Fuzzy Sets Research Articles

Hamacher Aggregation Operators for Pythagorean Fuzzy Set and its Application in Multi-Attribute Decision-Making Problem

Pythagorean fuzzy set is a useful expansion of intuitionistic fuzzy set for dealing with ambiguities, which mostly occur in real-life problems. Hamacher t-norm also has important and compatible norms that incorporate a parameter that offers various options to decision-makers during the information fusion process, thereby enhancing their ability to model decision-making problems effectively compared to alternative methods. In this study, Hamacher operators are being used to introduce several Pythagorean fuzzy Hamacher interactive weighted averaging (PFHIWA), Pythagorean fuzzy Hamacher interactive ordered weighted averaging (PFHIOWA), Pythagorean fuzzy Hamacher interactive weighted geometric (PFHIWG), and Pythagorean fuzzy Hamacher interactive ordered weighted geometric (PFHIOWG) operators. The properties of these operators are examined in detail. The benefit of using progressive operators is that they deliver more understanding of the scenario to the decision-makers. Proposed operators are utilized to elaborate multi-attribute decision-making (MADM). By showing the sensitivity analysis, our proposed operator has high stability related to multi-attribute decision-making (MADM) under the Pythagorean fuzzy data set.

A Study on AG-Groups in Spherical Fuzzy Environment

An AG-group is an algebraic structure that satisfies the left invertive law and includes its left identity and inverse elements. This framework is naturally suited for representing and manipulating various real-life applications in civil engineering, information engineering, artificial intelligence, and more. In this paper, we present the structural application of AG-groups in data encryption and in the rotational transformation of water molecules. Additionally, numerous authors have explored fuzzy set theory over AG-group systems, yielding many valuable results. Spherical fuzzy set theory, an extension of fuzzy set theory, allows for the representation of uncertainty in decision-making, where there may be multiple possible choices or uncertainty about the degree of membership of an element in a set. However, no prior work has combined spherical fuzzy set theory with AG-groups, which motivates our study. In this paper, we apply spherical fuzzy set theory to AG-groups and introduce the concept of spherical fuzzy AG-subgroupoids. We provide the characterization of spherical fuzzy AG-subgroupoids over AG-groupoids and examine their related properties. As an application of spherical fuzzy sets over AG-groups, we develop the concept of normal spherical fuzzy groups over AG-groups and investigate their various properties.

Correction: Intuitionistic fuzzy rough set model based on k-means and its application to enhance prediction of aptamer–protein interacting pairs

Correction: Intuitionistic fuzzy rough set model based on k-means and its application to enhance prediction of aptamer–protein interacting pairs

Explainable Prediction Technique for Analyzing Information Disorder Using Fuzzy Rough Sets

A persistent challenge in the domain of social media pertains to the comprehension and representation of information disorder incidents, which include but are not limited to erroneous information, theories of conspiracy, and racial discrimination. These issues frequently become apparent in the written content of posts that are shared on networking platforms and multiple sites. The complexity of information disorder research stems from the wide range of internet epidemic genres and the diverse effects that such information can have on people. Furthermore, the difficulty is exacerbated by the emergence of generative AI models that are capable of generating information that is difficult to identify as synthetic. The findings can assist analysts and decision-makers in acquiring a more in-depth comprehension of the phenomenon occurring in the field of information disorder. Hence, Information Disorder Prediction using Fuzzy Rough Set (IDP-FRS) has been proposed to predict the disinformation in the collected domain accurately and identify fake and real information. Through the incorporation of fuzzy sets of data into modelling and prediction techniques, the research improves the accuracy and interpretability of models, hence facilitating the discovery of disinformation in a more trustworthy manner. Moreover, the introduction of explainable prediction approaches gives users the ability to make educated choices concerning the appropriateness and dissemination of information, which in turn promotes openness and confidence in predictive models.

