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Pythagorean fuzzy hypersoft sets (PFHSSs) are a novel model that is projected to address the limitations of Pythagorean fuzzy soft sets (PFSSs) regarding the entitlement of a multi-argument domain for the approximation of parameters under consideration. It is more flexible and reliable as it considers the further classification of parameters into their relevant parametric valued sets. This article aims to be multi-faced. Firstly, several axiomatic properties, operational results, and aggregation operations on PFHSSs will be developed. Secondly, matrices are developed for PFHSSs, called Pythagorean fuzzy hypersoft matrices (PFHSMs). The essential basic properties and aggregation operations of PFHSMs are then characterized with the support of numerical examples. Thirdly, the matrix theory of PFHSSs is implemented in real-world decision-making scenarios for Mobile selection using the proposed choice matrix theory. At the end of the article, we go on a real-life problem for wastewater treatment. Wastewater treatment is crucial for preserving the environment and public health. It comprises purifying wastewater of contaminants and pollutants so that it may be utilized for other things or discharged safely into the environment. It is essential to protect the environment and the public health by removing toxins from domestic, industrial, and commercial sewages. We finally apply our proposed algorithm in the selection of wastewater treatment plants by employing the proposed algorithm based on PFHSMs. In fact, PFHSMs are flexible enough to be used in a wide range of fields, including image processing, expert systems, pattern recognition, and medical diagnosis. The future directions are discussed with these PFHSMs to develop MCDM techniques such as TOPSIS, VIKOR, and SAW so that they can be applied in a wider range of fields.

Big data analytics (BDA), along with the resource efficiency and sustainability perspectives of a circular economy, supports the transition to circular agri-food supply chains (AFSCs), contributing to a country's achievement of the United Nations' Sustainable Development Goals. However, there is still limited research demonstrating the importance and awareness of BDA implementation in circular AFSCs in developing countries. As a result of the barriers to BDA adoption in these regions, circular AFSCs in developing countries are still in their infancies. This study sought to identify the barriers to BDA adoption in circular AFSCs in Turkey using a Delphi-based Pythagorean fuzzy analytic hierarchy process. The proposed method removes the potential for bias and produces consensus among managers of companies in various AFSCs in Turkey. The findings of this study show that the most impactful barriers to BDA are technical, economic and social, followed by environmental and organisational. The most crucial sub-barriers to BDA adoption are "lack of trust, privacy and security", "lack of financial resources" and "lack of skilled human resources". This research can guide industry managers and policymakers in the development of strategies for overcoming barriers to BDA adoption in circular AFSCs in developing nations. [ABSTRACT FROM AUTHOR]

This study explores how to enhance the decision-making processes in the phases of idea generation or alternative selection during the new product development (NPD) process. NPD is acknowledged as the central function of businesses in an increasingly competitive marketplace. In the current era, the highly uncertain and rapidly changing market environment makes the NPD extremely vague and complex. To be able to find a suitable solution to this complexity, the proposed research aims to categorize the decision points in the process of NPD regarding software development and identify the fuzziness elements affecting the process. The goal of a decision-making process is to prioritize several alternatives with respect to some required objectives and to select the best among them. Multi-Criteria Decision-Making (MCDM) may support reaching a consensus judgment with the collective assessment of Decision Makers (DMs). We introduce a novel evaluation approach for this problem. The proposed approach employs a MULTIMOORA (Multi-objective Optimization by Ratio Analysis plus the Full Multiplicative Form) MCDM technique under Pythagorean Fuzzy Sets (PFSs) objective world environment to cope with an ambiguous environment using Group Decision Making (GDM) setting to shape the decisions. The PFSs have demonstrated their advantages in dealing with vagueness and uncertainty over crisp, fuzzy, or intuitionistic fuzzy sets. Therefore, PFSs can represent the DMs’ judgments and preferences in a better structure, ensuring enhanced decision-making in a group consensus. A case study on gaming software and app development is presented to validate the functionality of the proposed method. The results are compared and assessed with the help of a sensitivity analysis. This research makes a real contribution to the literature by proposing a novel evaluation method to rate and select NPD (gaming software and apps) to deal with the inexactness and vagueness associated with the criteria and alternatives.

