Fuzzy Set Model Research Articles

Refined Fuzzy Soft Sets: Properties, Set-Theoretic Operations and Axiomatic Results

This article discusses the results of an investigation into refined fuzzy soft sets, a novel variant of traditional fuzzy sets. Refined fuzzy soft sets provide a versatile method of data analysis, inspired by the need to deal with uncertainty and ambiguity in real-world data. This research expands on prior work in fuzzy set theory by investigating the nature and characteristics of refined fuzzy soft sets. They are useful in decision-making, pattern recognition, image processing, and control theory because of their capacity to deal with uncertainty, ambiguity, and the inclusion of expert information. This study analyzes these fuzzy set models and compares them to others in the field to reveal their advantages and disadvantages. The practical uses of enhanced fuzzy soft sets are also examined, along with possible future research strategies on this exciting new topic.

A new multi-objective decision-making method with diversified weights and Pythagorean fuzzy rough sets

In reality, there are many multi-objective decision-making problems with fuzziness and uncertainty, such as the choice of clinical treatment schemes. To effectively cope with such problems, it is urgent to scientifically handle fuzzy and uncertain information. Given the fact that the Pythagorean fuzzy set is a useful tool to tackle fuzzy information, and the rough set theory is superior in dealing with uncertain data, this paper aims to establish a novel decision-making method for scheme selection from the perspective of Pythagorean fuzzy rough sets. Pythagorean fuzzy numbers (PFNs) are first employed to express fuzzy preference information, and then multi-objective Pythagorean fuzzy information systems are introduced. Subsequently, we develop a new fuzzy rough set using an improved correlation coefficient method to deal with the uncertainty of PFNs. Furthermore, considering the diversified weights, we present a weight calculation method based on approximate accuracies. Meanwhile, a weighted fuzzy rough set model is constructed to achieve multi-objective information fusion. Accordingly, a multi-objective decision-making method is put forward with the help of overlap functions. Finally, we apply the built method to three cases from different decision scenarios to illustrate the applicability of the method. By some comparative analyses, the effectiveness and superiority of the method are also exhibited. Moreover, we discuss the establishment of decision support systems regarding scheme selection. On the whole, the work of this paper is helpful to support the solution of complex multi-objective decision-making problems.

Local double quantitative fuzzy rough sets over two universes

As an important expanded quantification fuzzy rough set model, the local fuzzy rough set model is used to measure relative quantitative information between the fuzzy similarity classes and the basic concept. Although many studies have taken on this topic, the existing local fuzzy rough sets ignore the absolute quantitative information in the fuzzy information system over two universes. Therefore, based on this observation, we propose a local double quantitative fuzzy rough set model over two universes, which considers the problems from the double quantization form of the local fuzzy rough sets over two universes. Furthermore, the corresponding properties and decision rules of the local double quantitative “logical and” fuzzy rough set model over two universes are studied. Then, in order to improve the applicability of the model, an effective reduction method is introduced. Finally, we conduct experimental comparisons showing the computational efficiency and approximate accuracy of the model in concept approximation and reduction.

Asymmetric models of intuitionistic fuzzy rough sets and their applications in decision-making

Asymmetric models of intuitionistic fuzzy rough sets and their applications in decision-making

Gaussian Coordinate Feature Set Optimisation (GCFSO) Model for Analysing the Impact of Urbanisation on Cultural Identities and City Images

Urbanization, characterized by the rapid growth of cities and the associated changes in social, economic, and physical landscapes, has been a significant global phenomenon in recent decades. As cities expand and transform, they play a crucial role in shaping cultural identity and projecting a distinct city image. The constructed framework process comprises the multi-modal image processing with the Gaussian Coordinate estimation with the Optimization model. The proposed model comprises the estimation of the feature sets associated with the feature set for the classification of cultural identity. The model comprises the Gaussian Coordinate Feature Set Optimization (GcFSO). The GcFSO model estimates the feature sets in the data related to the cultural identity for the shaping of images to analyze the urbanization process. The GcFSO model computes the feature set based on the Mandami Fuzzy set model for the classification of cultural identity in China. The fuzzy set rules are computed for the estimation of the features in the process of Urbanization. The performance of the GcFSO model is examined with the deep learning model for classification. The simulation analysis stated that GcFSO model achieves a higher classification accuracy of 0.99 with a minimal error rate.

