Pythagorean Fuzzy Numbers Research Articles

Evaluating ergonomic requirements of graphical user interface: A DEMATEL method integrating linguistic Pythagorean fuzzy rough numbers

Evaluating ergonomic requirements of graphical user interface: A DEMATEL method integrating linguistic Pythagorean fuzzy rough numbers

Shortest Path Problem under Pythagorean Fuzzy Network Using Dijkstra’s Algorithm

In this article investigates the Shortest Path Problem (SPP) in uncertain settings using Pythagorean fuzzy numbers (PFNs). A heuristic methodology using modified Dijkstra's algorithm is developed to exploit error, uncertainty, and partial truth for a low-cost solution. The method calculates minimum distance between starting and destination nodes and evaluates its effectiveness. Pythagorean fuzzy graphs can handle ambiguous situations.

Enhanced Cross-Entropy Exponential TODIM Framework for Interval-Valued Pythagorean Fuzzy Information and Applications to Art Teaching Quality Evaluation

Art teachers in preschool education need to possess not only high professional competence but also a commitment to continuous learning to enhance their comprehensive teaching abilities. The art teaching quality evaluation in preschool education programs at vocational colleges is multiple-attribute group decision-making (MAGDM). Currently, the Exponential TODIM and cross-entropy approach was employed to address MAGDM. Interval-valued Pythagorean fuzzy sets (IVPFSs) serve as a strategy for characterizing uncertain data during the art teaching quality evaluation in preschool education programs at vocational colleges. In this study, the interval-valued Pythagorean fuzzy number cross-entropy Exponential TODIM (IVPFN-CE-ExpTODIM) approach is developed to bring up MAGDM problems under IVPFSs. To validate the proposed method, a numerical study is conducted on the art teaching quality evaluation in preschool education programs at vocational colleges.

Evaluation of psychosocial risks affecting academician using the sine trigonometric pythagorean fuzzy (ST-PFN) DEMATEL method.

In the realm of academia, psychosocial risk factors play a pivotal role, exerting considerable influence on the well-being and performance of scholars. Factors such as excessive workloads, unrelenting performance expectations, time constraints, and competitive atmospheres can detrimentally affect their health and overall quality of life. Moreover, issues like social isolation, work-life imbalance, and academic anxiety further compound these challenges, impeding academic progress and success. Thus, it is imperative to identify, mitigate, and manage psychosocial risk factors effectively to foster a conducive academic environment conducive to productivity and achievement. This study employs a novel approach, integrating expert opinions and utilizing sine trigonometry Pythagorean fuzzy numbers to ascertain the degrees of importance and rank psychosocial risk factors through the DEMATEL method. This methodology presents a unique contribution to existing literature, offering fresh insights into this critical area of study. Evaluation of 25 factors reveals burnout, job dissatisfaction, precarious working conditions, lack of trust, unfair treatment, job insecurity, and limited developmental opportunities as primary concerns, underscoring the multifaceted nature of these challenges. In the occupational sphere, active participation from all stakeholders in addressing psychosocial risks is paramount for effective problem resolution. It is incumbent upon parties involved to discharge their duties, foster collaboration, enhance working conditions, ensure equity, and facilitate avenues for professional growth. Each identified risk factor addressed and preempted translates into a tangible reduction in workplace accidents and occupational ailments, underscoring the tangible benefits of proactive risk management.

Novel similarity measures under complex pythagorean fuzzy soft matrices and their application in decision making problems

Complex fuzzy soft matrices play a crucial role in various applications, including decision-making, pattern recognition, signals processing, and image processing. The main objective of this study is to introduce the unique notions of complex Pythagorean fuzzy soft matrices (CPFSMs), which provide more flexibility and accuracy in modelling uncertainty. CPFSMs incorporate Pythagorean fuzzy soft matrices, allowing for more sophisticated uncertainty modeling. The key findings of CPFSMs, specific instances, and certain fundamental set-theoretic operations and principles were covered. A set of new distance metrics between two CPFSMs has been defined. In the context of complex Pythagorean fuzzy soft sets and complex Pythagorean fuzzy soft matrices, we created a CPFS decision-making technique. Moreover, the application’s numerical example and comparison analysis have been effectively demonstrated. Thus, by integrating the concepts of Pythagorean fuzzy sets, soft matrices, and complex numbers, CPFSMs provide a robust framework with membership and non-membership degrees for complex decision-making modeling and analyzing uncertain data.