Suitable management and treatment of healthcare waste (HCW) have become a key issue due to its potential risk to human health and the environment, predominantly in emerging nations. The selection of an optimal HCW treatment (HCWT) option is a complicated multicriteria decision-making (MCDM) problem that includes several incompatible qualitative and quantitative attributes. This article presents an extended MCDM methodology for assessing and choosing the HCWT options using Pythagorean fuzzy stepwise weight assessment ratio analysis (PF-SWARA) and additive ratio assessment (PF-ARAS) approaches. To do this, attribute weights are estimated by the SWARA model and the ARAS framework decides the preference order of the options on Pythagorean fuzzy sets (PFSs). Furthermore, a selection problem of HCWT options in India is presented within PFSs to illustrate the efficiency and practicality of the introduced framework. Comparative discussions and sensitivity analysis are presented to demonstrate the rationality and stability of the developed approach for prioritizing HCWT options. [ABSTRACT FROM AUTHOR]

In this paper, considering the traditional geometric operation laws and Pythagorean fuzzy information, a varies of new distance measures of Pythagorean fuzzy set are proposed, such as generalized Pythagorean fuzzy ordered geometric distance (GPFOWGD) measures and generalized Pythagorean fuzzy hybrid weighted geometric distance (GPFHWGD) measures. Besides, some special issues including Hamming distance, Euclidean distance and Hausdorff distance of these raised geometric distance measures are investigated. To testify the valid of these new presented distance measures, a decision-making model is built and illustrated by a mathematical calculation example to evaluate the service quality of sports clubs using Pythagorean fuzzy information. The results display that the approach is uncomplicated, valid and simple to compute. The example illustrates that the method presented in the paper can be used to deal with problems of uncertainty such as dynamic multiple attribute decision making. [ABSTRACT FROM AUTHOR]

Dempster–Shafer (D-S) evidence theory is an effective methodology to handle unknown and imprecise information because it can assign probability into the power set. However, the process of obtaining information is a complex task, which can consider the rational, conscious, objective evaluation of utility with behavioral effects. Besides, in most cases, information can be obtained from different angles at the same time. The quantum model of mass function (QM) uses amplitude and phase angle to easily express those properties of information that can extend D-S evidence theory to the unit circle in a complex plane. Moreover, everything in nature will have its opposite, which is a kind of universality. The Bayes theorem is essentially the process of negation. However, in most cases, decisions can be made by only fully considering the known information without considering the other side of the information. Hence, considering the negation of information is a question to be investigated deeply, which can analyze information from the other point. This article proposes negation of QM by using the subtraction of vectors in the unit circle, which can degenerate into negation proposed by Yager in standard probability theory and negation proposed by Yin et al. in D-S evidence theory. Negation can provide us more information to consider the problem from both positive and negative aspects. In this article, negation can be understood information, which does not belong to event $A$ , that is to say, negation can be regarded as nonmembership by using the fuzzy terms. Based on the above discussion, this article proposes the quantum pythagorean fuzzy evidence theory (QPFET), which is the novel work to consider QPFET from the point of negation. Besides, there are some numerical examples to explain the proposed method. In order to explore the applications of QPFET, this article discusses the possibility of the VI $\check{s}$ ekriterijumsko Kompromisno Rangiranje method under QPFET to handle multicriteria decision-making that enables us to capture 2-D data, considering not only amplitude but also phase angle. [ABSTRACT FROM AUTHOR]

Distance measure is one of the research hotspot in Pythagorean fuzzy environment due to its quantitative ability of distinguishing Pythagorean fuzzy sets (PFSs). Various distance functions for PFSs are introduced in the literature and have their own pros and cons. The common thread of incompetency for these existing distance functions is their inability to distinguish highly uncertain PFSs distinctly. To tackle this point, we introduce a novel distance measure for PFSs. An added advantage of the measure is its simple mathematical form. Moreover, superiority and reasonability of the prescribed definition are demonstrated through proper numerical examples. Boundedness and nonlinear behaviour of the distance measure is established and verified via suitable illustrations. In the current scenario, selecting an antivirus face-mask as a preventive measure in the COVID-19 pandemic and choosing the best school in private sector for children are some of the burning issues of a modern society. These issues are addressed here as multi-attribute decision-making problems and feasible solutions are obtained using the introduced definition. Applicability of the distance measure is further extended in the areas of pattern recognition and medical diagnosis. [ABSTRACT FROM AUTHOR]

