Geometric Aggregation Operators Research Articles

An Innovative Approach on Yao’s Three-Way Decision Model Using Intuitionistic Fuzzy Sets for Medical Diagnosis

In the realm of medical diagnosis, intuitionistic fuzzy data serves as a valuable tool for representing information that is uncertain and imprecise. Nevertheless, decision-making based on this kind of knowledge can be quite challenging due to the inherent vagueness of the data. To address this issue, we employ power aggregation operators, which prove effective in combining several sources of data, such as expert thoughts and patient information. This allows for a more correct diagnosis; a particularly crucial aspect of medical practice where precise and timely diagnoses can significantly impact medication policy and patient results. In our research, we introduce a novel methodology to the three-way decision idea. Initially, we revamp the three-way decision model using rough set theory and incorporate interval-valued classes to handle intuitionistic fuzzy data. Secondly, we explore the use of intuitionistic fuzzy power weighted and intuitionistic fuzzy power weighted geometric aggregation operators to consolidate attribute values within the data system. Furthermore, we present a case study in the medical field to exhibit the validity and efficiency of our offered technique. This innovative method enables us to classify participants into three distinct zones based on their symptoms. The manuscript concludes with a summary of key points provided by the authors.

Utilizing Sine Trigonometric q-Spherical Fuzzy Rough Aggregation Operators for Group Decision-Making and Their Role in Digital Transformation

q-spherical fuzzy rough set (q-SFRS) is also one of the fundamental concepts for addressing more uncertainties in decision problems than the existing structures of fuzzy sets, and thus its implementation was more substantial. The well-known sine trigonometric function maintains the periodicity and symmetry of the origin in nature and thus satisfies the expectations of the experts over the multi-parameters. Taking this feature and the significance of the q-SFRSs into consideration, the main objective of the article is to describe some reliable sine trigonometric laws for SFSs. Associated with these laws, we develop new average and geometric aggregation operators to aggregate the q-spherical fuzzy rough numbers. Then, we presented a group decision-making strategy to address the multi-attribute group decision-making problem using the developed aggregation operators. To verify the value of the defined operators, a MAGDM strategy is provided along with applications for selecting a Cloud Service Provider and a Digital Transformation Vendor for digital transformation. Moreover, a comparative study is also performed to present the effectiveness of the developed approach.

Linguistic q-rung orthopair fuzzy Z-number and its application in multi-criteria decision-making

This paper proposes a new linguistic model called Linguistic q-Rung Orthopair fuzzy Z-number (LqROFZN), which combines the advantages of linguistic variables, Z-number and q-Rung Orthopair Fuzzy numbers. It can be used as a powerful tool for uncertain decision-making, which can effectively improve the accuracy and reliability of the decision-making results, and has a notable application prospect for the fields of information decision-making, risk assessment, diagnosis and so on. In this paper, firstly, the definition of LqROFZN and its operational rules are given, a new distance measure and the concept of entropy are given under LqROFZN, and the entropy of LqROFZN can assess the credibility situation of LqROFZN. Next, two aggregation operators under LqROFZN are given, namely the Linguistic q-Rung Orthopair fuzzy Z-number weighted aggregation (LqROFZWA) operator and the Linguistic q-Rung Orthopair fuzzy Z-number weighted Geometric aggregation (LqROFZWGA) operator. Finally, the MCDM method under LqROFZN is given and the credibility of the evaluation results is assessed using the entropy of LqROFZN. In a set of actual airline aircraft selection cases, the feasibility and advantages of the proposed method are verified through comparative analysis with other methods.

Determination of the most influential robot in the medical field by utilizing the bipolar complex fuzzy soft aggregation operators

From science fiction to the hospital, robots are transforming the medical field. These robots mostly look like R2D2 from Star Wars more than humanoids, yet they are having a substantial impact on the medical field. Robots in the medical field support by releasing medical staff from repetitive chores that distract their consideration to more vital responsibilities and by dropping the danger and expenditure of medical treatment for patients. The robots can also move hazardous materials and execute accurate surgery in small spaces. Considering this influence of robots on the medical field, in this manuscript, we investigate the influence of robots on the medical field and discover which robot is more influential in the medical field. For this, the bipolar complex fuzzy soft set (BCFSS) is a substantial mathematical model that covers genuine decision-making (DM) dilemmas where the obscurity and imprecision contain a negative pole, 2nd dimension, and parameterization at one time. Moreover, in this study, we establish arithmetic and geometric aggregation operators (AOs) in the setting of BCFSS, like bipolar complex fuzzy soft-weighted arithmetic averaging (BCFSWAA) and bipolar complex fuzzy soft-weighted geometric averaging (BCFSWGA) operators. Moreover, for discovering the most influential robot, we invent a technique of DM relying on the diagnosed AOs in the environment of BCFSS, and then, we describe a numerical example (determination of the most influential robot in the medical field). To demonstrate the superiority and condescension of our work we compare it with prevailing work.