EDAS method for circular pythagorean fuzzy with improved Dombi power aggregation operators and their application in policy analysis and decision support systems

A circular Pythagorean fuzzy set is a very dominant and reliable technique for coping with uncertain and vague information in genuine life problems because it contains the membership function, non-membership function, and radius between both grades with a condition that is the sum of the pair will be contained in the unit interval. The objective of this article is to define some improved Dombi operational laws based on circular improved Pythagorean fuzzy values. Moreover, we discuss some drawbacks of the existing Dombi aggregation operators based on circular improved Pythagorean fuzzy numbers. We also defined some improved Dombi averaging and geometric aggregation operators and their properties. Later on, a technique of evaluation based on distance from the average solution is stated by using the proposed operators. Additionally, we resolve the problem of policy analysis and decision support systems based on multi-attribute decision-making problems for initiated techniques to enhance the worth of the derived theory. Finally, we illustrate some examples for showing the supremacy and validity of the proposed theory with the help of comparative analysis between proposed ranking values and some existing ranking values.

A multiple attribute group decision making model based on 2-tuple linguistic pythagorean fuzzy dombi aggregation operators for optimal selection of potential global suppliers

Multiple-Attribute Group Decision-Making (MAGDM) is a significant area of research in decision-making, and its principles and methodologies are widely implemented. A Pythagorean Fuzzy Set (PFS) is an extension of an Intuitionistic Fuzzy Set (IFS) that is highly valuable for representing uncertain information in real-world scenarios. The 2-Tuple Linguistic Pythagorean Fuzzy Number (2TLPFN) is a specific type of Pythagorean Fuzzy Number (PFN) that can be used to represent uncertainty in real-world decision making through the use of 2-Tuple Linguistic Terms (2TLTs). This paper focuses on the examination of Multiple Attribute Group Decision Making (MAGDM) using 2TLPFNs. Dombi's t-norm and t-conorm operations were commonly referred to as Dombi operations, which might have been greater degree of applicability if offered in a new form of flexibility within the general parameter. In this research, we implement Dombi operations to construct some 2-Tuple Linguistic Pythagorean Fuzzy (2TLPF) Dombi Aggregation operators. These operators include the 2TLPF Dombi Weighted Averaging (2TLPFDWA) operator, 2TLPF Dombi Ordered Weighted Averaging (2TLPFDOWA) operator, 2TLPF Dombi Weighted Geometric (2TLPFDWG) operator, and 2TLPF Dombi Ordered Weighted Geometric (2TLPFDOWA) operator. An analysis is conducted to examine the unique characteristics of these suggested operators. Subsequently, we leveraged the proposed operators to develop a model aimed at tackling the MAGDM problems in the 2TLPF environment. Eventually, a suitable instance has been demonstrated to validate the formation of the model as well as exhibit its implementation and resilience.

Solving Fuzzy Assignment Problem of Pythagorean Fuzzy Numbers Exploiting a Software Tool

A fresh approach to computing assignment issues in the pythagorean fuzzy domain is the focus of this body of work. Pythagorean fuzzy numbers are utilised in this work for the sake of analysing working hours and working costs. For converting fuzzy sets integers into a crisp number, a new ranking process is used. Optimal solutions have to be found by using software techniques for minimization, maximization and unbalanced assignment problems. In the end, numerical examples are being solved by using the proposed technique.

Addressing uncertainty in closed-loop supply chain networks: a multi-objective approach to integrated production and transportation problems

Purpose This study aims to address the inherent uncertainties within closed-loop supply chain (CLSC) networks through the application of a multi-objective approach, specifically focusing on the optimization of integrated production and transportation processes. The primary purpose is to enhance decision-making in supply chain management by formulating a robust multi-objective model. Design/methodology/approach In dealing with uncertainty, this study uses Pythagorean fuzzy numbers (PFNs) to effectively represent and quantify uncertainties associated with various parameters within the CLSC network. The proposed model is solved using Pythagorean hesitant fuzzy programming, presenting a comprehensive and innovative methodology designed explicitly for handling uncertainties inherent in CLSC contexts. Findings The research findings highlight the effectiveness and reliability of the proposed framework for addressing uncertainties within CLSC networks. Through a comparative analysis with other established approaches, the model demonstrates its robustness, showcasing its potential to make informed and resilient decisions in supply chain management. Research limitations/implications This study successfully addressed uncertainty in CLSC networks, providing logistics managers with a robust decision-making framework. Emphasizing the importance of PFNs and Pythagorean hesitant fuzzy programming, the research offered practical insights for optimizing transportation routes and resource allocation. Future research could explore dynamic factors in CLSCs, integrate real-time data and leverage emerging technologies for more agile and sustainable supply chain management. Originality/value This research contributes significantly to the field by introducing a novel and comprehensive methodology for managing uncertainty in CLSC networks. The adoption of PFNs and Pythagorean hesitant fuzzy programming offers an original and valuable approach to addressing uncertainties, providing practitioners and decision-makers with insights to make informed and resilient decisions in supply chain management.