Digital supply chains (DSCs) can be useful in unlocking supply chains to gain competitive advantage as a driver of growth, while enabling rapid response, supporting novel technology-driven approaches, and creating innovative products and services. Partner selection (PS) is one of the crucial tasks in the successful digitalization of supply chain. However, the selection of a suitable partner is not an easygoing process and is mostly associated with complexity. Various criteria are considered during the partner evaluation process. This paper delivers an efficient evaluation process to assess alternative DSC partners. The proposed approach integrates the Pythagorean fuzzy sets (PFSs), analytic hierarchy process, and complex proportional assessment under a group decision making environment for the first time in the literature. PFSs can depict experts’ evaluations with a richer structure, allowing for a more representative decision making. A case study from Turkey is conducted to validate proposed approach. This study contributes to the existing literature by developing a new evaluation model to improve DSC PS process and by proposing a new hybrid PFSs-based framework. This paper can be useful to practitioners and researchers to better understand DSC PS problem and designing effective DSC partner evaluation systems. [ABSTRACT FROM AUTHOR]

The risk assessment of science and technology projects could be regarded as a classical multiple attribute group decision-making (MAGDM) issue. The Pythagorean fuzzy sets (PFSs) can fully describe the uncertain information for the risk assessment of science and technology projects. Furthermore, the classical TODIM method based on the cumulative prospect theory (CPT-TODIM) is built, which is a selectable method in reflecting the DMs' psychological behavior. Thus, in this paper, the Pythagorean fuzzy CPT-TODIM (PF-CPT-TODIM) method is proposed for MAGDM issue. At the same time, it is enhancing rationality to get the weight information of attributes by using the entropy weight method under PFSs. And focusing on hot issues in contemporary society, this article applies the discussed method to risk assessment of science and technology projects, and demonstrates risk assessment model of science and technology projects based on the proposed method. Finally, through comparing the outcome of comparative analysis, we conclude that this improved approach is acceptable. [ABSTRACT FROM AUTHOR]

The green supplier selection could be regarded as a classical multiple attribute group decision making (MAGDM) issue. The interval-valued Pythagorean fuzzy set (IVPFSs) can fully describe the uncertain information for the risk assessment of science and technology projects. Furthermore, the classical TODIM method based on the cumulative prospect theory (CPT-TODIM) is built, which is a selectable method in reflecting the decision makers' psychological behavior. Thus, in this paper, the interval-valued Pythagorean fuzzy CPT-TODIM (IVPF-CPT-TODIM) method is proposed for MAGDM issue. At the same time, it is enhancing rationality to get the weight information of attributes by using the entropy weight method under IVPFSs. And focusing on hot issues in contemporary society, this article applies the discussed method to green supplier selection, and demonstrates risk assessment model of science and technology projects based on the IVPF-CPT-TODIM method. Finally, through comparing the outcome of comparative analysis, we conclude that this improved approach is acceptable. [ABSTRACT FROM AUTHOR]

In some real-world situations, Pythagorean fuzzy sets are more powerful and effective than intuitionistic fuzzy sets to describe vague and uncertain information, and there are many Pythagorean fuzzy information systems for conflicts in which attitudes of agents on issues are depicted by Pythagorean fuzzy numbers. In this paper, we first provide the concepts of positive, neutral, and negative alliances with two thresholds and employ examples to illustrate how to compute positive, neutral, and negative alliances in Pythagorean fuzzy information systems for conflicts. Then, we focus on three-way conflict analysis based on the Bayesian minimum risk theory and explore examples to show how to compute the positive, neutral, and negative alliances with a Pythagorean fuzzy loss function given by an expert. Finally, we study how to calculate positive, neutral, and negative alliances with group decision theory and take examples to demonstrate how to construct the positive, neutral, and negative alliances with a group of Pythagorean fuzzy loss functions given by more experts. [ABSTRACT FROM AUTHOR]

High-technology projects are known as tools that help achieving productive forces through scientific and technological knowledge. These knowledge-based projects are associated with high levels of risks and returns. The process of hightechnology project and project portfolio selection has technical complexities and uncertainties. This paper presents a novel two-parted method of high-technology project portfolio selection. In the first part, a new decision-making model under Pythagorean fuzzy set (PFS) uncertainty is introduced that is last aggregation and avoids defuzziffcation until the last step of the process. In the last step, a new PFS ranking method is used to make crisp and comparable values. Outcomes from this part form the objective function of a new integer programming (IP) of the project portfolio selection. To display the models application, data from a real case study of high-technology project evaluation and selection is presented, and the steps of the approach are illustrated in addition to presenting the effcacy of the model. [ABSTRACT FROM AUTHOR]

