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Identifying the most optimal wearable health technology devices for hospitals is a crucial step in emergency decision-making. The multi-attribute group decision-making method is a widely used and practical approach for selecting wearable health technology devices. However, because of the various factors that must be considered when selecting devices in emergencies, decision-makers often struggle to create a comprehensive assessment method. This study introduced a novel decision-making method that took into account various factors of decision-makers and has the potential to be applied in various other areas of research. First, we introduced a list of aggregation operators based on Pythagorean hesitant fuzzy rough sets, and a detailed description of the desired characteristics of the operators under investigation were provided. The proposed operators were validated by a newly defined score and accuracy function. Second, this paper used the proposed approach to demonstrate the Pythagorean hesitant fuzzy rough technique for order of preference by similarity to ideal solution (TOPSIS) model for multiple attribute decision-making and its stepwise algorithm. We developed a numerical example based on suggested operators for the evaluation framework to tackle the multiple-attribute decision-making problems while evaluating the performance of wearable health technology devices. In the end, the sensitivity analysis has confirmed the performance and reliability of the proposed framework. The findings indicated that the models being examined demonstrated greater reliability and efficacy compared to existing methodologies. [ABSTRACT FROM AUTHOR]

In this research, we introduce the intuitionistic hesitant fuzzy rough set by integrating the notions of an intuitionistic hesitant fuzzy set and rough set and present some intuitionistic hesitant fuzzy rough set theoretical operations. We compile a list of aggregation operators based on the intuitionistic hesitant fuzzy rough set, including the intuitionistic hesitant fuzzy rough Dombi weighted arithmetic averaging aggregation operator, the intuitionistic hesitant fuzzy rough Dombi ordered weighted arithmetic averaging aggregation operator, and the intuitionistic hesitant fuzzy rough Dombi hybrid weighted arithmetic averaging aggregation operator, and demonstrate several essential characteristics of the aforementioned aggregation operators. Furthermore, we provide a multi attribute decision-making approach and the technique of the suggested approach in the context of the intuitionistic hesitant fuzzy rough set. A real-world problem for selecting a suitable worldwide partner for companies is employed to demonstrate the effectiveness of the suggested approach. The sensitivity analysis of the decision-making results of the suggested aggregation operators are evaluated. The demonstrative analysis reveals that the outlined strategy has applicability and flexibility in aggregating intuitionistic hesitant fuzzy rough information and is feasible and insightful for dealing with multi attribute decision making issues based on the intuitionistic hesitant fuzzy rough set. In addition, we present a comparison study with the TOPSIS approach to illustrate the advantages and authenticity of the novel procedure. Furthermore, the characteristics and analytic comparison of the current technique to those outlined in the literature are addressed. [ABSTRACT FROM AUTHOR]

The role of transportation in international trade cannot be overlooked; hence, the need for regular upgrades of roads and marketplaces. The Karakorum Highway (KKH), a vital part of the China–Pakistan economic corridor that connects China with Arabian waters, has not received significant attention from the National Highway Authority (NHA) due to uncertainties in many regions. To address this issue, the study employs Dombi operations using Polytopic fuzzy sets to explore uncertainty in decision-making. The Dombi t-norm and t-co-norm can capture inconsistencies, making it an effective tool in the decision-making process. The study applies the Polytopic fuzzy Dombi-weighted averaging (PF-DWA) operator, the Polytopic fuzzy Dombi-ordered weighted averaging (PF-DOWA) operator, and the Polytopic fuzzy Dombi hybrid-weighted averaging (PF-DHWA) operator to demonstrate how the model can help the NHA open bidding for interested companies to repair damaged areas, bridges, and side barriers affected by floods. The study reveals that infrastructure is essential for the development of any country, and the most suitable choice for reconstruction can be made using the proposed methods. [ABSTRACT FROM AUTHOR]