Multi-criteria group decision-making for evaluating efficient and smart mobility sharing systems using Pythagorean fuzzy rough numbers

Multi-criteria group decision-making for evaluating efficient and smart mobility sharing systems using Pythagorean fuzzy rough numbers

Clustering analysis for Pythagorean fuzzy sets and its application in multiple attribute decision making

Pythagorean fuzzy sets, as a generalization of intuitionistic fuzzy sets, have a wide range of applications in many fields including image recognition, data mining, decision making, etc. However, there is little research on clustering algorithms of Pythagorean fuzzy sets. In this paper, a novel clustering idea under Pythagorean fuzzy environment is presented. Firstly, the concept of feature vector of Pythagorean fuzzy number (PFN) is presented by taking into account five parameters of PFN, and some new methods to compute the similarity measure of PFNs by applying the feature vector are proposed. Furthermore, a fuzzy similarity matrix by utilizing similarity measure of PFNs is established. Later, the fuzzy similarity matrix is transformed into a fuzzy equivalent matrix which is utilized to establish a novel Pythagorean fuzzy clustering algorithm. Based on the proposed clustering algorithm, a novel multiple attribute decision making (MADM) method under Pythagorean fuzzy environment is presented. To illustrate the effectiveness and feasibility of the proposed technique, an application example is offered.

APPLICATION OF PFAHP-GTOPSIS METHODS FOR THIRD-PARTY LOGISTICS PROVIDER SELECTION

Companies are now considering the option of outsourcing as hedges cost and increase productivity by concentrating on their core skills to update their supply chains due to the competition in global markets, the use of higher-quality products, and rising customer demands. They must carefully select and identify which company to collaborate with before outsourcing their numerous logistics-related tasks to Third-Party Logistics Providers (3PLP). However, the existence of uncertainties and human influence in 3PLP selection problems leads to the usage of fuzzy or related set theories. By incorporating Multi-Criteria Decision Making (MCDM) methods with fuzzy numbers and grey numbers, practical tools can be composed to address the imprecision of subjective judgments. From this perspective, an integrated MCDM model is proposed to provide insight into the 3PLP evaluation and selection. The model comprises an integrated framework with Pythagorean fuzzy numbers and grey numbers. The proposed model has applied a 3PLP a company in the food industry to fulfill customer orders. The evaluation criteria weights are calculated using the Pythagorean Fuzzy Analytic Hierarchy Process (PFAHP) method, and the 3PLPs are ranked using the grey Technique for Order Preference by Similarity to Ideal Solution (GTOPSIS) methods to find the best 3PLP. The analyses and findings concluded that cost, service quality, and on-time delivery were the three criteria that had the greatest influence

A novel approach towards multiattribute decision making using q-rung orthopair fuzzy Dombi–Archimedean aggregation operators

When dealing with real-life problems, the q-rung orthopair fuzzy set is a core concept because the qth power of the membership and non-membership degrees is less than or equal to one. The process of selecting and evaluating alternatives based on several criteria or characteristics is known as multi-attribute decision-making (MADM) problems. The overview of the attribute values is a significant problem in MADM. It must be done in an accurate, consistent, and meaningful way. q-rung orthopair fuzzy numbers (q-ROFNs) are more flexible and powerful for representing uncertain or fuzzy information than other fuzzy number systems such as intuitionistic fuzzy numbers or Pythagorean fuzzy numbers. The paper introduces a new operator within the q-ROF framework or environment. This operator combines the characteristics of Dombi and Archimedean operations. These two operations likely have defined rules and properties within the q-ROF environment. The paper then proceeds to propose some weighted aggregation operators (AOs) based on the Dombi and Archimedean operations under q-ROF. These weighted AOs are likely used for combining or aggregating multiple attributes or criteria in decision-making processes. The paper explores the properties of these operators, which could include aspects like monotonicity, idempotence, or other desirable mathematical properties. Furthermore, the paper emphasizes applying the proposed operators within the q-ROF environment to MADM. This suggests that operators may be used in decision-making scenarios involving multiple attributes or criteria. The paper provides a procedure or methodology for applying the proposed operators in such decision-making processes. Lastly, the paper presents a practical example related to human resource selection. It demonstrates how the suggested strategy can be employed in real-world scenarios with its decision steps and the new operator. The example aims to demonstrate the viability and efficacy of the suggested strategy in solving decision-making problems related to human resource selection.

