Urban populations, coupled with increased healthcare service usage, highlight the need for safe and sustainable medical waste management (MWM). Choosing the right technology for MWM is a crucial challenge for decision-makers aiming to protect public health. Multi-criteria decision making (MCDM) techniques are often used to address uncertainty and complexity inherent in such decisions. MCDM techniques based on traditional fuzzy sets (such as spherical and t-spherical fuzzy sets) leave significant membership value. In this response, a f, g, h-fractional fuzzy set (f, g, h-FrFS) based MCDM model is introduced. This study introduces the f, g, h-FrFS based Hamming and normalized Hamming distances. Additionally, we propose an improved Criteria Importance through Inter-Criteria Correlation (CRITIC) method to assess criteria weights and a novel distance-based Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to evaluate and rank MWM technologies. To test the robustness of the proposed approach, a sensitivity analysis is conducted, demonstrating the stability of the model under varying conditions. The result is the development of a comprehensive MCDM framework, referred to as f, g, h-FrF-CRITIC-TOPSIS, which incorporates relevant criteria for evaluating MWM technologies. The effectiveness of this framework is further validated through a comparative study. The results align with the actual situation and offer valuable insights into the implementation of suitable treatment technologies for MWM. This methodology proves to be highly effective in addressing the complex decision-making challenges associated with MWM, particularly in uncertain environments. Ultimately, this technique offers significant value for policymakers and organizations involved in medical systems. In medical premises, MWM is complicated, so this tool can assist them in navigating the complexities.
Proper disposing of medical waste is critical in medical facilities, safeguarding public health and safety. Medical waste management involves the efficient administration, collection, transportation, processing, and disposal of hazardous materials produced in healthcare settings, research centers, and laboratories. In partnership with the World Health Organization (WHO), the National Health Insurance (NHI) will assess the technologies employed to manage medical waste in these environments. This study aims to closely examine the handling and disposal techniques of healthcare waste in these institutions, ensuring that stringent guidelines are met. The global COVID-19 pandemic has led to a significant surge in medical waste production. Most of this waste, produced in medical facilities, poses a serious threat due to the varying levels of harmful compounds it contains. Studies by Rume and Padmanabhan emphasize the importance of proper management of this type of waste to mitigate its harmful effects on public health, the environment, and all living species.
The foundation of medical waste management (MWM) lies in processing technology, which determines how healthcare waste (HCW) is processed and decomposed. Hospitals and healthcare facilities rely on specific suppliers for medical waste treatment and disposal, with several options often available. For healthcare facility executives, selecting the most suitable treatment solution involves a thorough evaluation process, where various factors related to the treatment technology must be considered. These include factors such as the type of waste, loading capacity, technical reliability, environmental emissions, health and safety concerns, as well as the reduction in waste mass and volume. Consequently, choosing the right HCW treatment can be viewed as a complex multi-criteria decision-making (MCDM) problem. To address this, suitable MCDM methods can be applied to identify the most effective treatment technology for MWM. Real-life situations are often complex, and decision-making techniques are essential to deal with them. MCDM methodologies are particularly useful in these circumstances. According to Darici et al., technological projections in the AI age can be justified by ambiguous interactions of MCDM.
Today, Managing complex problems requires the ability to make well-informed decisions. In fields like engineering, agriculture, economics, and industrial production, data uncertainty is a significant challenge. This issue has been addressed by several researchers. Accurate data collection is often hindered by challenges such as missing information, privacy concerns, or complex data. These challenges can be addressed through fuzzy number extensions. In 1965, Zadeh introduced the concept of fuzzy sets (FS) to represent vague, uncertain, and imprecise information. In this framework, an element is assigned a membership degree (MB) that determines whether it belongs to a particular set. These degrees range from 0 to 1, offering a flexible and precise way to handle uncertain or vague data. However, FS does not account for non-membership degrees (NMB). To address this limitation, Atanassov introduced the concept of intuitionistic fuzzy sets (IFS) in 1986. Unlike FS, IFS considers both MB and NMB when making decisions. In certain cases, a decision maker might encounter situations where the squares of MB and NMB are less than or equal to 1, but their sum exceeds 1. To resolve this mathematical issue, Yager introduced the Pythagorean fuzzy set (PFS) in 2013. The PFS model offers a more sophisticated approach, considering MB and NMB in a more nuanced manner to handle these situations. In multi-criteria decision-making (MCDM), PFS has been widely recognized as one of the best tools for managing and describing ambiguity. However, PFS still has limitations, particularly in handling indeterminacy degrees (ID). To address this gap, Gundogdu proposed the concept of a spherical fuzzy set (SFS). The decision-making process in SFS is more flexible than in PFS, allowing for better handling of uncertain situations. Building on this, Mahmood et al. introduced t-spherical fuzzy sets (t-SFS), which are considered one of the most comprehensive types of fuzzy systems. Garg explored the relationship between t-SFS, their associated aggregation operators, and the operational laws governing t-SFS. Notably, in t-SFS, there is no distinction in the power levels of MB, ID, and NMB.
The previous analysis shows that the research conducted in this area utilizes different powers to control membership levels. For example, in SF frameworks, decision-makers apply a power of 2 to the membership function, while in t-SF frameworks, a power of t is used. By employing these distinct powers, decision-makers regulate the impact of membership tiers based on the strategies they adopt to address varying degrees of ambiguity and uncertainty. In some real-world scenarios, a decision-maker may feel confident in a particular strategy and assign it a score of 1 when evaluating that strategy. However, existing models may not easily accommodate such evaluations, particularly when the set representation is where . To address this limitation, Gulistan et al. (2024) introduced the concept of p, q, r-fractional fuzzy sets. This new model improves the functionality and flexibility of traditional fuzzy sets, enabling the visualization and handling of information that conventional fuzzy models cannot adequately represent. The MCDM methods, when applied within conventional fuzzy sets, overlook the maximum value inherent in experts’ judgments. Therefore, this study aims to enhance MCDM models within the f, g, h-FrFNs environment.
