Interval-valued Pythagorean Research Articles

Entropy-Based LogTODIM–MACONT Techniques for Satisfaction Evaluation of Rural Living Environment Governance with Interval-Valued Pythagorean Fuzzy Information

Entropy-Based LogTODIM–MACONT Techniques for Satisfaction Evaluation of Rural Living Environment Governance with Interval-Valued Pythagorean Fuzzy Information

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 renewable energy projects based on sustainability goals using a hybrid pythagorean fuzzy-based decision approach

Due to the growth in energy demand and the need to pay attention to sustainable development, many developing countries face the challenge of making policies for growing sustainable energy. With attention to industrial expansion and population growth, Iran, a developing country, is confronting an energy shortage problem. Despite the appropriate capacity of renewable resources in Iran, due to the lack of proper planning for adopting renewable resources in Iran, these resources have a small share of the energy supply. This study aims to present a decision framework for assessing renewable energies in developing countries, in the case of Iran. In addition to technical aspects, sustainability aspects such as economic, social, and environmental factors are proposed to assess renewable sources in this work. The Best-Worst Method (BWM) and the Interval-Valued Pythagorean Fuzzy Weighted Aggregated Sum Product Assessment (IVPF-WASPAS) techniques are suggested to prioritize renewable sources. The findings indicated that solar energy was Iran's most suitable renewable resource. Also, the validation and sensitivity analysis confirmed the findings. This research provides a comprehensive perspective for policy-making and planning of sustainability in the energy industry.

Some distance measures for pythagorean cubic fuzzy sets: Application selection in optimal treatment for depression and anxiety

Pythagorean cubic fuzzy sets represent an advancement beyond conventional interval-valued Pythagorean sets, integrating the principles of Pythagorean fuzzy sets and interval-valued Pythagorean fuzzy sets. Given the critical significance of distance measures in real-world decision-making and pattern recognition tasks, it is noteworthy that there exists a notable gap in the literature regarding distance measures specifically tailored for Pythagorean cubic fuzzy sets. The objectives of this paper are:•To define novel generalized distance measures between Pythagorean cubic fuzzy sets (PCFSs) to tackle intricate decision-making challenges.•These novel distance measures are undergoing testing on a real-world scenario concerning the management of anxiety and depression to evaluate their effectiveness and practical application.•We have illustrated the boundedness and nonlinear characteristics inherent in these distance measures.In addition, we conduct comparative analyses with existing approaches to validate the proposed methodology, thereby providing insights into its advantages and potential applications.

Aczel–Alsina T-norm based group decision-making technique for the evaluation of electric cars using generalized orthopair fuzzy aggregation information with unknown weights

Data management and finding precise outcomes from large amounts of information are among the biggest challenges for scientists. The technique of multi-attribute group decision-making (MAGDM) is a valuable tool for investigating fuzzy data precisely. The key objective of the paper is to redefine the q-rung orthopair (q-RO) fuzzy set (FS) (q-ROFS) in the term of interval-valued and proposed new aggregation operators (AOs) based on the Aczel-Alsina (AA) t-norm (TN) and t-conorm (TCN) operations. The AA operational laws are a generalized form of existing TNs and TCNs and give more reliable results because they can fluctuate in their parametric values. The concept of interval-valued enlarges the space of membership degree (MD) and non-membership degree (NMD) for decision-makers. By taking qth power, the interval-valued q-ROFS (IV-q-ROFS) structure. The IV-q-ROFS can handle the uncertainty and vagueness in data, then interval-valued intuitionistic FS (IV-IFS) and interval-valued Pythagorean FS (PyFS) (IV-PyFS) and provide accurate results. The thought of power AOs (PAOs) makes the relationship between weight vectors and reduces the chances of uncertainty in aggregated results. By taking advantage of PAOs, this article is devoted to introducing the interval-valued q-ROF Aczel-Alsina power-weighted averaging (IV-q-ROFAAPWA) and interval-valued q-ROF Aczel-Alsina power-weighted geometric (IV-q-ROFAAPWG) operators. The fundamental axioms of AOs, idempotency, boundedness, and monotonicity, are also discussed. To illustrate the importance of suggested AOs, the real-life problem of electric car selection was solved by applying the MAGDM method using the proposed IV-q-ROFAAPWA and IV-q-ROFAAPWG operators. The comparison of proposed AOs with currently present AOs is also part of the article. We finally constructed solid conclusions.