Novel results on G -lower L -fuzzy rough approximation operator in ( O , G ) -fuzzy rough set model1

Lately, Jiang and Hu (H.B. Jiang, B.Q. Hu, On ( O , G ) -fuzzy rough sets based on overlap and grouping functions over complete lattices, Int. J. Approx. Reason. 144 (2022) 18-50.) put forward ( O , G ) -fuzzy rough sets via overlap and grouping functions over complete lattices. Meanwhile, they showed the characterizations of O -upper and G -lower L -fuzzy rough approximation operators in ( O , G ) -fuzzy rough set model based on some of specific L -fuzzy relations and studied the topological properties of the proposed model. Nevertheless, we discover that the partial results given by Jiang and Hu could be further optimized. So, as a replenish of the above article, in this paper, based on G -lower L -fuzzy rough approximation operator in ( O , G ) -fuzzy rough set model, we further explore several new conclusions on the relationship between G -lower L -fuzzy rough approximation operator and different L -fuzzy relations. In particular, the equivalent descriptions of relationship between G -lower L -fuzzy rough approximation operator and O -transitive ( O -Euclidean) L -fuzzy relations are investigated, which are not involved in above literature and can make the theoretical results of this newly fuzzy rough set model more perfect.

Hesitant fuzzy β-covering ( T , I ) rough set models: An application to multi-attribute decision-making

Covering rough sets have been successfully applied to decision analysis because of the strong representing capability for uncertain information. As a research hotspot in decision analysis, hesitant fuzzy multi-attribute decision-making (HFMADM) has received increasing attention. However, the existing covering rough sets cannot handle hesitant fuzzy information, which limits its application. To tackle this problem, we set forth hesitant fuzzy β-covering rough set models and discuss their application to HFMADM. Specifically, we first construct four types of hesitant fuzzy β-covering ( T , I ) rough set models via hesitant fuzzy logic operators and hesitant fuzzy β-neighborhoods, which can handle hesitant fuzzy information without requiring any prior knowledge other than the data sets. Then, some intriguing properties of these models and their relationships are also discussed. In addition, we design a new method to deal with HFMADM problems by combining the merits of the proposed models and the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method. In this method, we not only consider the risk preferences of decision-makers, but also present a new hesitant fuzzy similarity measure expressed by hesitant fuzzy elements to measure the degree of closeness between two alternatives. Finally, an enterprise project investment problem is applied to illustrate the feasibility of our proposed method. Meanwhile, the stability and effectiveness of our proposed method are also verified by sensitivity and comparative analyses.

Spatio-temporal evaluation of water-energy-food nexus system risk from the provincial perspective: A case study of China

Abstract This study first defined the concept of the water–energy–food nexus system risk (WEF-R). Then, the WEF-R evaluation index system was established from three aspects: stability, coordination, and sustainability subsystems. Finally, the set pair analysis-variable fuzzy set model was used to evaluate the risk levels of subsystems, and the risk matrix was applied to assess provincial WEF-R levels in China from 2009 to 2018. The results showed that the stability subsystem had the greatest influence on provincial WEF-R, followed by the sustainability subsystem. The provinces with a higher risk of the stability subsystem and lower risk of the sustainability subsystem were mainly centralized in southeast coastal and central regions, which were consistent with the provinces with better socio-economic development. The provinces with lower risk of the stability subsystem and higher risk of the sustainability subsystem were mainly concentrated in northwest regions, which correspond with the provinces with better natural resources endowment but lower socio-economic development. As for the temporal evolution of risk levels, the risk levels of the coordination and sustainability subsystems showed downward trends during the study period, while the risk level of the stability subsystem displayed a small fluctuation, and the provincial WEF-R level in China presented a decreasing trend.