A combination of the single-valued neutrosophic set (SV-NS) and the probabilistic hesitant fuzzy set is the single-valued neutrosophic probabilistic hesitant fuzzy (SV-NPHF) environment (PHFS). It is intended for some unsatisfactory, ambiguous, and contradictory circumstances in which each element has a number of various values that are brought about by the situation's actuality. The decision-maker can quickly gather and analyze the facts by employing a strategic decision-making technique. On the other hand, uncertainty will be a big part of our daily lives when we are learning. We present a decision-making strategy for the SV-NPHF context to address this data ambiguity. The fundamental operational concepts for SV-NPHF information under Dombi aggregation operators were initially developed on the basis of this study. The SV-NPHF Dombi weighted arithmetic average (SV-NPHFDWAA) operator and SV-NPHF Dombi weighted arithmetic geometric (SV-NPHFDWAG) operators are two SV-NPHF Dombi aggregation Operators that are then examined. Following that, we look into further characterizations of the proposed operators, including idempotency, boundedness, and monotonicity. For the derived operators, we additionally developed the score and accuracy functions. When using SV-NPHF data in a multi attribute decision support system (MADSS), it is necessary to compare the effectiveness of various (AOs) in order to make the best decision. In addition, it is demonstrated how to use symmetry analysis to choose the optimal social media platform for earning and learning in a practical application of SV-NPHFDWAA and SV-NPHFDWAG. [ABSTRACT FROM AUTHOR]

Hepatitis is an infectious disease typified by inflammation in internal organ tissues, and it is caused by infection or inflammation of the liver. Hepatitis is often feared as a fatal illness, especially in developing countries, mostly due to contaminated water, poor sanitation, and risky blood transfusion practices. Although viruses are typically blamed, other potential causes of this kind of liver infection include autoimmune disorders, toxins, medicines, opioids, and alcohol. Viral hepatitis may be diagnosed using a variety of methods, including a physical exam, liver surgery (biopsy), imaging investigations like an ultrasound or CT scan, blood tests, a viral serology panel, a DNA test, and viral antibody testing. Our study proposes a new decision-support system for hepatitis diagnosis based on spherical q-linear Diophantine fuzzy sets (Sq-LDFS). Sq-LDFS form the generalized structure of all existing notions of fuzzy sets. Furthermore, a list of novel Einstein aggregation operators is developed under Sq-LDF information. Also, an improved VIKOR method is presented to address the uncertainty in analyzing the viral hepatitis categories demonstration. Interesting and useful properties of the proposed operators are given. The core of this research is the proposed algorithm based on the proposed Einstein aggregation operators and improved VIKOR approach to address uncertain information in decision support problems. Finally, a hepatitis diagnosis case study is examined to show how the suggested approach works in practice. Additionally, a comparison is provided to demonstrate the superiority and efficacy of the suggested decision technique.

Since three way decision making is a better tool in order to deal with uncertain decision making problem. Therefore, in this paper a three way decision making approach is presented under q-rung orthopair fuzzy rough set environment. We first define some Dombi-operational laws for q-rung orthopair fuzzy rough set. Further, using the proposed operational laws some q-rung orthopair fuzzy rough Dombi aggregation operators namely, q-Rung Orthopair fuzzy rough Dombi weighted average (q-ROFRDWA) operator, q-Rung Orthopair fuzzy rough Dombi ordered weighted average (q-ROFRDOWA) operator and q-Rung Orthopair fuzzy rough Dombi hybrid weighted average (q-ROFRDHWA) operator are proposed. Also, some properties of the developed operators are investigated in details. Moreover, we present a three way decision making approach based on the developed aggregation operators with q-rung orthopair fuzzy rough set setting. Furthermore, a numerical example is presented for the effectiveness and application of the proposed method. Finally, a comparative study is conducted with other existing methods.

