Geometric Operator Research Articles

Multi-criteria group decision-making based on dombi aggregation operators under p, q-quasirung orthopair fuzzy sets

In this study, we introduce The p, q-quasirung orthopair fuzzy Dombi operators, including p, q-quasirung orthopair fuzzy Dombi weighted averaging (p, q-QOFDWA), p, q-quasirung orthopair fuzzy Dombi ordered weighted averaging (p, q-QOFDOWA), p, q-quasirung orthopair fuzzy Dombi weighted geometric (p, q-QOFDWG), and p, q-quasirung orthopair fuzzy Dombi ordered weighted geometric (p, q-QOFDOWG) operators. These operators effectively manage imprecise and uncertain information, outperforming other fuzzy sets like the Pythagorean fuzzy set (PFS) and q-rung orthopair fuzzy set (q-ROFS). We investigate their properties, including boundedness and monotonicity, and demonstrate their applicability in multiple criteria decision-making (MCDM) problems within a p, q-quasirung orthopair fuzzy (p, q-QOF) environment. To showcase the practicality, we present a real-world scenario involving the selection of investment alternatives as an illustrative example. Our findings highlight the significant advantage and potential of these operators for handling uncertainty in decision-making.

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.

A novel CE-PT-MABAC method for T-spherical uncertain linguistic multiple attribute group decision-making

A T-spherical uncertain linguistic set (TSULS) is not only an expanded form of the T-spherical fuzzy set and the uncertain linguistic set but can also integrate the quantitative judging ideas and qualitative assessing information of decision-makers. For the description of complex and uncertain assessment data, TSULS is a powerful tool for the precise description and reliable processing of information data. However, the existing multi-attribute border approximation area comparison (MABAC) method has not been studied in TSULS. Thus, the goal of this paper is to extend and improve the MABAC method to tackle group decision-making problems with completely unknown weight information in the TSUL context. First, the cross-entropy measure and the interactive operation laws for the TSUL numbers are defined, respectively. Then, the two interactive aggregation operators for TSUL numbers are developed, namely T-spherical uncertain linguistic interactive weighted averaging and T-spherical uncertain linguistic interactive weighted geometric operators. Their effective properties and some special cases are also investigated. Subsequently, a new TSULMAGDM model considering the DM’s behavioral preference and psychology is built by integrating the interactive aggregation operators, the cross-entropy measure, prospect theory, and the MABAC method. To explore the effectiveness and practicability of the proposed model, an illustrative example of Sustainable Waste Clothing Recycling Partner selection is presented, and the results show that the optimal solution is h3. Finally, the reliable, valid, and generalized nature of the method is further verified through sensitivity analysis and comparative studies with existing methods.

Multi-Criteria Decision Making Model For Hotel Selection Problem Under Complex Dual Hesitant Fuzzy Information

ABSTRACT The notion of the “complex dual hesitant fuzzy set (CDHFS)” is the combination of the “dual hesitant fuzzy set (DHFS)” and the “complex fuzzy set (CFS).” It is characterized by two degrees, namely the membership and nonmembership, in the form of a finite subset on a unit disc in the complex plane. CDHFS is useful for dealing with real-world problems involving uncertain or hard-to-predict information. Also, to approximate smoothly, the Einstein operators are well-known aggregation operators, while prioritized operators are effective tools for prioritization among criteria. Therefore, the goal of this study is to develop some prioritized aggregation operators under the CDHFS environment; namely the complex dual hesitant fuzzy prioritized averaging (CDHFPA) operator, the complex dual hesitant fuzzy prioritized geometric (CDHFPG) operator, the complex dual hesitant fuzzy Einstein prioritized averaging (CDHFEPA) operator, and complex dual hesitant fuzzy Einstein prioritized geometric (CDHFEPG) operator. Some properties of the proposed operators are investigated in detail. In addition, a multi-criteria decision-making (MCDM) method based on the proposed operators with the complex dual hesitant fuzzy setting is developed. Moreover, a numerical example is given for the application and effectiveness of the developed MCDM approach. A comparison study is also done with existing methods to show that the proposed MCDM method is better and more reliable. The study finds that if the expert’s preference is used to choose the right aggregation operators, the decision maker will have access to a wide range of compromise solutions.