Uncertainty plays an important role in project decision-making problems that involve incomplete and imperfect information of real-world situations. To completely considering the uncertainty of decision-making methods, Pythagorean fuzzy sets (PFSs) are used. PFSs in comparisons with classic fuzzy sets provide degrees of membership, non-membership and hesitancy, and in comparisons with intuitionistic fuzzy sets (IFSs), they prepare the larger space to explain the agreement, disagreement and hesitancy grades. In this paper, to tackle the uncertainty of real-world projects and determine the critical path of projects by considering efficient criteria, such as time, cost, risk, quality and safety, a new group decision methodology is extended based on concepts of technique for order of preference by similarity to ideal solution (TOPSIS) and complex proportional assessment (COPRAS) methods under PFSs. Furthermore, a new modified version of the proposed methodology is used to specify the weight of each expert. Finally, a case study from the literature, concerning workflow schema of marble processing plants project, is presented to better express the capability of the proposed methodology. [ABSTRACT FROM AUTHOR]

Low-carbon tourism plays the increasingly significant role in carbon emission reduction and natural environmental protection. The choice of low-carbon tourist destination (LCTD) often involves the multiple attributes or criteria and can be regarded as the corresponding multiple attribute group decision making (MAGDM) issues. Since the Pythagorean fuzzy sets (PFSs) could well depict uncertain information or fuzzy information and cope with the LCTD selection, thus this essay develops a framework to tackle such MAGDM issues under the Pythagorean fuzzy environment. In this essay, due to few methods can compare with different alternatives along with their advantages from designed attributes, therefore, to overcome this challenge, the taxonomy method is utilized to integrate with PFSs. What’s more, the entropy method is also utilized to determine the attribute weights. Eventually, an application related to LCTD selection and some comparative analysis have been given to demonstrate the superiority of the designed method. The results illustrate that the designed framework is useful for identifying optimal tourist destination among the potential tourist destinations.

Uncertainty is an important factor in any decision-making process. Different tools and approaches have been introduced to handle the uncertain environment of group decision making. One of the latest tools in dealing with uncertainty is Pythagorean fuzzy sets (PFSs). These sets extend the concept of intuitionistic fuzzy sets. To show the advantages of these new sets, this paper offers a novel last aggregation group decision-making process for weighting and evaluating. The methodology employs a new approach in computing the weight of decision makers. Moreover, the concept of entropy is applied to address the fuzziness of weights of evaluation criteria in the process. The method develops a new index in ranking the alternatives. Finally, the proposed method is last aggregation, which means it will be more precise in situations with high variations in decision makers’ judgments. To show the applicability of the method, an example from the literature is adopted and solved for internet companies. [ABSTRACT FROM AUTHOR]

This study explores how to enhance the decision-making processes in the phases of idea generation or alternative selection during the new product development (NPD) process. NPD is acknowledged as the central function of businesses in an increasingly competitive marketplace. In the current era, the highly uncertain and rapidly changing market environment makes the NPD extremely vague and complex. To be able to find a suitable solution to this complexity, the proposed research aims to categorize the decision points in the process of NPD regarding software development and identify the fuzziness elements affecting the process. The goal of a decision-making process is to prioritize several alternatives with respect to some required objectives and to select the best among them. Multi-Criteria Decision-Making (MCDM) may support reaching a consensus judgment with the collective assessment of Decision Makers (DMs). We introduce a novel evaluation approach for this problem. The proposed approach employs a MULTIMOORA (Multi-objective Optimization by Ratio Analysis plus the Full Multiplicative Form) MCDM technique under Pythagorean Fuzzy Sets (PFSs) objective world environment to cope with an ambiguous environment using Group Decision Making (GDM) setting to shape the decisions. The PFSs have demonstrated their advantages in dealing with vagueness and uncertainty over crisp, fuzzy, or intuitionistic fuzzy sets. Therefore, PFSs can represent the DMs' judgments and preferences in a better structure, ensuring enhanced decision-making in a group consensus. A case study on gaming software and app development is presented to validate the functionality of the proposed method. The results are compared and assessed with the help of a sensitivity analysis. This research makes a real contribution to the literature by proposing a novel evaluation method to rate and select NPD (gaming software and apps) to deal with the inexactness and vagueness associated with the criteria and alternatives., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper, (© 2023 The Authors.)