The multidimensional influence structure of college students’ online gamified learning engagement: A hybrid design based on QCA-SEM

In the post-epidemic era, gamification is widely recognized for its potential to enhance the asynchronous nature of college students' online learning interactions and mitigate efficiency deficits. However, the intrinsic structure and core conditions influencing online gamified learning engagement remain unclear. The challenge lies in understanding the mechanisms through which gamification alters learning behaviors. This study employs fuzzy set qualitative comparative analysis (FSQCA) for core condition identification and robustness testing, innovatively combining it with structural equation modelling (SEM). Drawing on the extended technology acceptance model (TAM) theory, this research delves deeply into the structural relationships that influence student engagement in online gamified learning. The evaluation reveals that immersive experience and habit are core conditions fostering high engagement among college students in online gamified learning. A lack of immersive experience leads to non-high engagement results. Structural equation modelling confirms the mediating role of immersive experience and habit in the effects of performance expectations and perceived fun in student engagement. Furthermore, the study substantiates the moderating influence of learning style on perceptual factors and normalizing elements and describes an interactive relationship between perceived behavioral control, subjective norms, and online gamification behavior. This research extends our understanding of perceptions, norms, and structural factors within a gamified learning environment. It uncovers the mechanisms of engagement from perception to normalization factors, highlighting the positive bidirectional influence of subjective cognition and objective factors on gamified learning and emphasizing the moderating role of learning style between perceptual factors and normalization elements. These findings provide a solid foundation for future research and practice in online gamified learning.

Design and implementation of an adaptive unscented Kalman filter with interval Type-3 fuzzy set for an attitude and heading reference system considering gyroscope bias

Low-cost microelectromechanical sensors used in attitude and heading reference systems (AHRS) suffer from unstable on–off biases, scaling errors, and nonlinearities that lead to an increase of navigation errors over time. To damp these errors and uncertainties from ultimate attitude and heading angles, the bias term of gyroscopes is augemented in under estimation state vector for high frequency feedback compensation. In this paper, an adaptive estimation algorithm to combine the strong tracking filter (STF) and interval type-3 fuzzy set (IT3FS) with an unscented Kalman filter (UKF) is proposed to deal with the large uncertainties in the microelectromechanical AHRS. The UKF, involving strong capability of dealing with nonlinearity, is limited by large instable bias uncertainty. By combining the STF to adaptively tuning of the UKF gain matrix and the IT3FS to determine the STF fading factor as well, the new IT3FS-STUKF algorithm is developed for high estimation performance against the significant uncertainties. To validate the proposed IT3FS-STUKF, real experiments are conducted with ground vehicles in urban areas, which show an improved accuracy compared to the extended Kalman filter (EKF) at reasonable computational burden.

Analysis of green energy-oriented sustainable development goals for emerging economies

Countries should focus on the improvements to achieve sustainable development goals. However, taking these actions create some operational costs. Thus, it is appropriate for rising nations to prioritize sustainable development objectives. Due to this condition, more critical sustainable development goals should be identified. Accordingly, this study evaluates green energy-oriented sustainable development goals for emerging economies. Within this context, a model is generated by considering the golden cut and bipolar q-rung orthopair fuzzy sets (q-ROFSs). The novelty of this study is to identify key green energy-oriented sustainable development goals for the improvement of emerging economies by an original model based on the golden cut and bipolar q-ROF decision making approach. All results are similar, indicating the proposed model's validity and coherency. It is concluded that increasing renewable energy is the most significant target with a weight of 0.235 regarding green energy-oriented sustainable development. Cooperation and efficiency are other significant issues for this condition, with weights of 0.198 and 0.196. It is also identified that Turkey and Mexico are the most successful countries in reaching green energy-oriented sustainable development goals. Increasing the share of renewable energy in total energy production and consumption is important for emerging countries. For this situation, governments should provide subsidies for renewable energy investors to provide a cost advantage. In this context, issues such as tax cuts and loans with low-interest rates can increase the motivation of clean energy investors.