Selecting the foremost big data tool to optimize YouTube data in dynamic Fermatean fuzzy knowledge.

Big data pertains to extensive and intricate compilations of information that necessitate the implementation of proficient and cost-effective evaluation and analysis tools to derive insights and support decision making. The Fermatean fuzzy set theory possesses remarkable capability in capturing imprecision due to its capacity to accommodate complex and ambiguous problem descriptions. This paper presents the study of the concepts of dynamic ordered weighted aggregation operators in the context of Fermatean fuzzy environment. In numerous practical decision making scenarios, the term "dynamic" frequently denotes the capability of obtaining decision-relevant data at various time intervals. In this study, we introduce two novel aggregation operators: Fermatean fuzzy dynamic ordered weighted averaging and geometric operators. We investigate the attributes of these operators in detail, offering a comprehensive description of their salient features. We present a step-by-step mathematical algorithm for decision making scenarios in the context of proposed methodologies. In addition, we highlight the significance of these approaches by presenting the solution to the decision making problem and determining the most effective big data analytics platform for YouTube data analysis. Finally, we perform a thorough comparative analysis to assess the effectiveness of the suggested approaches in comparison to a variety of existing techniques.

Impact of AI Techniques in Electrical Engineering With Spherical Fuzzy Soft Geometric Aggregation Operators

Impact of AI Techniques in Electrical Engineering With Spherical Fuzzy Soft Geometric Aggregation Operators

Linguistics complex intuitionistic fuzzy aggregation operators and their applications to plastic waste management approach selection

<p>Linguistic complex intuitionistic fuzzy aggregation operators are a novel idea for the description of intuitionistic fuzzy information, where linguistic complex concepts are used to describe membership and non-membership. This can convey the hazy information more clearly, and some findings on linguistic complex intuitionistic fuzzy aggregation operators have been attained. Nonetheless, several linguistic complex intuitionistic fuzzy aggregation operators in the literature are founded on conventional operational principles, which have certain limitations when used to multi-attribute group decision-making (MAGDM). In this study, we presented some improved operating rules based on linguistic complex intuitionistic fuzzy variables (LCIFVs) and changed their features to address these issues. Next, we created a few aggregation operators, such as the enhanced linguistic complex intuitionistic fuzzy weighted average (LCIFWA) and the linguistic complex intuitionistic fuzzy ordered weighted averaging (LCIFOWA) operator, to fuse the decision information represented by LCIFVs. We also demonstrated that they had a few favorable qualities. We introduced many novel approaches to address the MAGDM issues in the context of the linguistic complex intuitionistic fuzzy environment, based on the LCIFOWA and linguistic complex intuitionistic fuzzy ordered weighted geometric (LCIFOWG) operators. In short, we employed few real-world scenarios to demonstrate the viability and soundness of the suggested techniques through comparison with other approaches. This unique technique has been applied to plastic waste management selection, and the results are more accurate than the previously used materials and methods.</p>

L^p(\mathbb{R}^2) bounds for geometric maximal operators associated with homothecy invariant convex bases

L^p(\mathbb{R}^2) bounds for geometric maximal operators associated with homothecy invariant convex bases

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 . 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.