Multi-criteria assessment of climate change due to green house effect based on Sugeno Weber model under spherical fuzzy Z-numbers

Using the multi-criteria decision-making (MCDM) approach, this research piece addresses the urgent problems of environmental degradation and climate change. The method provides a structured way to examine and compare different criteria and options, which improves the precision of decision-making. In order to make this method even better, we combine Zadeh's Z´-numbers with limitations and reliability factors in an effort to fill the current knowledge vacuum about their maximum potential. We investigate Z´-numbers, which are unexpected and fuzzy, in an effort to use them to our advantage by combining them with spherical fuzzy sets (SFSs). We present the idea of spherical fuzzy Z´-numbers (SFZ´Ns) that allow for flexible and adaptive handling of uncertain data by facilitating fast pairwise comparisons of decision-making options. We develop a full set of operational rules and create aggregation operators (AOs) based on the Sugeno Weber Γ¯-norm and Γ¯-conorm to formalize this new method. We use the average and geometric AOs, two of these operators, to show how our suggested technique works and how practical it is. In decision-making situations including climate change assessment, our comparison study highlights the importance of the suggested operators and approaches, especially in relation to the greenhouse effect. Our study helps us understand Z´-numbers better and how they might be used to handle uncertain data by tackling the interaction between fuzziness and randomness. By emphasizing clarity and specificity, our research provides a solid basis for better decision-making and handling of ambiguity in several fields.

The Characteristics of Circular Fermatean Fuzzy Sets and Multicriteria Decision-Making Based on the Fermatean Fuzzy t-Norm and t-Conorm

When diverse decision makers are involved in the decision-making process, taking average of decision values might not reflect an accurate point of view. To overcome such a scenario, the circular Fermatean fuzzy (CFF) set, an advancement of the Fermatean fuzzy (FF) set, and the interval-valued Fermatean fuzzy set (IVFFS) are introduced in this current study. The proposed CFF set is a circle with a centre as association value (AV) and nonassociation value (NAV) with a radius at most equal to 2. It is built in such a way that it covers all the decision makers’ opinion value through a circle. Due to its geometric structure, the CFF set resolves ambiguity and risk more accurately and effectively than FF and IVFF. FF t-norm and t-conorm are used to investigate the properties of CFF sets, subsequent to which the algebraic operations between them are defined. A couple of CFF distance measures between CFF numbers are introduced and used in the selection of an electric autorickshaw along with the CFF weighted averaging and geometric aggregation operators. The overview and comparison analysis of the generated reports exemplifies the viability and compatibility of the CFF set strategy for selecting the best choices.

QNN-MAGDM strategy for E-commerce site selection using quadripartition neutrosophic neutrality aggregative operators

In this paper, we define the Quadripartition Neutrosophic Weighted Neutrality Aggregative (QNWNA) operator and Quadripartition Neutrosophic Ordered Weighted Neutrality Aggregative (QNOWNA) operator for solving Multi-Attribute Group Decision Making (MAGDM) problems. The basic properties of both operators are discussed thoroughly. A new MAGDM strategy is developed using these developed operators. A case study of e-commerce site selection in India is discussed to show the applicability of the proposed MADM strategy. Moreover, the performance of the QNWNA and QNOWNA operators are compared with Quadripartition Neutrosophic Weighted Arithmetic Aggregation (QNWAA) operator and Quadripartition Neutrosophic Weighted Geometric Aggregation (QNWGA), Quadripartition Single valued Neutrosophic Dombi Weighted Arithmetic Aggregation (QSVNDWAA) and QSVN Dombi Weighted Geometric Aggregation (QSVNDWAA) operator.