An integrated group decision support framework utilizing Pythagorean fuzzy DEMATEL–CoCoSo approach for medicine cold chain logistics provider selection

PurposeThe purpose of this study is to establish a synthetic group decision framework based on the Pythagorean fuzzy (PF) set to select the optimal medicine cold chain logistics provider (MCCLP). Fierce market competition makes enterprises must constantly improve every link in the process of enterprise sustainable development. The evaluation of MCCLP in pharmaceutical enterprises is an important link to enhance the comprehensive competitiveness. Because of the fuzziness of expert cognition and the complexity of the decision procedure, PF set can effectively handle the uncertainty and ambiguity in the process of multi-criteria group decision decision-making (MCGDM).Design/methodology/approachThis paper develops an integrated group decision framework through combining the Decision-Making Trial and Evaluation Laboratory (DEMATEL) technique and combined compromise solution (CoCoSo) approach to select a satisfactory MCCLP within PF circumstances. First, the PF set is used to process the ambiguity and uncertainty of the cognition ability of experts. Second, a novel PF knowledge measure is propounded to measure the vagueness of the PF set. Third, a comprehensive criterion weight determination technique is developed through aggregating subjective weights attained utilizing the PF DEMATEL approach and objective weight deduced by knowledge measure method. Furthermore, an integrated MCGDM approach based on synthetic weight and CoCoSo method is constructed.FindingsThe outcomes of sensibility analysis and comparison investigation show that the suggested decision framework can help decision experts to choose a satisfactory MCCLP scientifically and reasonably. Accordingly, the propounded comprehensive decision framework can be recommended to enterprises and organizations to assess the MCCLP for their improvement of core competitiveness.Originality/valueMCCLP selection is not only momentous for pharmaceutical enterprises to improve transportation quality and ensure medicine safety but also provides a strong guarantee for enterprises to improve their core competitiveness. Nevertheless, enterprises face certain challenges due to the uncertainty of the assessment environment as well as human cognition in the process of choosing a satisfactory MCCLP. PF set possesses a formidable capability to address the uncertainty and imprecision information in the process of MCGDM. Therefore, pharmaceutical enterprises can implement the proposed method to evaluate the suppliers to further improve the comprehensive profit of enterprises.

Prioritization of renewable energy for offshore ship charging stations based on intuitionistic fuzzy GLDS method: A case of China

Offshore ship charging station (OSCS) projects can help to address the current demand for electric ships for ocean voyages to a large extent. The proper selection of the energy source for power generation is a key part of the OSCS project. To select the optimal renewable energy for OSCS with many difficulties such as the ambiguity of the decision-making environment, the differences in group assessment information, and the conflict and compensation between criteria, this paper proposed a fuzzy multi-criteria decision-making (MCDM) framework. First, a comprehensive criteria system was constructed. Second, the intuitionistic fuzzy set (IFS) was introduced to express experts’ fuzzy cognition. Third, based on the quality of evaluation, a novel expert weighting method was proposed, and the generalized intuitionistic fuzzy weighted geometric interaction averaging (GIFWGIA) operator was used to aggregate the individual evaluations. Fourth, the criteria importance through intercriteria correlation (CRITIC) method, and the stepwise weight assessment ratio analysis II (SWARA II) method were introduced to determine the criteria weights. Fifth, considering criteria compensation, and individual and group ranks, the gained and lost dominance score (GLDS) method were used for ranking. Finally, to verify the applicability and reliability of the framework, a case study was conducted in Pingtan Island, Fujian Province. The results show that wind energy was the best alternative, followed by solar, wave and nuclear energy.

A decision support system for cooling tower technologies evaluation in the oil and gas industry

Mitigating the impacts of thermal pollution caused by the oil and natural gas (O&G) industry by applying the appropriate cooling tower technology has advantages for environmental, economic, and health goals. We aim at implementing an intelligent decision support system (DSS). The DSS involves the Delphi and criteria importance through intercriteria correlation (CRITIC) integrated method (DEACRIM) and ranking of alternatives through functional mapping of criterion sub-intervals into a single interval (RAFSI) model under the linear Diophantine fuzzy set (LDFS). Ten criteria based on water-energy nexus and circularity policies and four cooling tower technologies including Natural draft cooling tower technology, Induced draft cooling tower technology, Crossflow cooling tower technology, and Forced draft cooling tower technology have been chosen for evaluation. The evaluation results reveal that the Natural draft cooling tower technology is the most suitable scenario for Iran's O&G energy system facilities in order to mitigate thermal pollution.

