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In this paper, we present four categories of covering-based intuitionistic hesitant fuzzy rough set (CIHFRS) models using intuitionistic hesitant fuzzy β-neighborhoods (IHF β-neighborhoods) and intuitionistic hesitant fuzzy complementary β-neighborhoods (IHFC β-neighborhoods. Through theoretical analysis of covering-based IHFRS models, we propose the intuitionistic hesitant fuzzy TOPSIS (IHF-TOPSIS) technique for order of preference by similarity to an ideal solution, addressing multicriteria decision-making (MCDM) challenges concerning the assessment of IHF data. A compelling example aptly showcases the suggested approach. Furthermore, we address MCDM problems regarding the assessment of IHF information based on CIHFRS models. Through comparison and analysis, it is evident that addressing MCDM problems by assessing IHF data using CIHFRS models proves more effective than utilizing intuitionistic fuzzy data with CIFRS models or hesitant fuzzy information with CHFRS models. IHFS emerges as a unique and superior tool for addressing real-world challenges. Additionally, covering-based rough sets (CRSs) have been successfully applied to decision problems due to their robust capability in handling unclear data. In this study, by combining CRSs with IHFS, four classes of CIFRS versions are established using IHF β-neighborhoods and IHFC β-neighborhoods. A corresponding approximation axiomatic system is developed for each. The roughness and precision degrees of CBIHFRS models are specifically talked about. The relationship among these four types of IHFRS versions and existing related versions is presented based on theoretical investigations. A method for MCDM problems through IHF information, namely, IHF-TOPSIS, is introduced to further demonstrate its effectiveness and applicability. By conducting a comparative study, the effectiveness of the suggested approach is evaluated.

This article uses the Aczel-Alsina t-norm and t-conorm to make several new linguistic interval-valued intuitionistic fuzzy aggregation operators. First, we devised some rules for how linguistic interval-valued intuitionistic fuzzy numbers should work. Then, using these rules as a guide, we created a set of operators, such as linguistic interval-valued intuitionistic fuzzy Aczel-Alsina weighted averaging (LIVIFAAWA) operator, linguistic interval-valued intuitionistic fuzzy Aczel-Alsina weighted geometric (LIVIFAAWG) operator, linguistic interval-valued intuitionistic fuzzy Aczel-Alsina ordered weighted averaging (LIVIFAAOWA) operator, linguistic interval-valued intuitionistic fuzzy Aczel-Alsina ordered weighted geometric (LIVIFAAOWG) operator, linguistic interval-valued intuitionistic fuzzy Aczel-Alsina hybrid weighted averaging (LIVIFAAHWA) operator and linguistic interval-valued intuitionistic fuzzy Aczel-Alsina hybrid weighted geometric (LIVIFAAHWG) operators are created. Several desirable qualities of the newly created operators are thoroughly studied. Moreover, a multi-criteria group decision-making (MCGDM) method is proposed based on the developed operators. The proposed operators are then applied to real-world decision-making situations to demonstrate their applicability and validity to the reader. Finally, the suggested model is contrasted with the currently employed method of operation.

Since intuitionistic fuzzy set only deals with uncertainty but not periodicity, therefore to overcome, this situation complex intuitionistic fuzzy set is a better tool that deals with both uncertainty and periodicity. Also, Bonferroni mean operator has the advantage of considering interrelationships between parameters, but it deals with only the crisp data. Recently, to deal with fuzzy data, many extensions of Bonferroni operators have been developed. Motivated by the CIFS and BM operators, in this paper, we proposed some Dombi Bonferroni mean operators to deal with CIF information. Dombi Bonferroni mean operators are special cases of general T-conorm and T-norm, which have the advantage of good flexibility with a general parameter. We proposed the complex intuitionistic fuzzy Dombi Bonferroni mean (CIFDBM) operator, complex intuitionistic fuzzy Dombi weighted Bonferroni mean (CIFDWBM) operator, complex intuitionistic fuzzy Dombi geometric Bonferroni mean (CIFDGBM) operator, and complex intuitionistic fuzzy Dombi weighted geometric Bonferroni mean (CIFDWGBM) operator. Some properties of the developed operators are discussed in detail, and different cases are investigated. Moreover, a multicriteria group decision-making (MCGDM) method is developed based on the proposed aggregation operators. Finally, a numerical example of information security management evaluation is given in order to demonstrate the application and effectiveness of the proposed approach. A comparative study is also conducted in order to show the advantage of the developed method.