CODAS method for Pythagorean 2-tuple linguistic multiple attribute group decision making

The evaluation of the financial performance of universities is conducive to the sustainable development of universities. Based on this, we extend the traditional CODAS (COmbinative Distance-based ASsessment) method to the Pythagorean 2-tuple linguistic fuzzy environment and propose a P2TL-CODAS model to evaluate the financial management performance of universities. Firstly, we briefly describe the definition, the score function, accuracy function, operational laws and the distance calculating method of P2TLSs. Next, two aggregation operators of P2TL including Pythagorean 2-tuple linguistic weighted averaging (P2TLWA) operator and Pythagorean 2-tuple linguistic weighted geometric (P2TLWG) operator are also introduced to fuse overall Pythagorean 2-tuple linguistic evaluation information. Then the steps of CODAS method are depicted briefly. Moreover, we use linguistic Pythagorean 2-tuple linguistic fuzzy numbers to extend the CODAS method. The P2TL-CODAS model is established and all computing steps are simply presented. Furthermore, we apply the proposed method to evaluate the financial management performance about five universities. Finally, a comparison between P2TL-CODAS method and P2TL-TODIM method is made to demonstrate the stability of the new method. The results show that the proposed method has unique advantages.

Crafting optimal cardiovascular treatment strategy in Pythagorean fuzzy dynamic settings

<p>The prevalence of cardiovascular disease (CVD) is a major issue in world health. There is a compelling desire for precise and effective methods for making decisions to determine the most effective technique for treating CVD. Here, we focused on the urgent matter at hand. Pythagorean fuzzy dynamic settings are exceptionally proficient at capturing ambiguity because they can handle complex problem specifications that involve both Pythagorean uncertainty and periodicity. In this article, we introduced a pair of novel aggregation operators: The Pythagorean fuzzy dynamic ordered weighted averaging (PFDOWA) operator and the Pythagorean fuzzy dynamic ordered weighted geometric (PFDOWG) operator, and we proved various structural properties of these concepts. Using these operators, we devised a systematic methodology to handle multiple attribute decision-making (MADM) scenarios incorporating Pythagorean fuzzy data. Moreover, we endeavored to address a MADM problem, where we discerned the most efficacious strategy for the management of CVD through the application of the proposed operators. Finally, we undertook an exhaustive comparative analysis to evaluate the ability of the suggested methods in connection with several developed procedures, therefore demonstrating the reliability of the generated methodologies.</p>

Rough Neutrosophic Multisets Geometric Aggregation Operator with Entropy Weight Combined Roughness Dice Similarity Measure and Its Application

Rough Neutrosophic Multisets Geometric Aggregation Operator with Entropy Weight Combined Roughness Dice Similarity Measure and Its Application

Innovative approaches to solar cell selection under complex intuitionistic fuzzy dynamic settings

<abstract> <p>The need to meet current energy demands while protecting the interests of future generations has driven people to adopt regulatory frameworks that promote the careful use of limited resources. Among these resources, the sun is an everlasting source of energy. Solar energy stands out as a prime example of a renewable and environmentally friendly energy source. An imperative requirement exists for precise and dependable decision-making methods for the selection of the most efficacious solar cell. We aimed to address this particular issue. The theory of complex intuitionistic fuzzy sets (CIFS) adeptly tackles ambiguity, encompassing complex problem formulations characterized by both intuitionistic uncertainty and periodicity. We introduced two aggregation operators: The complex intuitionistic fuzzy dynamic ordered weighted averaging (CIFDOWA) operator and the complex intuitionistic fuzzy dynamic ordered weighted geometric (CIFDOWG) operator. Noteworthy features of these operators were stated, and significant special cases were meticulously outlined. An updated score function was devised to address the deficiencies, identified in the current score function within the context of CIF knowledge. In addition, we devised a methodical strategy for managing multiple attribute decision-making (MADM) problems that involve CIF data by implementing the proposed operators. To demonstrate the efficacy of the formulated algorithm, we presented a numerical example involving the selection of solar cells together with a comparative analysis with several well-established methodologies.</p> </abstract>

Selection of artificial neutral networks based on cubic intuitionistic fuzzy Aczel-Alsina aggregation operators