Analysis of Critical Success Factors of Logistics 4.0 using D-number based Pythagorean Fuzzy DEMATEL method

Logistics 4.0 is a concept related to Industry 4.0, encompassing skills and notions of supply chain organization, integrating logistics with advanced technology in order to satisfy consumer demand for customized goods and services. Industry 4.0 is transforming businesses and supply chains through advanced technologies like analytics, big data, Internet of things, and cyber-physical systems, enhancing warehousing, manufacturing, and logistics. Logistics 4.0 can be regulated by properly analyzing specific Critical Success Factors using a Multi-Criteria Decision Making model in uncertain or ambiguous circumstances. Hence, it is necessary to explore the CSFs while bringing logistics 4.0 into action. These CSFs are interlinked, and this interlinkage is examined through the D-number-based Pythagorean fuzzy Decision Making Trial and Evaluation Laboratory method, which is suitable for group decision-making in incomplete and uncertain data. The proposed research paradigm incorporates the abilities of Trapezoidal Pythagorean Fuzzy Numbers for dealing with fuzziness and D-Numbers for getting an improved and further precise decision from a heterogeneous group of decision-makers using their linguistic choices. Additionally, it is adaptive and versatile in managing the intrinsic uncertainty brought on by ambiguous and subjective information.

Solution strategy for sustainable additive manufacturing design problem using Pythagorean fuzzy MCGDM methodology

To solve difficulties involving various groups’ decision-making problems, this work has been proposed to develop a logical aggregation approach to aggregate decision-makers’ crisp data into Pythagorean fuzzy numbers. By combining the established strategy with the Pythagorean fuzzy TOPSIS method, a hybrid Pythagorean fuzzy multiple criteria group decision-making methodology is presented. Based on fuzzy rules inference and the Takagi–Sugeno technique, a novel function is created to represent the degrees of uncertainty in decision-makers’ data. As an example, the material selection process in practical additive manufacturing designs is provided to show how the proposed methodology may be applied to actual applications. Sensitivity analysis is used to evaluate the effectiveness of the suggested methodology. The outcomes demonstrate that the plan was successful in producing a PFN that accurately reflects the decision-maker’s knowledge.

Conflict Analysis Triggered by Three-Way Decision and Pythagorean Fuzzy Rough Set

Conflict is ubiquitous in human society and has a profound impact on various fields such as the economy, politics, law, and military. Many scholars have focused on exploring the internal mechanisms and potential solutions to conflicts. Notably, describing agents’ attitudes is an effective way to construct a conflict model. However, in decision-making, agents’ attitudes on issues are often vague and ambiguous. Pythagorean fuzzy set can deal with fuzzy information more accurately than intuitionistic fuzzy set. On the basis of this understanding, we investigate the conflicts from the perspective of Pythagorean fuzzy set. Firstly, we use Pythagorean fuzzy numbers to express the attitudes of agents on issues, and subsequently establish a Pythagorean fuzzy conflict information system. Secondly, we classify agents into three categories by a pair of thresholds to establish a trisected agent set model with risk preference. Thirdly, we construct a three-way conflict analysis model based on multi-granulation Pythagorean fuzzy decision-theoretic rough set and discuss both global and local conflicts by combining conflict analysis with multi-granulation decision-theoretic rough set. Finally, we discuss the relationships and properties of the proposed conflict analysis models.

TODIM-GRA technique for performance evaluation of financial management in provincial colleges under 2-tuple linguistic Pythagorean fuzzy sets

Higher provincial education is a very important component of higher education, and it will become a key focus of the higher education development in the future. The purpose of performance evaluation of financial management in provincial colleges is to assess and evaluate the current situation of financial management in provincial colleges based on cost-effectiveness principles, with a performance-oriented approach. A specific, standardized, easy to quantify, and operable evaluation system is designed for its fund operation and financial management. By evaluating the financial management performance of provincial colleges, a new assessment standard can be provided for the “input-output result” of public education, providing an important basis for achieving a performance allocation mechanism. The performance evaluation of financial management in provincial colleges is MAGDM. In recent years, the TODIM and grey relational analysis (GRA) technique was employed to deal with MAGDM. The 2-tuple linguistic Pythagorean fuzzy sets (2TLPFSs) are employed as an effective tool for expressing uncertain decision information during the performance evaluation of financial management in provincial colleges. In this paper, the 2-tuple linguistic Pythagorean fuzzy number TODIM-GRA (2TLPFN-TODIM-GRA) technique is constructed to deal with MAGDM under 2TLPFNs. Finally, a numerical example for performance evaluation of provincial colleges financial management is constructed to verify the proposed technique.