Analisis Manajemen Rantai Pasok dengan Metode Supply Chain Operation Reference PT Fourmi Asha Sejahtera

In an era of economic development, business competition demands the acquisition of as many consumers as possible. This naturally requires a sound strategy in order to gain a competitive edge over rivals. The aim of this research is to evaluate the supply chain performance of Multi-level Marketing (MLM) companies by measuring SCM performance. SCM performance measurement is carried out using the SCOR model with the weights for each level divided equally and processing the actual data for each performance metric. After processing the data there are 7 SCOR performance metrics. Based on the results of data processing, the actual values are then normalized using the De Boer Snorm to obtain SCOR performance metric measurement values. The results obtained were a total score of 72.2 which is included in the good category, these results indicate that there is still a need to evaluate and improve performance

An ExpTODIM-MACONT Based Multiple-Attribute Group Decision-Making Technique for Smart Classroom Teaching Evaluation of Basic English Under Interval-Valued Pythagorean Fuzzy Circumstances

An ExpTODIM-MACONT Based Multiple-Attribute Group Decision-Making Technique for Smart Classroom Teaching Evaluation of Basic English Under Interval-Valued Pythagorean Fuzzy Circumstances

A two-phase multi-criteria decision-making with interval-valued Pythagorean normal fuzzy information and its application for module hospital site selection in combating COVID-19

During the fight against COVID-19, module hospital saved tens of thousands of lives and families. Therefore, how to effectively select the site of module hospital is a critical issue. The site selection of module hospital is a multi-criteria decision-making (MCDM) problem. Recently, interval-valued Pythagorean normal fuzzy (IPNF) number has become an effective and powerful tool for handling ambiguity in decision-making. However, the weights of experts in existing IPNF decision-making are often directly given, lacking objectivity and persuasiveness. Moreover, the current research on aggregation operators in IPNFN only involves simple weighted average and geometry, while ignoring the interaction among fuzzy information. Motivated by these issues, this paper aims to develop a two-phase IPNF MCDM approach and apply it to the site selection of module hospital. Firstly, IPNF Einstein weighted averaging (IPNFEWA) operator, IPNF Einstein order weighted averaging (IPNFEOWA) operator, IPNF Einstein weighted geometric (IPNFEWG) operator, and IPNF Einstein order weighted geometric (IPNFEOWG) operator are proposed. Moreover, numerical and theoretical proofs of the proposed operators are carried out. Secondly, an algorithm for determining experts’ weights is developed using the proposed IPNF social network in the first phase, and the decision-making process is conducted in the second phase. Finally, a numerical example on the site selection of module hospital is provided to demonstrate the feasibility of the proposed method. The numerical results of comparisons and sensitivity analysis are further analyzed to confirm the advantages of the proposed method.

An Improved TOPSIS Method Based on a New Distance Measure and Its Application to the House Selection Problem

It is difficult to choose an appropriate house for homebuyers. This is due to the difficulty of evaluating the multitude of factors, such as price, location, size, and so on. In order to help homebuyers in choosing an appropriate house, a method integrating the interval-valued Pythagorean FAHP and FTOPSIS is proposed. In the proposed approach, the evaluation criteria were determined by the experts, and the linguistic variables of interval-valued Pythagorean fuzzy numbers were used in the evaluations of the homebuyers and experts. A new distance between two IVPFNs is proposed. The weights of the evaluation criteria were determined by the interval-valued Pythagorean FAHP method by the homebuyers, and house selections were evaluated by interval-valued Pythagorean FTOPSIS method taking into account the new distance. Finally, a case study was executed to verify the feasibility of the proposed approach. The case study results reveal that the weights of criteria obtained by FAHP are not the same according to opinions of the different homebuyers.