<p>Artificial neural networks (ANNs) are the collection of computational techniques or models encouraged by the shape and purpose of natural or organic neural networks. Furthermore, a cubic intuitionistic fuzzy (CIF) set is the modified or extended form of a Fuzzy set (FS). Our goal was to address or compute the model of Aczel-Alsina operational laws under the consideration of the CIF set as well as Aczel-Alsina t-norm (AATN) and Aczel-Alsina t-conorm (AATCN), where the model of Algebraic norms and Drastic norms were the special parts of the Aczel-Alsina norms. Further, using the above invented operational laws, we aimed to develop the model of Aczel-Alsina average/geometric aggregation operators, called CIF Aczel-Alsina weighted averaging (CIFAAWA), CIF Aczel-Alsina ordered weighted averaging (CIFAAOWA), CIF Aczel-Alsina hybrid averaging (CIFAAHA), CIF Aczel-Alsina weighted geometric (CIFAAWG), CIF Aczel-Alsina ordered weighted geometric (CIFAAOWG), and CIF Aczel-Alsina hybrid geometric (CIFAAHG) operators with some well-known and desirable properties. Moreover, a procedure decision-making technique was presented for finding the best type of artificial neural networks with the help of multi-attribute decision-making (MADM) problems based on CIF aggregation information. Finally, we determined a numerical example for showing the rationality and advantages of the developed method by comparing their ranking values with the ranking values of many prevailing tools.</p>

The Perfect Score Function and Optimized Weighted Geometric Operator for Ranking Single‐Valued Neutrosophic Numbers in the Decision‐Making Process

The single‐valued neutrosophic set (SVNS) is a more common platform for representing the degree of truth, indeterminacy, and falsity memberships. Indeterminacy is an important aspect of SVNS, and the score function (SF) is important in ranking alternatives in decision‐making scenarios. When the score and accuracy values for different SVNNs were equal, existing SFs were unable to rank the alternatives. To address the limitations, this paper introduces the perfect score function (PSF) as a solution for ranking single‐valued neutrosophic numbers (SVNNs) without any errors and presents the concepts of strong and weak SVNSs. This article has emphasized the drawbacks of the existing SF in SVNNs. Additionally, we propose an optimized weighted geometric operator (OWGO) for SVNNs, and its properties such as idempotency, boundedness, monotonicity, and commutativity are explored. Furthermore, the decision‐making approach has been depicted based on the proposed score function and OWGO to select the finest faculty for a university.

Dynamic bipolar fuzzy aggregation operators: A novel approach for emerging technology selection in enterprise integration

<abstract> <p>Emerging technology selection is crucial for enterprise integration, driving innovation, competitiveness, and streamlining operations across diverse sectors like finance and healthcare. However, the decision-making process for technology adoption is often complex and fraught with uncertainties. Bipolar fuzzy sets offer a nuanced representation of uncertainty, allowing for simultaneous positive and negative membership degrees, making them valuable in decision-making and expert systems. In this paper, we introduce dynamic averaging and dynamic geometric operators under bipolar fuzzy environment. We also establish some of the fundamental crucial features of these operators. Moreover, we present a step by step mechanism to solve MADM problem under bipolar fuzzy dynamic aggregation operators. In addition, these new techniques are successfully applied for the selection of the most promising emerging technology for enterprise integration. Finally, a comparative study is conducted to show the validity and practicability of the proposed techniques in comparison to existing methods.</p> </abstract>

T-Spherical Fuzzy Valued Neutrosophic Aggregation Operators: Applications in Multi-Attribute Decision Making

This paper aims to introduce and explore the innovative concept of T-spherical fuzzy valued neutrosophic sets (T-SFVNSs) in the context of multi-attribute decision making (MADM). The T-SFVNSs are utilized to develop two key aggregation operators: the T-spherical fuzzy valued neutrosophic weighted average operator (T-SFVNWAO) and the T-spherical fuzzy valued neutrosophic weighted geometric operator (T-SFVNWGO). These operators are defined based on the operational rules of T-SFVNNs. The properties of these operators, including idempotency, boundedness, and monotonicity, are rigorously examined and established. To demonstrate the practicality and relevance of the T-SFVN operators, an algorithm and a numerical application are presented. The algorithm illustrates the step-by-step implementation of these operators, while the numerical application showcases their effectiveness in real-world scenarios. Additionally, a comparative analysis is conducted to evaluate the accuracy and performance of the proposed operators in relation to existing ones.