Evaluation of Spare Parts Support Capacity of Civil Aircrafts Based on Type-2 Hesitant Pythagorean Fuzzy Sets and Improved Technique for Order Preference by Similarity to Ideal Solution

To improve the spare parts support capacity of civil aircrafts and given the actual lack of evaluation methods at present, the evaluation problem of spare parts support capacity was solved in this study by proposing a multi-attribute decision method based on Type-2 hesitant Pythagorean fuzzy sets and an improved Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). First, the basic definitions of Type-2 hesitant Pythagorean fuzzy sets were given, which were further promoted to Type-n hesitant Pythagorean fuzzy sets, and the basic order relation criterion of Type-2 hesitant Pythagorean fuzzy sets was introduced. Second, a complete evaluation system for spare parts supply support capacity was established with the spare parts of civil aircrafts as the study objects, and each evaluation indicator was introduced in detail. Then, the spare parts support solutions were preferentially sorted using the correlation coefficient formula of Type-2 hesitant Pythagorean fuzzy sets and improved TOPSIS. Finally, the reliability and reasonability of the proposed method were verified through an example calculation and comparative analysis. The experimental results indicate that the proposed method can acquire the evaluation results of spare parts support capacity more scientifically and can be referenced by relevant studies.

A novel algorithmic multi-attribute decision-making framework for solar panel selection using modified aggregations of cubic intuitionistic fuzzy hypersoft set

To address the shortcomings of the cubic intuitionistic fuzzy sets (CIFSs) for the entitlement of multi-argument approximate function, the cubic intuitionistic fuzzy hypersoft set (Ω-set) is an emerging study area. This type of setting associates the sub-parametric tuples with the collection of CIFSs. Categorizing the evaluation of parameters into their corresponding sub-parametric values based on non-overlapping sets has significance in decision making and optimization related situations. Some operations of Ω-set are proposed in this study, along with certain practical features. We provide the complement, P-order, and R-order subsets, P-union (∪P), R-union (∪R), P-intersection (∩P) and R-intersection (∩R) of Ω-sets. The internal cubic intuitionistic fuzzy hypersoft set (ΩI-set) and the external cubic intuitionistic fuzzy hypersoft set (ΩE-set) are also proposed in this paper, which will aid researchers in applying this new theory to other areas of study. We show a few examples in this context and look into some more aspects of ∪P, ∪R, ∩P and ∩R of ΩI-sets and ΩE-sets. Arguments for a few significant theorems about ΩI-sets and ΩE-sets are also presented. Lastly, an algorithm is presented that assists decision-makers in evaluating appropriate solar panels to establish solar plants. The proposed algorithm uses the idea of ∪P and ∪R for two Ω-sets constructed based on expert opinions of decision makers.

FRRI: A novel algorithm for fuzzy-rough rule induction

Interpretability is the next frontier in machine learning research. In the search for white box models — as opposed to black box models, like random forests or neural networks — rule induction algorithms are a logical and promising option, since the rules can easily be understood by humans. Fuzzy and rough set theory have been successfully applied to this archetype, almost always separately. As both approaches offer different ways to deal with imprecise and uncertain information, often with the use of an indiscernibility relation, it is natural to combine them. The QuickRules [20] algorithm was a first attempt at using fuzzy rough set theory for rule induction. It is based on QuickReduct, a greedy algorithm for building decision superreducts. QuickRules already showed an improvement over other rule induction methods. However, to evaluate the full potential of a fuzzy rough rule induction algorithm, one needs to start from the foundations. Accordingly, the novel rule induction algorithm, Fuzzy Rough Rule Induction (FRRI), we introduce in this paper, uses an approach that has not yet been utilised in this setting. We provide background and explain the workings of our algorithm. Furthermore, we perform a computational experiment to evaluate the performance of our algorithm and compare it to other state-of-the-art rule induction approaches. We find that our algorithm is more accurate while creating small rulesets consisting of relatively short rules.