P, q-Spherical fuzzy sets and their aggregation operators with application to third-party logistic provider selection

The selection of an appropriate third-party logistics (3PL) provider has become an inescapable option for shippers in today’s business landscape, as the outsourcing of logistics activities continues to increase. Choosing the 3PL supplier that best meets their requirements is one of the most difficult difficulties that logistics consumers face. Effective decision-making (DM) is critical in dealing with such scenarios, allowing shippers to make well-informed decisions within a restricted timeframe. The importance of DM arises from the possible financial repercussions of poor decisions, which can result in significant financial losses. In this regard, we introduce p, q-spherical fuzzy set (p, q-SFS), a novel concept that extends the concept of T-spherical fuzzy sets (T-SFSs). p, q-SFS is a comprehensive representation tool for capturing imprecise information. The main contribution of this article is to define the basic operations and a series of averaging and geometric AOs under p, q-spherical fuzzy (p, q-SF) environment. In addition, we establish several fundamental properties of the proposed aggregation operators (AOs). Based on these AOs, we propose a stepwise algorithm for multi-criteria DM (MCDM) problems. Finally, a real-life case study involving the selection of a 3PL provider is shown to validate the applicability of the proposed approach.

Intuitionistic fuzzy geometric aggregation operators based on Yager’s triangular norms and its application in multi-criteria decision making

Intuitionistic fuzzy (IF) information aggregation in multi-criteria decision making (MCDM) is a substantial stream that has attracted significant research attention. There are various IF aggregation operators have been suggested for extracting more informative data from imprecise and redundant raw information. However, some of the aggregation techniques that are currently being applied in IF environments are non-monotonic with respect to the total order, and suffer from high computational complexity and inflexibility. It is necessary to develop some novel IF aggregation operators that can surpass these imperfections. This paper aims to construct some IF aggregation operators based on Yager’s triangular norms to shed light on decision-making issues. At first, we present some novel IF operations such as Yager sum, Yager product and Yager scalar multiplication on IF sets. Based on these new operations, we propose the IF Yaeger weighted geometric operator and the IF Yaeger ordered weighted geometric operator, and prove that they are monotone with respect to the total order. Then, the focus on IF MCDM have motivated the creation of a new MCDM model that relies on suggested operators. We show the applicability and validity of the model by using it to select the most influential worldwide supplier for a manufacturing company and evaluate the most efficient method of health-care disposal. In addition, we discuss the sensitivity of the proposed operator to decision findings and criterion weights, and also analyze it in comparison with some existing aggregation operators. The final results show that the proposed operator is suitable for aggregating both IF information on “non-empty lattice" and IF data on total orders.

Extension of Interaction Geometric Aggregation Operator for Material Selection Using Interval-Valued Intuitionistic Fuzzy Hypersoft Set

A recently emerged area of research named intuitionistic fuzzy hypersoft set (IFHSS) attempts to describe the internal limitations of intuitionistic fuzzy soft sets on multiparameter functions. A computation of such a type connects a power set of the universe with a tuple of sub-parameters. The strategy shows the allocation of attributes to their respective sub-attribute values in distinct groupings. The above features make it a unique methodical tool for handling obstacles of hesitation. The aggregation operators have an important role in the assessment of both types of potential and in identifying problems from their assessment. This research extends the use of the interaction aggregation operator to the interval-valued intuitionistic fuzzy hypersoft set (IVIFHSS), which is an entirely new structure generated through the interval-valued intuitionistic fuzzy soft set (IVIFSS). The IVIFHSS significantly condenses information that is inaccurate and imprecise compared to the frequently utilized IFSS and IVIFSS. Fuzzy reasoning is recognized as the prevalent strategy for improving imperfect data in decision-making processes. The core objective of the research is to develop operational rules for interval-valued intuitionistic fuzzy hypersoft numbers (IVIFHSNs), which promote interactions. This research is designed to broaden the utilization of the interaction geometric aggregation operator in the framework of IVIFHSS. In particular, we propose a novel operator known as the Interval-Valued Intuitionistic Fuzzy Hypersoft Interactive Weighted Geometric (IVIFHSIWG) operator. The aggregation operator indicates industry professional support for the implementation of a robust MCGDM material selection technique in order to address this need. The practical application of the intended MCGDM technique has been introduced in selecting materials (MS) for cryogenic storage containers. The influence advocates that the anticipated model is more operational and stable in demonstrating anxious facts based on IVIFHSS.