Multi-criteria decision-making (MCDM) is essential for handling complex decision problems under uncertainty, especially in fields such as criminal justice, healthcare, and environmental management. Traditional fuzzy MCDM techniques have failed to deal with problems where uncertainty or vagueness is involved. To address this issue, we propose a novel framework that integrates group and overlap functions with Aczel-Alsina (AA) operational laws in the intuitionistic fuzzy set (IFS) environment. Overlap functions capture the degree to which two inputs share common features and are used to find how closely two values or criteria match in uncertain environments, while the Group functions are used to combine different expert opinions into a single collective result. This study introduces four new aggregation operators: Group Overlap function-based intuitionistic fuzzy Aczel-Alsina (GOF-IFAA) Weighted Averaging (GOF-IFAAWA) operator, intuitionistic fuzzy Aczel-Alsina (GOF-IFAA) Weighted Geometric (GOF-IFAAWG), intuitionistic fuzzy Aczel-Alsina (GOF-IFAA) Ordered Weighted Averaging (GOF-IFAAOWA), and intuitionistic fuzzy Aczel-Alsina (GOF-IFAA) Ordered Weighted Geometric (GOF-IFAAOWG), which are rigorously defined and mathematically analyzed and offer improved flexibility in managing overlapping, uncertain, and hesitant information. The properties of these operators are discussed in detail. Further, the effectiveness, validity, activeness, and ability to capture the uncertain information, the developed operators are applied to the AI-based Criminal Justice Policy Selection problem. At last, the comparison analysis between prior and proposed studies has been displayed, and then followed by the conclusion of the result.

ABSTRACT Objective: The present study aimed to assess the thyroid outcomes six-months after radioactive Iodine-131 therapy (RIT) among hyperthyroid patients and identify the factors associated with them. Methods: This retrospective observational study was conducted at the department of Nuclear Medicine and Molecular Imaging, Northwest General Hospital and Research Centre during 2013 to 2019. For the study purpose, the thyroid outcomes of 153 hyperthyroid patients were studied retrospectively for six months after RIT. The data was obtained from the medical records. Patient baseline characteristics, clinical features, laboratory investigations, results of thyroid imaging, and therapeutic investigations were acquired and recorded in a structured questionnaire. Results: Out of the 153 screened records of hyperthyroid patients, 19.6% became euthyroid, 9.2% remained hyperthyroid, and 25.5% developed hypothyroidism after six months of RIT. The observed remission rate by the end of six months was 80.95%. Three months post-RIT, gender and RAI doses had a significant effect on thyroid function. The frequency of hypothyroidism was higher among those treated with an RAI dose of ≤ 20 mCi (83.0%) than those treated with a higher dose > 20 mCi (17%). Moreover, most patients receiving > 20 mCi radioiodine became euthyroid (64.5%). Similar outcomes were observed after six months of the therapy, except gender was replaced by etiologies of hyperthyroidism (p=0.009). Conclusion: Radioactive iodine (131-I) therapy is effective for the treatment of hyperthyroidism. However, the appropriate dose is still debatable, as there was a high incidence of hypothyroidism post-therapy.

The complex interval-valued intuitionistic fuzzy set (CIIFS), as an extension of the complex intuitionistic fuzzy set (CIFS), is one of the better tools for dealing with time-periodic information in a single set of two-dimensional information. So, this paper makes some new operators based on Aczel-Alsina’s t-norm and t-conorm in the CIIFS environment. First, some Aczel-Alsina t-norm and t-conorm operational laws are defined for complex interval-valued intuitionistic fuzzy numbers (CIIFNs). Then, using the proposed operational laws, Aczel-Alsina The operators Complex interval-valued intuitionistic Aczel-Alsina weighted average (CIIFAAWA), Complex interval-valued intuitionistic Aczel-Alsina weighted geometric (CIIFAAWG), Complex interval-valued intuitionistic Aczel-Alsina ordered weighted average (CIIFAAOWA), and Complex interval-valued intuitionistic Aczel-Alsina ordered weighted geometric (CIIFAAOWG) are developed. Further, some properties of the proposed operators are discussed and investigated in detail. A group decision-making method is also suggested based on developed operators in the CIIFS environment. The proposed operators are more adaptable and give more accurate results than existing ones. Furthermore, a multi-criteria decision-making technique is developed based on the proposed operators. A decision-making problem for healthcare facilities in public hospitals is provided to demonstrate the benefits and applicability of the proposed method. Finally, a comparative study is also investigated using the existing methods.