An accurate and reliable ranking of alternatives in MCDM depends on a proper weighting of the criteria. Since not all criteria are equally critical in every MCDM problem, it’s crucial to determine the weight of each criterion to reflect its significance. There are various methods available for calculating subjective and objective weights in MCDM scenarios. One such approach is the Intercriteria Correlation Technique (CRITIC), developed by Diakoulaki et al. (1995). This method computes weights based on correlation coefficients between criteria. The CRITIC model is a versatile MCDM approach tailored to address complex decision-making scenarios including multiple criteria. Ke et al. presented a novel combined weighting method integrating the best worst method and the CRITIC based on an IFSs for urban integrated energy system plan selection. Han and Rani proposed a novel CRITIC approach based on Pythagorean fuzzy sets to evaluate the barriers of the blockchain technology adoption in supply chain management. Wang et al. analyzed and rank the barriers to resilient supply chain adoption in the food industry. Over the years, the CRITIC model has been extensively explored and applied in various studies (Table 1).
The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a widely adopted method pioneered by Hwang and Yoon to address Multi-Criteria Decision-Making (MCDM) problems in various fields. This approach is commonly used to rank alternatives, offering a more thorough comparison than other decision-making methods. At its core, TOPSIS revolves around identifying positive and negative ideal solutions. The ranking of alternatives is accomplished by calculating their relative closeness to the ideal solution. Specifically, when an ideal solution becomes farther away from the negative ideal solution, it gets closer to the positive ideal solution. In this study, TOPSIS is applied to evaluate and rank medical waste management technologies based on their performance in a fractional fuzzy environment. Table 2 summarizes the research conducted based on the TOPSIS method.
Medical waste is categorized into hazardous and non-hazardous categories based on its inherent properties. It is inherently dangerous as it may contain flammable, toxic, radioactive, oxidized, or poisonous substances. Mishandling such waste poses serious risks to human health and the environment. MCDM methodologies for hazardous waste, including medical waste, have been extensively investigated. Hsu et al. proposed an analytical hierarchy process (AHP)-based technique for selecting infectious medical waste disposal firms, utilizing expert interviews to mitigate subjective bias. Ozkan analyzed medical waste management practices in Turkey and proposed two treatment option selection methods. Aung et al. evaluated medical waste management practices across eight hospitals in Myanmar using AHP. Yazdani et al. integrated the BWM with interval rough numbers to optimize medical waste disposal location selection. Jangre et al. identified and prioritized 18 factors influencing business practices in MWM through BWM. Further studies are outlined in Table 3.
The grading of MB, ID, and NMB has been applied in a number of previous studies, including SFS and t-SFS. However, these models face certain limitations when dealing with grade-related constraints. For instance, they struggle to compute maximum values, such as those equal to 1. As an example, take a set with the description . Clearly, these models cannot handle this type of information adequately. Because SFSs can only accommodate datasets if the square sum of MB , ID , and NMB is equal to or less than 1 . Additionally, t-SFSs can only accommodate datasets if the t-th power sum of , , and is equal to or less than 1 . Due to the limitations of existing fuzzy set structures such as SFS and t-spherical sets, Gulistan et al. presented the p, q, r-fractional fuzzy set framework. Besides providing enhanced flexibility and versatility, this structure is capable of displaying and manipulating information that is not adequately accommodated by traditional fuzzy sets. Complex data can be handled nuancedly by using parameters p, q, and r in this approach. In recent research, advanced MCDM methodologies such as CRITIC, AHP, and TOPSIS have been utilized for evaluating MWM. However, these techniques are often applied independently or within constrained hybrid frameworks. A more refined approach that integrates these methodologies with advanced fuzzy logic techniques is required to effectively address complex decision-making challenges. Existing methodologies frequently lack the adaptability necessary to tackle these emerging issues, particularly within the domain of MWM.
The CRITIC and TOPSIS methods, when based on conventional fuzzy sets, fail to account for the maximum value embedded in experts’ judgments. To address this limitation, it is essential to develop a robust CRITIC method for determining criteria weights and a TOPSIS method for ranking alternatives. This method will effectively handles the maximum judgments provided by experts. This proposed model seeks to deliver a more robust, flexible, and accurate approach to evaluating MWM, addressing existing gaps and contributing significantly to MWM decision-making. The study underscores the inadequacy of current MWM assessment methods. It notes that despite extensive research into various assessment techniques, there remains a notable absence of integration with advanced fuzzy sets principles, particularly fractional fuzzy sets. To improve MWM evaluation accuracy and depth, this study introduces a hybrid methodology that combines CRITIC and TOPSIS methods. This innovative approach addresses a critical gap in the literature by providing a more robust framework for assessing MWM viability. The study is driven by the urgent need for more reliable and efficient decision-making methodologies in MWM evaluation.
Real-world problems are increasingly capturing the attention and efforts of DMs, who are developing realistic strategies to address them. As the situations grow more complex, DMs operating within the adaptive decision-making paradigm face significant difficulty identifying optimal responses. This study will help overcome numerous obstacles by providing practical and sustainable solutions to these real-life challenges. This research addresses the identified gaps in existing literature:
