficial for resolving a variety of issues, and a lot of progress is being made right now. In order to develop crossing cubic structures ($ \mathcal{CCS}s $), Jun et al. amalgamate interval-valued fuzziness and $ \mathcal{N} $-structures. In this manuscript, our main contribution is to originate the concepts of crossing cubic ($ \mathcal{CC} $) Lie algebra, $ \mathcal{CC} $ Lie sub-algebra, ideal, and homomorphism. We investigate some properties of these concepts. In a Lie algebra, the construction of a quotient Lie algebra via the $ \mathcal{CC} $ Lie ideal is provided. Furthermore, the $ \mathcal{CC} $ isomorphism theorems are presented.