The q-rung orthopair fuzzy-valued neutrosophic sets: Axiomatic properties, aggregation operators and applications

<abstract><p>During the transitional phase spanning from the realm of fuzzy logic to the realm of neutrosophy, a multitude of hybrid models have emerged, each surpassing its predecessor in terms of superiority. Given the pervasive presence of indeterminacy in the world, a higher degree of precision is essential for effectively handling imprecision. Consequently, more sophisticated variants of neutrosophic sets (NSs) have been conceived. The key objective of this paper is to introduce yet another variant of NS, known as the q-rung orthopair fuzzy-valued neutrosophic set (q-ROFVNS). By leveraging the extended spatial range offered by q-ROFS, q-ROFVNS enables a more nuanced representation of indeterminacy and inconsistency. Our endeavor commences with the definitions of q-ROFVNS and q-ROFVN numbers (q-ROFVNNs). Then, we propose several types of score and accuracy functions to facilitate the comparison of q-ROFVNNs. Fundamental operations of q-ROFVNSs and some algebraic operational rules of q-ROFVNNs are also provided with their properties, substantiated by proofs and elucidated through illustrative examples. Drawing upon the operational rules of q-ROFVNNs, the q-ROFVN weighted average operator (q-ROFVNWAO) and q-ROFVN weighted geometric operator (q-ROFVNWGO) are proposed. Notably, we present the properties of these operators, including idempotency, boundedness and monotonicity. Furthermore, we emphasize the applicability and significance of the q-ROFVN operators, substantiating their utility through an algorithm and a numerical application. To further validate and evaluate the proposed model, we conduct a comparative analysis, examining its accuracy and performance in relation to existing models.</p></abstract>

A novel approach to decision making in rice quality management using interval-valued Pythagorean fuzzy Schweizer and Sklar power aggregation operators.

The Pythagorean fuzzy set and interval-valued intuitionistic fuzzy set are the basis of the interval-valued Pythagorean fuzzy set (IVPFS) which offers an effective approach to addressing the complex uncertainty in decision-analysis processes, making it applicable across a broad spectrum of applications. This paper introduces several aggregation operators within the IVPF framework, such as the interval-valued Pythagorean fuzzy SS power weighted average operator, and the interval-valued Pythagorean fuzzy SS power geometric operator using the notion of power aggregation operators through Schweizer and Sklar (SS) operations. The existence of SS t-norms and t-conorms in the IVPF framework for addressing multi-attribute decision-making problems gives the generated operator's ability to make the information aggregation approach more adaptable compared to other current ones. The application of the proposed approach holds the potential to enhance crop yield, optimize resource utilization, and contribute to the overall sustainability of agriculture. Additionally, sensitivity and comparative analyses are provided to clarify the stability and dependability of the results acquired through this approach.

Prioritized Aggregation Operators of GTHFNs MADM Approach for the Evaluation of Renewable Energy Sources

In this paper, firstly, we propose two new GTHFNs-prioritized aggregation operators called generalized trapezoidal hesitant fuzzy number prioritized weighted average operator and generalized trapezoidal hesitant fuzzy number prioritized weighted geometric operator. Secondly, we investigate the fundamental properties of the operators in detail such as idempotency, boundedness and monotonicity. Thirdly, we propose a method based on the developed GTHF-numbers prioritized aggregation operators for solving an MADM problem with GTHF-numbers. Fourthly, we give a numerical example of the developed method. Finally, a comparative analysis is given with some existing methods in solving an MADM problem with GTHF-numbers.