Determination of various factors to evaluate a successful curriculum design using interval-valued Pythagorean neutrosophic graphs

Determination of various factors to evaluate a successful curriculum design using interval-valued Pythagorean neutrosophic graphs

An Interval-Valued Pythagorean Fuzzy AHP and COPRAS Hybrid Methods for the Supplier Selection Problem

Companies must be able to identify their suppliers appropriately and effectively in order to survive in the competitive market conditions. In order to fulfill and surpass the expectations of the consumers and clients, companies need to interact with the relevant suppliers. It is a tough manner for companies to select the best supplier from a large number of relevant alternatives. The selection process of the appropriate supplier involves multiple interacting and competing factors. Generally, the selection process and its results cause a waste of time and money. For this purpose, MCDM methodologies are utilized to manage this complex process efficiently. MCDMs allows for consistent and accurate decision-making as well as the selection of the most appropriate supplier. MCDM is one the most preferred tool to select the best alternative under the conflicting and competitive criteria when the evaluations are made in crisp numbers. Therefore, MCDM methods are preferred in various applications in academia and real life. However, the evaluations could not be always possible with crisp numbers, especially in vague environments or evaluations needs qualitative data. This study is one of the first to combine the AHP and COPRAS supplier selection methods with interval-valued Pythagorean fuzzy (IPF) logic. The effectiveness of these IPF-AHP and IPF-COPRAS evaluations for the supplier selection problem is compared and examined. The experimental results of case scenarios show that IPF is an effective way to apply in decision-making applications. In addition, sensitivity analysis is conducted to evaluate the proposed methodologies. According to sensitivity analysis, the IPF-AHP and IPF-COPRAS be able to illustrate the effects of small changings in criteria weights. Therefore, companies can use the IPF-AHP and IPF-COPRAS to assist their decision-makers in identifying and selecting the best suppliers.

Optimizing Emergency Plane Selection in Civil Aviation Using Extended Dombi Hybrid Operators

Airports located in densely populated areas often face challenges due to asymmetrical traffic patterns. Efficient management and careful planning are required to handle the disproportionate flow of passengers, aircraft, and ground services. The significance of symmetry and asymmetry in civil aviation extends to international regulations and agreements. By harmonizing standards and practices among different nations, it is possible to achieve symmetry in safety measures and operational procedures, thereby promoting a unified and secure global aviation system. Conversely, asymmetry in regulations, infrastructure development, or technological advancements among countries can create obstacles in establishing a cohesive and equitable international aviation framework. This article discusses the weaknesses of the existing score function in handling the MADM problem in an Interval-Valued Pythagorean Fuzzy (IVPF) environment. To tackle this issue, an enhanced score function is developed as a solution. The article proposes the IVPF Dombi hybrid arithmetic and IVPF Dombi hybrid geometric operators based on IVPF information. Furthermore, the article proves some fundamental properties of these operators. In the context of recently introduced techniques using IVPF settings, an effective method is developed for selecting the best airline. Additionally, a comparative investigation is carried out to demonstrate the legitimacy and viability of this unique strategy in comparison to earlier approaches.