The Hamy mean (HM) operator, as a useful aggregation tool, can capture the correlation between multiple integration parameters, and the 2-tuple linguistic Pythagorean fuzzy numbers (2TLPFNs) are a special kind of Pythagorean fuzzy numbers (PFNs), which can easily describe the fuzziness in actual decision making by 2-tuple linguistic terms (2TLTs). In this paper, to consider both Hamy mean (HM) operator and 2TLPFNs, we combine the HM operator, weighted HM (WHM) operator, dual HM (DHM) operator, and dual WHM (DWHM) operator with 2TLPFNs to propose the 2-tuple linguistic Pythagorean fuzzy HM (2TLPFHM) operator, 2-tuple linguistic Pythagorean fuzzy WHM (2TLPFWHM) operator, 2-tuple linguistic Pythagorean fuzzy DHM (2TLPFDHM) operator and 2-tuple linguistic Pythagorean fuzzy DWHM (2TLPFDWHM) operator. Then some multiple attribute decision making (MADM) procedures are developed based on these operators. At last, an applicable example for green supplier selection is given.

In this paper, we extend the Hamy mean (HM) operator and dual Hamy mean (DHM) operator with Pythagorean fuzzy numbers (PFNs) to propose Pythagorean fuzzy Hamy mean (PFHM) operator, weighted Pythagorean fuzzy Hamy mean (WPFHM) operator, Pythagorean fuzzy dual Hamy mean (PFDHM) operator, weighted Pythagorean fuzzy dual Hamy mean (WPFDHM) operator. Then the multiple attribute group decision making (MAGDM) methods are proposed with these operators. In the end, we utilize an applicable example for supplier selection to prove the proposed methods.

Low-carbon tourism plays the increasingly significant role in carbon emission reduction and natural environmental protection. The choice of low-carbon tourist destination (LCTD) often involves the multiple attributes or criteria and can be regarded as the corresponding multiple attribute group decision making (MAGDM) issues. Since the Pythagorean fuzzy sets (PFSs) could well depict uncertain information or fuzzy information and cope with the LCTD selection, thus this essay develops a framework to tackle such MAGDM issues under the Pythagorean fuzzy environment. In this essay, due to few methods can compare with different alternatives along with their advantages from designed attributes, therefore, to overcome this challenge, the taxonomy method is utilized to integrate with PFSs. What's more, the entropy method is also utilized to determine the attribute weights. Eventually, an application related to LCTD selection and some comparative analysis have been given to demonstrate the superiority of the designed method. The results illustrate that the designed framework is useful for identifying optimal tourist destination among the potential tourist destinations. [ABSTRACT FROM AUTHOR]

The Hamy mean (HM) operator, as a useful aggregation tool, can capture the correlation between multiple integration parameters, and the 2-tuple linguistic Pythagorean fuzzy numbers (2TLPFNs) are a special kind of Pythagorean fuzzy numbers (PFNs), which can easily describe the fuzziness in actual decision making by 2-tuple linguistic terms (2TLTs). In this paper, to consider both Hamy mean (HM) operator and 2TLPFNs, we combine the HM operator, weighted HM (WHM) operator, dual HM (DHM) operator, and dual WHM (DWHM) operator with 2TLPFNs to propose the 2-tuple linguistic Pythagorean fuzzy HM (2TLPFHM) operator, 2-tuple linguistic Pythagorean fuzzy WHM (2TLPFWHM) operator, 2-tuple linguistic Pythagorean fuzzy DHM (2TLPFDHM) operator and 2-tuple linguistic Pythagorean fuzzy DWHM (2TLPFDWHM) operator. Then some multiple attribute decision making (MADM) procedures are developed based on these operators. At last, an applicable example for green supplier selection is given. [ABSTRACT FROM AUTHOR]

In this paper, we extend the Hamy mean (HM) operator and dual Hamy mean (DHM) operator with Pythagorean fuzzy numbers (PFNs) to propose Pythagorean fuzzy Hamy mean (PFHM) operator, weighted Pythagorean fuzzy Hamy mean (WPFHM) operator, Pythagorean fuzzy dual Hamy mean (PFDHM) operator, weighted Pythagorean fuzzy dual Hamy mean (WPFDHM) operator. Then the multiple attribute group decision making (MAGDM) methods are proposed with these operators. In the end, we utilize an applicable example for supplier selection to prove the proposed methods. [ABSTRACT FROM AUTHOR]