Generalized fuzzy neighborhood system-based multigranulation variable precision fuzzy rough sets with double TOPSIS method to MADM

Multigranulation fuzzy rough sets (MFRSs), variable precision fuzzy rough sets (VPFRSs) and their combinations with traditional decision-making methods are fundamental in the research of multi-attribute decision-making (MADM) problems. However, the existing theories and methods have two deficiencies: (1) many existing MFRSs are based on fuzzy relations or fuzzy coverings, which may not effectively solve some MADM problems; (2) VPFRSs usually do not meet the inclusion property, which hinders their further development in theory and application. Noted that both fuzzy relations and fuzzy coverings can generate fuzzy neighborhood systems in a natural way, so the fuzzy neighborhood system provides a broader multigranulation framework. Inspired by this, by using the generalized fuzzy neighborhood system, we propose three multigranulation variable precision fuzzy rough set models, namely optimistic, pessimistic and compromise, respectively. As expected, these models contain many existing models as special cases, thus broadening the framework of rough set. Additionally, we verify that these models fulfill many basic algebra properties, particularly the generalized inclusion properties, which overcome the limitation of VPFRSs. Finally, by combining the proposed fuzzy rough set models with the TOPSIS method, we develop a new method to MADM. A series of experiments show that our method has some obvious advantages.

Fuzzy rough feature selection using a robust non-linear vague quantifier for ordinal classification

Ordinal classification is a common classification problem, which widely exists in multi-attribute decision making problems. The dominance-based rough set approach (DRSA) is a knowledge acquisition tool for ordinal classification tasks. Nevertheless, the existence of noise information in the collected data greatly reduces the accuracy of the DRSA and some extended model. An effective way to solve this issue is to improve the robustness of these models. In addition, most existing feature selection strategies based on dominance rough sets mainly focus on the monotonic classification consistency between features and decision, but ignoring the classification information provided by features combination. Motivated by these two issues, this paper proposes a robust fuzzy dominance rough set model to combat noise interference and develop a feature selection approach based on the proposed model for ordinal classification tasks. First, a non-linear vague quantifier is adopted to construct the robust model, and related dependency function is introduced. Second, the rank entropy based uncertainty measures are explored to characterize the contribution of features combination for ordinal classification. Based on the proposed uncertainty measures, a new feature evaluation index is presented. Meanwhile, the corresponding feature selection algorithm is designed. Finally, numerical comparative experiments are performed to indicate that the proposed model and feature selection algorithm have good capability.

Techniques for Finding Analytical Solution of Generalized Fuzzy Differential Equations with Applications

Engineering and applied mathematics disciplines that involve differential equations include classical mechanics, thermodynamics, electrodynamics, and general relativity. Modelling a wide range of real-world situations sometimes comprises ambiguous, imprecise, or insufficient situational information, as well as multiindex, uncertainty, or restriction dynamics. As a result, intuitionistic fuzzy set models are significantly more useful and versatile in dealing with this type of data than fuzzy set models, triangular, or trapezoidal fuzzy set models. In this research, we looked at differential equations in a generalized intuitionistic fuzzy environment. We used the modified Adomian decomposition technique to solve generalized intuitionistic fuzzy initial value problems. The generalized modified Adomian decomposition technique is used to solve various higher-order generalized trapezoidal intuitionistic fuzzy initial value problems, circuit analysis problems, mass-spring systems, steam supply control sliding value problems, and some other problems in physical science. The outcomes of numerical test applications were compared to exact technique solutions, and it was shown that our generalized modified Adomian decomposition method is efficient, robotic, and reliable, as well as simple to implement.

Expanding Pythagorean fuzzy sets with distinctive radii: disc Pythagorean fuzzy sets

AbstractThis article presents the circular Pythagorean fuzzy set (C-PFS) model, a generalization of the circular intuitionistic fuzzy set model that improves its performance thanks to the acclaimed extension of intuitionistic fuzzy sets to Pythagorean fuzzy sets. Then, we generalize C-PFSs to produce the novel disc Pythagorean fuzzy sets (D-PFSs). The constituent elements of both C-PFSs and D-PFSs are circular Pythagorean fuzzy values, either with a common or a distinctive radius. We lay out some fundamental algebraic and arithmetic operations on D-PFSs (hence on C-PFSs), namely union, intersection, addition, multiplication, and scalar multiplication, and we explore the main features of these operations. We propose and investigate the properties of the novel circular Pythagorean fuzzy weighted average/geometric aggregation operators. The “COmbinative Distance based ASsesment" approach, which is based on the Hamming and Euclidean distances, is expanded to the D-PFS framework. To justify its implementability, we apply the new methodology to a case study (selection of the best supermarkets to buy fresh fruit for a hotel) and then we compare it to related solutions.