Development and Application of an Interval-Valued Pythagorean Fuzzy Set-Based Grade Evaluation Method to Foreign Fiber Content

ABSTRACT To solve the problem of the grade evaluation of foreign fiber content in cotton, this paper divided the problem into multi-criteria decision-making field and proposed an interval-valued Pythagorean fuzzy set foreign fiber content grade evaluation method. Taking into account the various properties of foreign fibers, the multi-criteria evaluation of single foreign fiber content and comprehensive foreign fiber content is carried out to improve the quality of cotton textiles. Based on the Pythagorean fuzzy set, we used AHP and TOPSIS methods to determine the relevant weight information, combined with the grade evaluation index of foreign fiber content and the interval-valued Pythagorean fuzzy weighted average or geometric operators to construct a fiber multi-criteria decision model. Then, the evaluation index function is improved to make the score function more consistent with the facts, and the digitization and intelligence methods required for foreign fiber content detection and grade evaluation are developed. Further, an example is given to verify the feasibility and effectiveness of the model. In addition, the multi-criteria decision-making method adopted has high theoretical innovation and application value for the textile industry.

Enhancing service quality of rural public transport during the COVID-19 pandemic: a novel fuzzy approach.

In order to encourage the use of public transportation, it is necessary to make it more appealing to commuters by conducting frequent Service Quality (SQ) evaluations and modifications. Understanding passengers' expectations of public transportation are important, and evaluating the SQ is an essential tool for assessing the overall performance of the public transportation system. The purpose of the present study was to examine the expectations and perceptions of core passengers regarding SQ in public bus transportation. By surveying 598 passengers in rural public transportation in India, the study results are illustrated and further discussed to guide possible bus SQ improvements in rural areas. In addition, the impact of these expectations and perceptions on satisfaction levels of rural public bus transportation services are explored by applying the Interval-Valued Pythagorean Fuzzy (IVPF). The outcomes of the survey indicated significant disparities among expectations and perceptions of passengers, as well as widespread dissatisfaction with the delivery of bus services in rural areas as a whole. The dependability and adaptiveness of the bus service have been critical in describing the overall quality of bus services in rural areas, and best practices from around the world were used to develop a set of recommendations for transportation operators and local officials.

A design model of FBS based on interval-valued Pythagorean fuzzy sets

The FBS (Function-Behaviour-Structure) model is a research model that stimulates creative thinking of designers in the design process. In order to reduce the influence of user requirement ambiguity on design results in the product design process and improve the accuracy of user requirements in the function-behavior-structure (FBS) design model, this paper proposes an interval-valued Pythagorean fuzzy set-based FBS model integrating AHP and HOQ methods. Firstly, the design model will use IVPF-AHP method to study user requirements and use interval-valued Pythagorean linguistic terms to replace the traditional scoring method of AHP to get the weight of each user requirement. Secondly, the conversion between user requirements and functions will be realized by IVPF-HOQ method, which converts customer requirements into functional characteristics and calculates the weights of each functional characteristic. Finally, the design focus will be filtered according to the order of importance of the functional characteristics, which will be used as functions to guide the development of the FBS model. In this paper, the feasibility and effectiveness of the proposed method will be verified by an application example of a hand-held fluorescence spectrometer. The results show that the proposed FBS model can effectively reduce the subjectivity and ambiguity in the decision-making process, improve the accuracy and information richness of user requirements, and effectively highlight the focus of the design study. The innovation of the proposed method is to provide a more objective and accurate innovative design method for user requirements through the integration of AHP, HOQ and FBS to effectively explore and analyze user requirements. The use of IVPFS to deal with fuzzy information in the design process in a more flexible manner can reduce the ambiguity of requirements when user data is small, and effectively improve the limitations of the FBS design model which is more subjective.