Hepatitis is an infectious disease typified by inflammation in internal organ tissues, and it is caused by infection or inflammation of the liver. Hepatitis is often feared as a fatal illness, especially in developing countries, mostly due to contaminated water, poor sanitation, and risky blood transfusion practices. Although viruses are typically blamed, other potential causes of this kind of liver infection include autoimmune disorders, toxins, medicines, opioids, and alcohol. Viral hepatitis may be diagnosed using a variety of methods, including a physical exam, liver surgery (biopsy), imaging investigations like an ultrasound or CT scan, blood tests, a viral serology panel, a DNA test, and viral antibody testing. Our study proposes a new decision-support system for hepatitis diagnosis based on spherical q-linear Diophantine fuzzy sets (Sq-LDFS). Sq-LDFS form the generalized structure of all existing notions of fuzzy sets. Furthermore, a list of novel Einstein aggregation operators is developed under Sq-LDF information. Also, an improved VIKOR method is presented to address the uncertainty in analyzing the viral hepatitis categories demonstration. Interesting and useful properties of the proposed operators are given. The core of this research is the proposed algorithm based on the proposed Einstein aggregation operators and improved VIKOR approach to address uncertain information in decision support problems. Finally, a hepatitis diagnosis case study is examined to show how the suggested approach works in practice. Additionally, a comparison is provided to demonstrate the superiority and efficacy of the suggested decision technique. [ABSTRACT FROM AUTHOR]

In recent years, the surge in online learning has eclipsed traditional classroom teaching, elevating the prominence of e-learning platforms. However, the quest for a reliable methodology to evaluate these platforms has remained pressing. While several studies have explored this domain, none have integrated decision experts' confidence levels. This study bridges this gap by seamlessly incorporating confidence levels into Dombi aggregation operators within an intuitionistic fuzzy framework. The study introduces two innovative operators: the confidence-level intuitionistic fuzzy Dombi weighted averaging operator (CIFDWA) and the confidence-level intuitionistic fuzzy Dombi weighted geometric operator (CIFDWG). These operators are employed to form a novel multi-attribute group decision-making (MAGDM) approach, which is demonstrated by applying them to select the optimal e-learning website in a real-world scenario. The "Stepwise Weight Assessment Ratio Analysis (SWARA)" method is utilized to determine criteria weights. The findings highlight the critical importance of sub-criteria such as topic diversity, pricing, content credibility, data security, and user interface simplicity. The analysis reveals Unacademy as the leading platform, closely followed by Byju's. Through meticulous comparative analysis and sensitivity evaluations, we underscore the stability and coherence of the proposed model. The study's novelty lies in its innovative approach to integrating confidence levels in multi-attribute group decision-making scenarios, promising broader applications across various real-world contexts. Educational advisers and management can leverage this methodology to empower students with informed choices. [ABSTRACT FROM AUTHOR]

Dombi t-norm (DTN) and t-conorm (TCN) are among the most effective triangular norms in fuzzy systems for aggregation purposes. The environment of interval-valued intuitionistic fuzzy (IVIF) set gives us precision in expressing uncertain information by using a membership grade (MG) and non-membership grade (NMG) in the form of closed subintervals of 0 ,   1 . The goal of this paper is to introduce DTN-based aggregation operators (AOs) for IVIF numbers (IVIFNs) and study their performance in the evaluation of the worth of energy recourses to be opted in Pakistan to deal with the energy crises situation. We first introduced some DTN and TCN-based operations for IVIFNs and developed two new AOs known as IVIF Dombi weighted averaging (IVIFDWA) and IVIF Dombi weighted geometric (IVIFDWG) operators. The validity and fitness of the proposed operators are tested. A case study is presented where the energy resources of Pakistan are discussed and the problem of the selection of sustainable energy resources in the context of Pakistan is investigated. The sensitivity analysis of the proposed IVIFDWA and IVIFDWG operators is studied and a comparative analysis of the current work with previous studies is established. [ABSTRACT FROM AUTHOR]

Bipolar complex fuzzy (BCF) is one of the massive, important, and dominant technique, which has been used for managing awkward and inconsistent information in genuine life dilemmas. BCF information has efficaciously employed it in the region of distinct circumstances. Additionally, the theory of Dombi aggregation (DA) operator is a massively modified version of the averaging/geometric operators to cope with unrealistic data and due to its structure, certain intellectuals have utilized it in the environment of distinct regions. Keeping the advantages of the prevailing ideas, the major contribution of this analysis is to elaborate the technique of BCF Dombi weighted averaging, BCF Dombi ordered weighted averaging, BCF Dombi hybrid averaging, BCF Dombi weighted geometric, BCF Dombi ordered weighted geometric, BCF Dombi hybrid geometric operators, and demonstrated their beneficial properties. After that, multi-attribute decision making (MADM) is a part of the decision-making procedure, which has been used for determining the best optimal from the family of alternatives. Based on the above analysis, we utilized the theory MADM technique under elaborated works by using the BCF information. Finally, we present a numerical example to verify the demonstrated method. Finally, we interpreted a comparative assessment of our work with existing work to demonstrate its usefulness and practicability. [ABSTRACT FROM AUTHOR]

