Interval-valued Pythagorean Fuzzy Research Articles

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.

Evaluation of sustainable energy systems in smart cities using a Multi-Expert Pythagorean fuzzy BWM & TOPSIS methodology

Smart cities are technological settlements using the collected data to utilize resources and services effectively by combining information and communication technologies with various tools connected to the internet of things network. Sustainable energy systems in smart cities are systems can be evaluated by using multiple criteria decision making methods or methodologies based on several vague/imprecise evaluation criteria. In this paper, sustainable energy systems in smart cities are evaluated by interval-valued Pythagorean fuzzy (IVPF) sets with an integrated optimization based multi-expert fuzzy Best Worst Method (BWM) and TOPSIS methodology that can better handle uncertainty and vagueness in experts’ linguistic assessments than existing methodologies. The considered criteria are weighted by multi-expert IVPF Best Worst Method, which has become a popular weighting method in recent years. Later, the energy alternatives for a real case study are prioritized by multi-expert IVPF TOPSIS method. In the analysis, the most important criterion is found as Environmental sustainability (C1) with the defuzzified weight of 0.218 while the other weights are as initial investment (C2) with 0.196, operating expenses (C3) with 0.163, technical feasibility (C4) with 0.154, social acceptability (C5) with 0.140, and scalability (C6) with 0.129. The obtained results indicate that “Investing in advanced technologies” in a smart city with relative degree of closeness (RDC) value of 0.798, has been determined as the best alternative among the considered five alternatives. It is closely followed by “Developing a transportation system” with the RDC value of 0.681. Sensitivity analysis shows that the ranking results are quite robust and reliable. The comparative analysis with crisp BWM and TOPSIS methodology is applied to check the validity of the proposed methodology.

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 purpose this study evaluate performance of Multi-level Marketing (MLM) company’s supply chain with the SCOR model, which is one of the essential strategies a company should possess. This study uses the hybrid Best worst method (BWM) and Interval-valued Pythagorean Fuzzy Analytical Hierarchy Process (AHP) method to determine the highest-weighted criteria, this research seeks to identify performance metrics that need improvement. The data were collected by filling in tables, there are three groups of experts who participate in determining the highest-weighted criteria.  The results show metric Reliability are significant at the Level 1 with important weight of 0.36, and at level 3 the most significant metric for the multi-level marketing’s supply chain is Source with an important weight of 0.36.  

IVPF-AHP integrated VIKOR methodology in supplier selection of three-dimensional (3D) printers

Complex geometries, fine details, and various designs that are difficult to create using traditional methods can easily be turned into a tangible object with Three-Dimensional (3D) printers. 3D printers have advantages such as providing design flexibility, obtaining prototypes in the shortest possible time, allowing for personalization, and reducing waste through the use of advanced technology. These advantages emphasize the significance of 3D printers in a sustainable production model. The widespread usage of 3D printers leads to increased efficiency and cost reduction in production. When the literature is examined, it is observed that there are limited studies on the evaluation of supplier performances for company using 3D printers. The aim of this study is to address 3D printers, which are highly significant for sustainable production, and to reveal the criteria that companies utilizing these printers need to consider for determining their suppliers. As a result of the literature review and expert interviews, a model has been developed that gathers the criteria to be considered for supplier selection, which is an important cost factor for companies involved in designing and producing 3D printers under five main and 18 sub-criteria. The importance weights of the criteria have been determined using the Interval Valued Pythagorean Fuzzy Analytic Hierarchy Process (IVPF-AHP) method, and the most suitable supplier among alternative suppliers has been selected using the Vise Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method. Finally, the supplier scores have been statistically analyzed to show the validation of the results of the proposed method. According to the results, it has been concluded that for company using 3D printers, quality and technical service criteria are more important in the supplier selection. Additionally, cost of the material/equipment, product price and easy maintenance criteria also play a critical role in the supplier selection of 3D printer.