The fundamental notions of the intuitionistic hesitant fuzzy set (IHFS) and rough set (RS) are general mathematical tools that may easily manage imprecise and uncertain information. The EDAS (Evaluation based on Distance from Average Solution) approach has an important role in decision-making (DM) problems, particularly in multi-attribute group decision-making (MAGDM) scenarios, where there are many conflicting criteria. This paper aims to introduce the IHFR-EDAS approach, which utilizes the IHF rough averaging aggregation operator. The aggregation operator is crucial for aggregating intuitionistic hesitant fuzzy numbers into a cohesive component. Additionally, we introduce the concepts of the IHF rough weighted averaging (IHFRWA) operator. For the proposed operator, a new accuracy function (AF) and score function (SF) are established. Subsequently, the suggested approach is used to show the IHFR-EDAS model for MAGDM and its stepwise procedure. In conclusion, a numerical example of the constructed model is demonstrated, and a general comparison between the investigated models and the current methods demonstrates that the investigated models are more feasible and efficient than the present methods.

Complex Intuitionistic Fuzzy Sets (CIFSs) are an advanced form of intuitionistic fuzzy sets that utilize complex numbers to effectively manage uncertainty and hesitation in multi-criteria decision making (MCDM). This paper introduces the Shapley Choquet integral (SCI), which is a powerful tool for integrating information from various sources while considering the importance and interactions among criteria. To address ambiguity and inconsistency, we apply the Aczel–Alsina (AA) t-norm and t-conorm, which offer greater flexibility than traditional norms. We propose two novel aggregation operators within the CIFS framework using the Aczel–Alsina Generalized Shapley Choquet Integral (AAGSCI): the Complex Intuitionistic Fuzzy Aczel–Alsina Weighted Average Generalized Shapley Choquet Integral (CIFAAWAGSCI) and the Complex Intuitionistic Fuzzy Aczel–Alsina Weighted Geometric Generalized Shapley Choquet Integral (CIFAAWGGSCI), along with their special cases. The properties of these operators, including idempotency, boundedness, and monotonicity, are thoroughly investigated. These operators are designed to evaluate complex and asymmetric information in real-life problems. A case study on selecting the optimal bridge design based on structural and aesthetic criteria demonstrates the applicability of the proposed method. Our results indicate that the proposed method yields more consistent and reliable outcomes compared to existing approaches.

Pythagorean cubic set (PCFS) is the combination of the Pythagorean fuzzy set (PFS) and interval-valued Pythagorean fuzzy set (IVPFS). PCFS handle more uncertainties than PFS and IVPFS and thus are more extensive in their applications. The objective of this paper is under the PCFS to establish some novel operational laws and their corresponding Einstein weighted geometric aggregation operators. We describe some novel Pythagorean cubic fuzzy Einstein weighted geometric (PCFEWG) operators to handle multiple attribute group decision-making problems. The desirable relationship and the characteristics of the proposed operator are discussed in detail. Finally, a descriptive case is given to describe the practicality and the feasibility of the methodology established.

Pythagorean fuzzy set is a useful tool to deal with the fuzziness and vagueness. Many aggregation operators have been proposed by many researchers based on Pythagorean fuzzy sets. But the current methods are under the assumption that the decision makers and the attributes are at the same priority level. However, in real group decision-making problems the attribute and decision makers may have different priority level. Therefore, in this paper, we develop multi-attribute group decision-making based on Pythagorean fuzzy sets where there exists a prioritization relationship over the attributes and decision makers. First, we develop Pythagorean fuzzy prioritized weighted average operator and Pythagorean fuzzy prioritized weighted geometric operator. Then we study some of its desirable properties such as idempotency, boundary and monotonicity in detail. Moreover, we propose a multi-attribute group decision-making approach based on the developed operators under Pythagorean fuzzy environment. Finally, a numerical example is provided to illustrate the practicality of the proposed approach.