An integrated methodology for enterprise financial management capability evaluation based on EDAS technique and group decision making

The financial management capability of enterprises, as an important component of their soft power, has a decisive impact on the success or failure of their operations. In the increasingly fierce market competition, enterprises must continuously improve their financial management capabilities in order to ensure efficient operation and achieve better economic benefits. Insufficient financial management capabilities in enterprises can seriously affect the stability of production and operation, hinder the realization of profits, and hinder the long-term development of enterprises. In order to better improve the financial management level of enterprises and promote the standardization of financial management, it is necessary to use scientific techniques to evaluate the financial management ability of enterprises, so as to accurately grasp the key links in the financial management process of enterprises and implement targeted effective measures. The enterprise financial management capability evaluation is a classical multiple attribute group decision making (MAGDM). In recent years, the MAGDM problem has become an important research field in modern decision science. This paper extends the EDAS technique to the 2-tuple linguistic Pythagorean fuzzy sets (2TLPFSs). On the basis of the original EDAS technique, 2-tuple linguistic Pythagorean fuzzy number EDAS (2TLPFN-EDAS) technique based on cosine similarity measure (CSM) and Hamming distances is managed for MAGDM. Finally, a case study for enterprise financial management capability evaluation and some comparative analysis with the other techniques show that the new technique proposed in this paper is effective, reasonable and accurate. The main contribution of the paper is summarized: (1) the 2TLPFN-EDAS technique based on CSM and Hamming distances is managed for MAGDM under 2TLPFSs; (2) The entropy is employed to manage the attribute weight based on cosine similarity measure(CSM) and Hamming distances under 2TLPFSs; (3) the 2TLPFN-EDAS technique is employed for enterprise financial management capability evaluation and were compared with some existing techniques; (4) Through the comparison, it is found that 2TLPFN-EDAS technique for enterprise financial management capability evaluation proposed are effective.

Utilization of neutrosophic Kuhn-Tucker’s optimality conditions for Solving Pythagorean fuzzy Two-Level Linear Programming Problems

This article considers a bi-level linear programming with single valued trapezoidal fuzzy neutrosophic cost coefficient matrix and Pythagorean fuzzy parameters in the set of constraints both in the right and left sides. Based on the score functions of the neutrosophic numbers and Pythagorean fuzzy numbers, the model is changed to the corresponding crisp bi-level linear programming (BLP) problem. This problem is designated as a Pythagorean fuzzy bi-level linear programming (PFBLP) problem under neutrosophic environment. Kuhn-Tucker's conditions for optimality are necessary and sufficient for the existence of the optimal solution to a BLP problem. Using the suggested methodology, the problem is formulated as a single-objective non-linear programming problem with several variables and constraints. Two typical numerical examples are examined to illustrate the proposed approach.

A pythagorean hesitant fuzzy programming approach and its application to multi objective reliability optimization problem

Decision-making problems can often be effectively solved using traditional optimization methods that have a clearly defined configuration. However, in real-world scenarios, decision-makers frequently encounter doubt or hesitation, making it challenging to precisely specify certain parameters. As a result, they often seek input from different experts, leading to conflicting values and varying levels of satisfaction among decision-makers. This uncertainty and lack of crisp values make decision-making problems inherently non-deterministic. In this paper, a novel Pythagorean hesitant fuzzy (PHF) programming method is designed to address the challenges of optimization problems with multiple objectives. Here PHF aggregation operators are used to aggregate the PHF memberships and non-memberships of the objectives. Additionally, to account the uncertainties of the parameters of the optimization problem Parabolic Pythagorean fuzzy number is used and centroid method is applied for defuzzification. We solved an example of multi objective optimization problem of manufacturing system to demonstrate our proposed method and finally, presented a case study on reliability optimization model for Life Support Systems, where the primary objectives are to maximize system reliability and minimize cost. The result is compared with other existing methods by degree of closeness.