Interval-valued Pythagorean fuzzy entropy and its application to multi-criterion group decision-making

<abstract><p>Entropy is an important tool of information measurement in the fuzzy set and its inference. The research on information measurement based on interval-valued Pythagorean fuzzy sets mostly involves the distance formula for interval-valued Pythagorean fuzzy numbers, but seldom involves the measurement of fuzziness. In view of this situation, we have aimed to propose new interval-valued Pythagorean fuzzy entropy and weighted exponential entropy schemes. Based on the interval-valued Pythagorean fuzzy weighted averaging operator, a strategy based on weighted exponential entropy is proposed to solve the multi-criteria group decision-making (MCGDM) problem in the interval-valued Pythagorean environment. Two examples illustrate that this paper provides a feasible new method to solve the MCGDM problem in an interval-valued Pythagorean fuzzy (IVPF) environment. Finally, by comparing with the existing methods, it is concluded that the entropy measure of IVPF schemes and the corresponding MCGDM method can select the optimal solution of the practical problem more precisely and accurately. Therefore, the comparative analysis shows that the proposed measurement method has the characteristics of flexibility and universality.</p></abstract>

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

Interval-valued Pythagorean fuzzy operational competitiveness rating model for assessing the metaverse integration options of sharing economy in transportation sector

The rise of the sharing economy (SE) has enabled new forms of urban mobility and had a substantial impact on the transportation sector. The applications of SE transportation lessen vehicle ownership and single-occupancy vehicles, which contributes to the sustainability of a region. Metaverse is a digital ecosystem that integrates SE applications with transportation sector and improves the sustainability of SE applications. The aim of this work is to assess and prioritize the Metaverse integration options of sharing economy from multiple criteria and uncertainty perspectives. In this regard, the proposed study develops a four stage decision-making method on interval-valued Pythagorean fuzzy (IVPF) setting. First, new score function is proposed to compare the interval-valued Pythagorean fuzzy numbers (IVPFNs) and further used to derive the weights of decision experts in the proposed method. Second, some IVPF interaction aggregation operators are proposed to aggregate the individual’s information in group decision-making. Third, an integrated weighting process is presented to obtain the objective weights of criteria using cross entropy-based formula and subjective weights by relative closeness coefficient-based model with IVPF information. For this purpose, a cross entropy is introduced for interval-valued Pythagorean fuzzy sets. Fourth, a hybrid operational competitiveness ratings assessment (OCRA) model is developed to rank the alternatives with IVPF information. Moreover, a case study of Metaverse integration options of sharing economy in transportation sector is taken to express the practicability and effectiveness of the presented method. Sensitivity analysis with respect to various values of parameter is discussed to reveal the stability of outcomes. It is also compared with some extant models to validate the superiority of developed method.

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.

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.

Rating pressure factors affecting logistics systems during the pandemic and the ideal logistic decision selection under the Pythagorean fuzzy environment

PurposeDue to the current pandemic, the importance of logistics functions and decisions is well understood both at the level of companies and users. Logistics systems and related decisions are of vital importance in making supply chains effective, efficient and without disruption. Logistic pressure factors may emerge at different points along the logistics process, and given the role of logistics decisions as one of the important indicators of competitiveness, the determination of the logistics pressures that are likely to increase the costs of business, and their causative factors are a vital aspect of the logistics decision-making process. The study aims to provide assistance in the selection of the most ideal logistics decision by ranking the pressure factors affecting the logistics system, especially during the pandemic period for logistics enterprises operating in Ordu and Giresun provinces and which have a corporate identity.Design/methodology/approachIn this study, it is aimed to make the most ideal logistics decision selection by ranking the pressure factors affecting the logistics system, especially during the pandemic period for the logistics enterprises operating in Ordu and Giresun provinces and having a corporate identity. For that purpose interval-valued Pythagorean fuzzy (IVPF)–analytic hierarchy process (AHP) based combinative distance-based assessment (CODAS) methodology was used. Additionally sensitivity and comparison analysis were discussed.FindingsCompetitive pressure was found as the most important pressure factor affecting the logistics system during the pandemic period. Change in regulatory rules was the pressure factor found to have the least effect on the logistics system. Using the weights of logistics pressure factors, “Operational Decisions” was found to be the most ideal logistics decision selection.Research limitations/implicationsThe findings provide support for the evaluation of logistical pressures and decision options by presenting a decision model capable of processing ambiguous information. During a pandemic or similar period, the study assists decision makers in determining a new route. The findings will also call business managers' attention to logistical pressure factors and lead them toward more realistic and feasible practices in the logistics decision-making process.Originality/valueThis study provided an effective and applicable solution to a decision-making problem in the logistics sector including logistics pressure factors and the selection of logistics decisions. In this context, a methodology was presented that will allow businesses to self-evaluate their own logistics pressure factors and the selection of optimal solutions.