An Integrated Group Decision-Making Framework for the Evaluation of Artificial Intelligence Cloud Platforms Based on Fractional Fuzzy Sets

Due to the rapid development of machine learning and artificial intelligence (AI), the analysis of AI cloud platforms is now a key area of research. Assessing the wide range of frameworks available and choosing the ideal AI cloud providers that may accommodate the demands and resources of a company is mandatory. There are several options, all having their own benefits and limitations. The evaluation of artificial intelligence cloud platforms is a multiple criteria group decision-making (MCGDM) process. This article establishes a collection of Einstein geometric aggregation operators (AoPs) and a novel Fractional Fuzzy VIKOR and Fractional Fuzzy Extended TOPSIS based on the entropy weight of criteria in fractional fuzzy sets (FFSs) for this scenario. The FFSs provide an evaluation circumstance containing more information, which makes the final decision-making results more accurate. Finally, this framework is then implemented in a computational case study for the evaluation of artificial intelligence cloud platforms and comparison of this model with other existing approaches, such as the extended GRA approach, to check the consistency and accuracy of the proposed technique. The most optimal artificial intelligence cloud platform is I1

Optimizing Material Selection with Fermatean Fuzzy Hybrid Aggregation Operators

In the pursuance of engineering excellence and sustainable practices, the optimization of material selection processes plays a crucial role. Using Fermatean fuzzy aggregation Operators (AOs), this study introduces an innovative method for improving material selection procedures. Combining the advantages of Fermatean fuzzy set (FrFS) and AOs, the proposed method enables a comprehensive evaluation of materials based on multiple criteria. The authors propose two operators: the “Fermatean fuzzy hybrid weighted arithmetic geometric aggregation (FrFHWAGA) operator” and the “Fermatean fuzzy hybrid ordered weighted arithmetic geometric aggregation (FrFHOWAGA) operator”. This method facilitates informed decision making in a number of industries by taking into account factors such as cost, durability, environmental impact, and availability. This research enables engineers, designers, and decision makers to optimize material selection, resulting in more efficient, cost-effective, and sustainable solutions across multiple domains.

Retracted: Some Novel Geometric Aggregation Operators of Spherical Cubic Fuzzy Information with Application

Retracted: Some Novel Geometric Aggregation Operators of Spherical Cubic Fuzzy Information with Application

Retracted: Some Generalized T-Spherical and Group-Generalized Fuzzy Geometric Aggregation Operators with Application in MADM Problems

Retracted: Some Generalized T-Spherical and Group-Generalized Fuzzy Geometric Aggregation Operators with Application in MADM Problems

Retracted: Analysis of Social Networks by Using Pythagorean Cubic Fuzzy Einstein Weighted Geometric Aggregation Operators

Retracted: Analysis of Social Networks by Using Pythagorean Cubic Fuzzy Einstein Weighted Geometric Aggregation Operators

MCDM technique using single-valued neutrosophic trigonometric weighted aggregation operators

Motivated based on the trigonometric t-norm and t-conorm, the aims of this article are to present the trigonometric t-norm and t-conorm operational laws of SvNNs and then to propose the SvNN trigonometric weighted average and geometric aggregation operators for the modelling of a multiple criteria decision making (MCDM) technique in an inconsistent and indeterminate circumstance. To realize the aims, this paper first proposes the trigonometric t-norm and t-conorm operational laws of SvNNs, which contain the hybrid operations of the tangent and arctangent functions and the cotangent and inverse cotangent functions, and presents the SvNN trigonometric weighted average and geometric operators and their properties. Next, a MCDM technique is proposed in view of the presented two aggregation operators in the circumstance of SvNNs. In the end, an actual case of the choice issue of slope treatment schemes is provided to indicate the practicability and effectivity of the proposed MCDM technique.

Innovative discussion of decision-making model based on complex cubic picture fuzzy information and geometric aggregation operators with applications

This article presents a novel concept of complex cubic picture fuzzy sets (CCPFS) and introduces one more new idea of complex interval-valued picture fuzzy sets (CIVPFS) as foundational framework of CCPFS. The proposed CCPFS combines CIVPFS and complex picture fuzzy sets (CPFS), where CPFS extends the complex intuitionistic fuzzy set by incorporating a neutral membership degree. This unique model offers an expanded range of values using degrees of membership, neutral membership, and non-membership, within the unit disk of a complex plane. Additionally, we introduce two more new ideas of internal complex cubic picture fuzzy sets (ICCPFS) and external complex cubic picture fuzzy sets (ECCPFS) to further enhance the versatility of the approach. To facilitate practical applications, complement, score, and accuracy functions are developed and defined for CCPFS. Moreover, three types of averaging aggregation operators based on complex cubic picture fuzzy sets are introduced, including complex cubic picture fuzzy weighted geometric (CCPFWG) operators, complex cubic picture fuzzy ordered weighted geometric (CCPFOWG) operator, and complex cubic picture fuzzy hybrid weighted geometric (CCPFHWG) operator. The CCPFHWG operator generalizes both CCPFWG and CCPFOWG operators, providing a comprehensive framework for aggregating complex cubic picture fuzzy data. To demonstrate the practicality of the proposed approach, a multi-criteria decision-making (MCDM) problem is presented, showcasing its effectiveness in addressing today's complex decision structures. The utilization of complex cubic picture fuzzy sets and the corresponding aggregation operators in MCDM highlights their applicability and relevance in tackling real-world complexities.