Selection of third-party logistics in supply chain finance under probabilistic complex hesitant fuzzy sets and distance measures

Financial institutions attach great importance to the multiple attribute decision-making (MADM) problems of selecting an effective third-party logistics (3PL) service provider in supply chain finance. A suitable 3PL service provider can not only assist financial institutions in carrying out supply chain finance activity but can also replace financial institutions in supervising the operation of a target financing supply chain, therefore minimizing financial institutions' operating risks. However, there is no sufficient study on the selection of a 3PL service provider. Hence, the objective of this paper is to establish an innovative concept of the “probabilistic complex hesitant fuzzy set” (PCHFS), which is a hybrid structure of the complex hesitant fuzzy set and the probabilistic fuzzy set to manage complex information in real-decision theory. This paper examines the periodicity of probabilistic fuzzy information and extends the range from [0,1] to the unit disc in the complex plane to provide more ability to describe the full meaning of the information in a mathematical model. Based on the internal structure of the set and to find the degree of discrimination between the pairs of PCHFSs, the generalized distance measures and modified generalized distance measures are defined. Several properties and their relationships between them are derived in detail. Also, several cases of the proposed measures are exposed, which reduces them to the existing studies. Furthermore, based on these proposed measures, a multiple-attribute decision-making (MADM) approach is established in an uncertain environment, and several numerical examples are given to examine the feasibility and validity of the explored measures. Finally, the modified and parameterized distance measures based on PCHFSs are verified by comparing them with some existing measures.

Uncertainty Minimization in the Human Visual Response Using an Interval Type-2 Fuzzy Set and Its Application to Rice Leaf Image Enhancement

Uncertainty Minimization in the Human Visual Response Using an Interval Type-2 Fuzzy Set and Its Application to Rice Leaf Image Enhancement

Linking the treadmills of production and destruction to disproportionate carbon emissions

Our case-oriented analysis of the drivers of climate change highlights the barriers and pathways to climate action. We employ Qualitative Comparative Analysis (QCA), specifically fuzzy set Qualitative Comparative Analysis (fsQCA), to trace the ways in which combinations of climate change drivers helps us develop a better understanding of climate change, with a special emphasis on nation-states making a disproportionate contribution to this problem. World Bank data is used to analyze 179 countries allowing us to explore how population, gross domestic product per capita (Treadmill of Production), and military spending as a percentage of GDP (Treadmill of Destruction) provide different recipes for understanding two climate change outcomes as they relate to UN Sustainable Development Goals (particularly SDGs 10 and 13). Our analysis yields new insights, illuminating two distinct recipes, thereby indicating that a focus on mechanisms provides new ways of understanding social processes and their connection to carbon emissions.

The path of depression in rural children: A fuzzy-set qualitative comparative analysis across multiple provinces in China

ObjectivesThis study explores the combinations of conditional variables contributing to depressive symptoms in rural children. MethodsWe analyzed data from 715 children from a rural mental health database, conducting detailed follow-up investigations on 129 children in Zhejiang and Henan provinces. We used fuzzy set Qualitative Comparative Analysis (fsQCA) and regression analysis to identify causal pathways leading to depression. ResultsThe results indicate that depression in rural children does not stem from a single, necessary condition but arises from multiple factors. Our findings highlight significant contributions from both maternal and paternal involvement. Specifically, maternal involvement, combined synergistically with peer support and problematic behaviors, as well as paternal involvement, together with peer support and anxiety, significantly affects depressive outcomes. Additionally, anxiety and strong peer relationships independently have a substantial impact on these outcomes. Effective mitigation strategies involve active parental engagement and robust peer support, reducing the influence of risk factors such as problematic behaviors and anxiety. LimitationsThe generalizability of the results is limited by cultural and geographical variations. The study also does not account for all potential factors influencing depression in rural children. ConclusionDepression in rural children results from multiple interacting factors. Tailored interventions addressing these specific combinations are recommended.