Dombi aggregation operators (DAOs) are massive flexible and much consistent to manage convoluted and awkward information genuine life troubles. The goal of this manuscript is to initiate the complex q-rung orthopair fuzzy Dombi-weighted averaging (CQROFDWA), complex q-rung orthopair fuzzy Dombi-ordered weighted averaging (CQROFDOWA), complex q-rung orthopair fuzzy Dombi hybrid-weighted averaging (CQROFDHWA), complex q-rung orthopair fuzzy Dombi weighted geometric (CQROFDWG), complex q-rung orthopair fuzzy Dombi-ordered weighted geometric (CQROFDOWG), complex q-rung orthopair fuzzy Dombi hybrid weighted geometric (CQROFDHWG) operators, and demonstrated their important properties. Moreover, by considering these elaborated operators, the multi-attribute decision-making (MADM) technique is developed with the help of certain examples and determined the dominancy and consistency of the presented operators. To determine the supremacy of the elaborated operators, the sensitivity analysis and geometrical expressions of the initiated works are also deliberated. [ABSTRACT FROM AUTHOR]

Dombi t-norm (DTN) and t-conorm (TCN) are among the most effective triangular norms in fuzzy systems for aggregation purposes. The environment of interval-valued intuitionistic fuzzy (IVIF) set gives us precision in expressing uncertain information by using a membership grade (MG) and non-membership grade (NMG) in the form of closed subintervals of 0, 1. The goal of this paper is to introduce DTN-based aggregation operators (AOs) for IVIF numbers (IVIFNs) and study their performance in the evaluation of the worth of energy recourses to be opted in Pakistan to deal with the energy crises situation. We first introduced some DTN and TCN-based operations for IVIFNs and developed two new AOs known as IVIF Dombi weighted averaging (IVIFDWA) and IVIF Dombi weighted geometric (IVIFDWG) operators. The validity and fitness of the proposed operators are tested. A case study is presented where the energy resources of Pakistan are discussed and the problem of the selection of sustainable energy resources in the context of Pakistan is investigated. The sensitivity analysis of the proposed IVIFDWA and IVIFDWG operators is studied and a comparative analysis of the current work with previous studies is established.

Multi-attribute decision-making (MADM) is commonly used to investigate fuzzy information effectively. However, selecting the best alternative information is not always symmetric because the alternatives do not have complete information, so asymmetric information is often involved. Expressing the information under uncertainty using closed subintervals of [0, 1] is beneficial and effective instead of using crisp numbers from [0, 1]. The goal of this paper is to enhance the notion of Dombi aggregation operators (DAOs) by introducing the DAOs in the interval-valued T-spherical fuzzy (IVTSF) environment where the uncertain and ambiguous information is described with the help of membership grade (MG), abstinence grade (AG), non-membership grade (NMG), and refusal grade (RG) using closed sub-intervals of [0, 1]. One of the key benefits of the proposed work is that in the environment of information loss is reduced to a negligible limit. We proposed concepts of IVTSF Dombi weighted averaging (IVTSFDWA) and IVTSF Dombi weighted geometric (IVTSFDWG) operators. The diversity of the IVTSF DAOs is proved and the influences of the parameters, associated with DAOs, on the ranking results are observed in a MADM problem where it is discussed how a decision can be made when there is asymmetric information about alternatives.