Enhancing Interval-Valued Pythagorean Fuzzy Decision-Making through Dombi-Based Aggregation Operators

The success of any endeavor or process is heavily contingent on the ability to reconcile and satisfy balance requirements, which are often characterized by symmetry considerations. In practical applications, the primary goal of decision-making processes is to efficiently manage the symmetry or asymmetry that exists within different sources of information. In order to address this challenge, the primary aim of this study is to introduce novel Dombi operation concepts that are formulated within the framework of interval-valued Pythagorean fuzzy aggregation operators. In this study, an updated score function is presented to resolve the deficiency of the current score function in an interval-valued Pythagorean fuzzy environment. The concept of Dombi operations is used to introduce some interval-valued Pythagorean fuzzy aggregation operators, including the interval-valued Pythagorean fuzzy Dombi weighted arithmetic (IVPFDWA) operator, the interval-valued Pythagorean fuzzy Dombi ordered weighted arithmetic (IVPFDOWA) operator, the interval-valued Pythagorean fuzzy Dombi weighted geometric (IVPFDWG) operator, and the interval-valued Pythagorean fuzzy Dombi ordered weighted geometric (IVPFDOWG) operator. Moreover, the study investigates many important properties of these operators that provide new semantic meaning to the evaluation. In addition, the suggested score function and newly derived interval-valued Pythagorean fuzzy Dombi aggregation (IVPFDA) operators are successfully employed to select a subject expert in a certain institution. The proposed approach is demonstrated to be successful through empirical validation. Lastly, a comparative study is conducted to demonstrate the validity and applicability of the suggested approaches in comparison with current techniques. This research contributes to the ongoing efforts to advance the field of evaluation and decision-making by providing novel and effective tools and techniques.

Applications of Interval-Valued Pythagorean Fuzzy Soft Graph in Bipolar Fuzzy Frame Works

The main contribution of this paper is to get extended ideas of various interval-valued bipolar Pythagorean fuzzy soft graphs (I-VBPFSGs) and to extend the concept of the Pythagorean fuzzy soft graph to the bipolar frameworks. Finally, in order to demonstrate, how to calculate an interval-valued Pythagorean bipolar fuzzy soft graph for a specific application, a numerical example using city data from the Yunnan province is presented.

Interval-Valued Pythagorean Fuzzy Extension of DEMATEL for Prioritizing and Casualty Analysis of Environmental Criteria of Organizational Behaviour in Higher Education Sector

Interval-Valued Pythagorean Fuzzy Extension of DEMATEL for Prioritizing and Casualty Analysis of Environmental Criteria of Organizational Behaviour in Higher Education Sector

Aggregation Operators for Interval-Valued Pythagorean Fuzzy Hypersoft Set with Their Application to Solve MCDM Problem

Experts use Pythagorean fuzzy hypersoft sets (PFHSS) in their investigations to resolve the indeterminate and imprecise information in the decision-making process. Aggregation operators (AOs) perform a leading role in perceptivity among two circulations of prospect and pull out concerns from that perception. In this paper, we extend the concept of PFHSS to interval-valued PFHSS (IVPFHSS), which is the generalized form of interval-valued intuitionistic fuzzy soft set. The IVPFHSS competently deals with uncertain and ambagious information compared to the existing interval-valued Pythagorean fuzzy soft set. It is the most potent method for amplifying fuzzy data in the decision-making (DM) practice. Some operational laws for IVPFHSS have been proposed. Based on offered operational laws, two inventive AOs have been established: interval-valued Pythagorean fuzzy hypersoft weighted average (IVPFHSWA) and interval-valued Pythagorean fuzzy hypersoft weighted geometric (IVPFHSWG) operators with their essential properties. Multi-criteria group decision-making (MCGDM) shows an active part in contracts with the difficulties in industrial enterprise for material selection. But, the prevalent MCGDM approaches consistently carry irreconcilable consequences. Based on the anticipated AOs, a robust MCGDM technique is deliberate for material selection in industrial enterprises to accommodate this shortcoming. A real-world application of the projected MCGDM method for material selection (MS) of cryogenic storing vessels is presented. The impacts show that the intended model is more effective and reliable in handling imprecise data based on IVPFHSS.

An Intelligent MCGDM Model in Green Suppliers Selection Using Interactional Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Sets

An Intelligent MCGDM Model in Green Suppliers Selection Using Interactional Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Sets