Interval Valued Pythagorean Fuzzy AHP Integrated Model in a Smartness Assessment Framework of Buildings

Buildings can be made more user-friendly and secure by putting “smart” design strategies and technology processes in place. Such strategies and processes increase energy efficiency, make it possible to use resources rationally, and lower maintenance and construction costs. In addition to using wireless technologies and sensors to improve thermal, visual, and acoustic comfort, “smart” buildings are known for their energy, materials, water, and land management systems. Smart buildings use wireless technologies and sensors to improve thermal, visual, and acoustic comfort. These systems are known for managing energy, materials, water, and land. The task of the study is to consider the indicators that form the basis of the framework for evaluating intelligent buildings. The indicators for the development of “smart” buildings are classified into six categories in this paper: green building construction, energy management systems, safety and security management systems, occupant comfort and health, building automation and control management systems, and communication and data sharing. The paper aims to develop a scoring model for the smartness of public buildings. In developing the scoring system, the decision-making process requires an appropriate selection of the optimal solution. The contents of the research are the methods known as the Pythagorean Fuzzy Analytic Hierarchy Process (PF-AHP), Interval Valued Pythagorean Fuzzy AHP with differences (IVPF-AHP d), and the proposed method Interval Valued Pythagorean Fuzzy AHP (IVPF-AHP p). The research focuses on the IVPF-AHP as one of the methods of Multi-Criteria Decision-Making (MCDM) and its implementation. The comparative analysis of the three presented methods indicates a significant degree of similarity in the ranking, which confirms the ranking similarity. The results highlight the importance of bioclimatic design, smart metering, ecological materials, and renewable energy systems.

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.

Membership Score of an Interval-Valued Pythagorean Fuzzy Numbers and Its Applications

The main aim of the paper is to define a new Membership score function on the class of interval-valued Pythagorean fuzzy numbers which can overcome the drawbacks of existing familiar ranking methods. In this paper, firstly, we show the limitations of various ranking functions in ordering/ comparing any two arbitrary interval-valued Pythagorean fuzzy numbers in detail. Secondly, we define a new Membership score function on the class of interval-valued Pythagorean fuzzy numbers and study their properties. Then we compare our proposed method with many other different existing methods for showing the efficacy of the proposed method. Finally, we show the applicability of the proposed Membership score function in solving interval-valued Pythagorean fuzzy multi-criteria decision-making problems using a numerical example.

Interval-Valued Pythagorean Fuzzy Information Aggregation Based on Aczel-Alsina Operations and Their Application in Multiple Attribute Decision Making

The multi-attribute decision-making (MADM) has really become widely utilized in many domains, including management, economics, and other disciplines. It plays a significant role in mainstream decision science. Its main process is the ranking of choices available and selecting the optimal option out of a group of options based on a set of attribute values. Aggregation operators (AOs) play a significant role in MADM techniques to aggregate uncertain and vague information. Aczel Alsina AOs are recently introduced to handle with ambiguous or uncertain information and has their significance. This article aims to generalize the concept “Aczel Alsina AOs of Pythagorean fuzzy sets” (PyFSs) to interval-valued Pythagorean fuzzy (IVPyF) information by utilizing the Aczel-Alsina t-norm (AA-TNM) and t-conorm (AA-TCNM). We developed a series of Aczel-Alsina AOs such as “IVPyF Aczel-Alsina weighted averaging” (IVPyFAAWA), “IVPyF Aczel-Alsina ordered weighted averaging” (IVPyFAAOWA), and “IVPyF Aczel-Alsina hybrid weighted averaging” (IVPyFAAHWA) operators. We also studied the “IVPyF Aczel-Alsina weighted geometric” (IVPyFAAWG) operator. We interpreted certain characteristics of our invented approaches. To check the effectiveness and reliability of our proposed approaches, we establish an illustrative numerical example for the selection of research scientist. The sensitivity analysis of the parameters is also established and their impact on ranking results is analyzed. We illustrated a realistic comparison in which we compare outcomes of exiting methodologies with the consequences of current discussed approaches.

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

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

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

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