Retracted: Multiple-Attribute Decision-Making Method Based on Normalized Geometric Aggregation Operators of Single-Valued Neutrosophic Hesitant Fuzzy Information

Retracted: Multiple-Attribute Decision-Making Method Based on Normalized Geometric Aggregation Operators of Single-Valued Neutrosophic Hesitant Fuzzy Information

A Novel Interval-Valued Decision Theoretic Rough Set Model with Intuitionistic Fuzzy Numbers Based on Power Aggregation Operators and Their Application in Medical Diagnosis

Intuitionistic fuzzy information is a potent tool for medical diagnosis applications as it can represent imprecise and uncertain data. However, making decisions based on this information can be challenging due to its inherent ambiguity. To overcome this, power aggregation operators can effectively combine various sources of information, including expert opinions and patient data, to arrive at a more accurate diagnosis. The timely and accurate diagnosis of medical conditions is crucial for determining the appropriate treatment plans and improving patient outcomes. In this paper, we developed a novel approach for the three-way decision model by utilizing decision-theoretic rough sets and power aggregation operators. The decision-theoretic rough set approach is essential in medical diagnosis as it can manage vague and uncertain data. The redesign of the model using interval-valued classes for intuitionistic fuzzy information further improved the accuracy of the diagnoses. The intuitionistic fuzzy power weighted average (IFPWA) and intuitionistic fuzzy power weighted geometric (IFPWG) aggregation operators are used to aggregate the attribute values of the information system. The established operators are used to combine information within the intuitionistic fuzzy information system. The outcomes of various alternatives are then transformed into interval-valued classes through discretization. Bayesian decision rules, incorporating expected loss factors, are subsequently generated based on this foundation. This approach helps in effectively combining various sources of information to arrive at more accurate diagnoses. The proposed approach is validated through a medical case study where the participants are classified into three different regions based on their symptoms. In conclusion, the decision-theoretic rough set approach, along with power aggregation operators, can effectively manage vague and uncertain information in medical diagnosis applications. The proposed approach can lead to timely and accurate diagnoses, thereby improving patient outcomes.

University’s recruitment process using Fermatean fuzzy Einstein prioritized aggregation operators

In comparison to intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS), the Fermatean Fuzzy Set (FFS) is more efficacious in dealing ambiguous and imprecise data when making decisions. In this paper, we propose unique operations on Fermatean fuzzy information based on prioritized attributes, as well as Einstein’s operations based on adjusting the priority of characteristics in the Fermatean fuzzy environment. We use Einstein’s operations with prioritized attributes to propose new operations on Fermatean fuzzy numbers (FFNs), and then introduce basic aspects of these operations. Motivated by Einstein operations on FFNs, we develop Fermatean fuzzy Einstein prioritized arithmetic and geometric aggregation operators (AOs). In the first place, the concepts of a Fermatean fuzzy Einstein prioritized average (FFEPA), Fermatean fuzzy Einstein prioritized weighted average (FFEPWA), and Fermatean fuzzy Einstein prioritized ordered weighted average (FFEPOWA)-operators are introduced. Then, Fermatean fuzzy Einstein prioritized geometric (FFEPG) operator, Fermatean fuzzy Einstein prioritized weighted geometric (FFEPWG) operator, Fermatean fuzzy Einstein prioritized ordered weighted geometric (FFEPOWG) operator, and Fermatean fuzzy Einstein hybrid geometric (FFEHG) operator are given. We also go through some of the key characteristics of these operators. Moreover, using these operators, we establish algorithm for addressing a multiple attribute decision-making issue using Fermatean fuzzy data and attribute prioritizing. The case of university faculty selection is taken as a scenario to analyze and demonstrate the applicability of our suggested model. In addition, a comparison of the proposed and current operators is conducted, and the impact of attribute priority on the ranking order of alternatives is explored.