Choosing the most capable organization to manage biomedical waste (BMW) is a typical multi-attribute group decision-making (MAGDM) problem. MAGDM is frequently used to deal with decision-making scenarios that are fraught with uncertainty and vagueness. As a novel extension of the fuzzy set, the interval-valued Fermatean fuzzy set (IVFFS) can more extensively express the uncertain and vague data in MAGDM issues. In order to combine the information of IVFFS, in this paper, we develop interval-valued Fermatean fuzzy Dombi weighted averaging (geometric) operators with the assistance of Dombi operations. The developed operators can consider the extremely large data sets and the relationships between all decision attributes. Then, utilizing our proposed aggregation operators, we present an integrated MAGDM methodology by combining Preference Ranking Organization METhod for Enrichment Evaluation II (PROMETHEE II) and Stepwise Weight Assessment Ratio Analysis (SWARA) methods. To do this, the attribute weights are estimated by the SWARA method and the PROMETHEE II method determines the preference order of the options. Afterwards, to illustrate the practicality of the proposed methodology, we consider a case study about selecting the most capable organization among the available ones that can handle BMW. The result of this study shows that the bio-chemistry lab is the best BMW management organization. Sensitivity and comparative analysis demonstrate the stability and reliability of the proposed method. According to the findings of this study, we conclude that the proposed methodology offers a comprehensive and systematic approach to evaluating BMW organizations within the IVFF context. [ABSTRACT FROM AUTHOR]

The widespread use of plastic products worldwide generates an enormous amount of waste. Plastic is a substance that is not biodegradable and is permanent in the environment. The environment and living beings are negatively affected by this waste if it is not managed properly. However, the assessment and selection of effective plastic waste management methods is a complex and uncertain decision-making problem due to the involvement of multiple conflicting attributes, the imprecise human mind, and a lack of information. Recently, interval-valued spherical fuzzy (IVSF) sets have been recognized as one of the suitable tools to handle vague information. In this paper, we introduce a hybrid multi-attribute group decision-making methodology based on the entropy method, deviation-based method, and Multi-Attribute Border Approximation area Comparison (MABAC) method with IVSF sets to choose the most effective plastic waste management process in which the decision experts' and attribute weights are completely unknown. In this model, the entropy and deviation-based methods are utilized to calculate the decision experts' and attribute weights, respectively. Also, the MABAC method is used to evaluate the priority order of the plastic waste management options. To do this, Dombi weighted averaging and Dombi weighted geometric operators are developed in the IVSF environment. In the proposed model, the Dombi weighted averaging operator is used to fuse several decision experts' information, and the Dombi weighted geometric operator is used to determine the border approximation area matrix. Then, to confirm the applicability of the suggested model, we look at a numerical example of choosing the most effective method for managing plastic waste with IVSF information. In the numerical example, we consider six alternatives and four important attributes with ten sub-attributes by consulting four decision experts. The result of this study shows that 'Recycling (A 2) ' is the most effective method to reduce plastic waste. Finally, we compare the proposed method with the existing ones to demonstrate its validity. • Dombi t-conorm and t-norm operations under the IVSF environment are introduced. • Dombi weighted averaging and geometric aggregation operators of IVSFNs are developed. • A novel MABAC model is presented to solve the MAGDM problem with IVSF data. • The subjective and objective weights are combined for weighting the attributes. • The developed model is utilized to select the most effective plastic waste management method. [ABSTRACT FROM AUTHOR]

Multi-attribute decision-making (MADM) is commonly used to investigate fuzzy information effectively. However, selecting the best alternative information is not always symmetric because the alternatives do not have complete information, so asymmetric information is often involved. Expressing the information under uncertainty using closed subintervals of [0, 1] is beneficial and effective instead of using crisp numbers from [0, 1]. The goal of this paper is to enhance the notion of Dombi aggregation operators (DAOs) by introducing the DAOs in the interval-valued T-spherical fuzzy (IVTSF) environment where the uncertain and ambiguous information is described with the help of membership grade (MG), abstinence grade (AG), non-membership grade (NMG), and refusal grade (RG) using closed sub-intervals of [0, 1]. One of the key benefits of the proposed work is that in the environment of information loss is reduced to a negligible limit. We proposed concepts of IVTSF Dombi weighted averaging (IVTSFDWA) and IVTSF Dombi weighted geometric (IVTSFDWG) operators. The diversity of the IVTSF DAOs is proved and the influences of the parameters, associated with DAOs, on the ranking results are observed in a MADM problem where it is discussed how a decision can be made when there is asymmetric information about alternatives. [ABSTRACT FROM AUTHOR]