Entropy measures of multigranular unbalanced hesitant fuzzy linguistic term sets for multiple criteria decision making

The hesitant fuzzy linguistic term set (HFLTS) is an efficient tool for modeling linguistic information in multi-criteria decision making (MCDM), and the entropy measure of HFLTS, as a substantial representation of uncertainty, merits additional investigation. This article aims to exploit a general framework to facilitate the construction of entropy measure for multigranular unbalanced HFLTS. An axiomatic definition of the entropy for HFLTSs that considers both types of uncertainty (fuzziness and hesitation) is presented, with the entropy measure subsequently derived from distance-based mapping. From this definition, several deduced results have been developed for the mapping that depicts the entropy expression in order to get such functions with ease. Whereafter, a MCDM weight-determining model for multigranular unbalanced linguistic information without preset weights is devised, and an empirical application of the suggested model in MCDM is illustrated. Ultimately, comparisons and analyses with existing studies are conducted to demonstrate the advantages of the proposed work.

Decision support system based on bipolar complex fuzzy Hamy mean operators

The important feature of the multi-attribute decision-making (MADM) technique is to identify an ideal solution and aggregate collective cognitive fuzzy information of human opinion. To serve this purpose, we explore the concepts of the bipolar complex fuzzy set with positive and negative support terms. A few applications of the Hamy mean (HM) and Dual Hamy mean (DHM) models are also discussed to find out the relationship among input arguments or different preferences. For this, we derive a family of mathematical approaches by incorporating the theory of bipolar complex fuzzy information such as bipolar complex fuzzy Hamy mean (BCFHM), bipolar complex fuzzy weighted Hamy mean (BCFWHM), bipolar complex fuzzy Dual Hamy mean (BCFDHM), and bipolar complex fuzzy weighted Dual Hamy mean (BCFWDHM) operators. Derived mathematical approaches are more applicable and can express the influence of uncertain information due to the involvement of additional parameter values. Based on diagnosed research work and mathematical methodologies, we establish a decision algorithm for the MADM problem to resolve real-life dilemmas. An experimental case study demonstrates the compatibility of derived approaches and evaluates the investment policy's sustainability based on certain parameters. The advantages and consistency of the proposed research work are verified in the comparative study with various existing aggregation operators.

Structural equation modeling and Fuzzy set theory: Advancing risk assessment in oil and gas construction projects

This research seeks to evaluate the critical risks associated with Oil and Gas Construction Projects (O&GCPs) in terms of their level of significance and quantifiable effects on Project Performance (PP) by surveying O&GCPs experts in the USA. A multiphase research methodology was adopted, including Systematic Literature Review (SLR) to identify the key O&GCPs risks; semi-structured interviews to identify PP indicators and establish hypotheses on the effect of O&GCPs risks on PP; surveys to assess the perceived agreement of O&GCPs experts regarding the effects of O&GCPs risks on PP, and to rank the probability and impact of the identified O&GCPs risks; Structural Equation Model (SEM) to quantitatively assess the effects of O&GCPs risks on PP; Fuzzy Set Theory (FST) to assess the level of significance of O&GCPs risks; and interviews to verify the developed assessment models and their outputs. The SLR analysis identified 35 articles on O&GCP risks from 2013 to 2023, revealing 51 risk factors in eight categories based on their sources. The SEM analysis indicated that the oil and gas safety risks category had the strongest direct impact on PP. Furthermore, the FST analysis revealed that non-compliance with PPE emerged as the most significant risk factor across all categories of O&GCP risks. This study enhances knowledge and practice by aiding researchers and practitioners in understanding how key O&GCP risks impact PP. This improved understanding is expected to facilitate the formulation of effective mitigation strategies during the early stages of the projects.