Feature Selection With Local Density-Based Fuzzy Rough Set Model for Noisy Data

Fuzzy rough set theory can model uncertainty in data and has been applied to feature selection for machine learning tasks. The existence of noise in data is one of the reasons for data uncertainty. However, most classical fuzzy rough set models are often sensitive to the noise in data, which somewhat degrades their applicability to process uncertainty of data. Furthermore, a robust feature evaluation function is nontrivial in a fuzzy rough set model as non-optimal feature subsets may be selected due to the perturbations from redundant features. In this paper, we delve into local density and indispensable features for fuzzy rough feature selection to address these challenges. We first propose a Local Density-based Fuzzy Rough Set (LDFRS) model to tackle noisy data. Mutual information is then plugged into the proposed LDFRS model to evaluate uncertainty in data. A joint feature evaluation function on the indispensability and relevance of features is constructed to evaluate the significance of features. On this basis, a fuzzy rough feature selection algorithm is built upon the LDFRS model. Experimental results using four typical classifiers demonstrate the robustness and effectiveness of the proposed model including our feature selection algorithm and its superiority against baseline methods.

Risk Assessment Model of Chemical Process Based on Interval Type-2 Fuzzy Petri Nets

An interval type-2 fuzzy set and fuzzy Petri net combined risk assessment model for chemical production was proposed to solve the problems of disorganized hierarchy and poorly targeted measures, as well as the requirement for complex equipment associated with chemical production risk assessment. First, four different types of risk databases were established according to the production process of cyclohexane. Considering the intrinsic relationship between the risk factors in the fault database, the interval type-2 fuzzy set was used to improve the semantic transformation accuracy and calculate the confidence in the risk factors. The fuzzy Petri net model was used to simulate the dynamic development of accidents, and the parallel relationship between risk factors was intuitively described. Thereafter, the external relationship between risk factors was analyzed, and the net structure of each layer was divided to build a multilevel model. Finally, the catalyst activation process during cyclohexane production was taken as an example for risk assessment calculation, and the accident risk probability was calculated by multilevel fuzzy reasoning. The results demonstrate that the model is an improvement over traditional methods and can be used for precise prevention and control. Moreover, it can accurately analyze risk probability during chemical production, determine the risk associated with the reaction process, effectively prevent accidents, and provide a reference for risk evaluation and risk classification.

Three-way conflict analysis and resolution based on q-rung orthopair fuzzy information

In solving some complex conflict problems, compared with intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs), q-rung orthopair fuzzy sets (q-ROFSs) can better express and model imprecise information. In addition, three-way decisions (TWDs), an emerging theory of simulating human decision-making behavior, play an increasingly important role in the study of conflict problems. In order to solve conflict problems under q-rung orthopair fuzzy information (q-ROFI), we propose a three-way conflict analysis and resolution model based on TWDs and decision-theoretic rough sets (DTRSs) theory, which provides another answer for Deja's fundamental questions about Pawlak's conflict model, namely, “what are the inherent causes of conflict?” and “how can a viable strategy be found?” different from the existing ones. To be specific, firstly, we define new conflict distances and conflict function for q-ROFI system using aggregation functions and weight determination method, and prove some of their properties. On this basis, the concepts of three-level of contention set and agent set, a trisection of conflict set under individual contention and contention set, and maximum doughty coalition of q-ROFI are introduced. Secondly, after introducing the rough approximation threshold calculation method on the basis of standard evaluation set, to find the optimal viable strategy under the given q-ROFI, we calculate and sort the score function by the upper and lower approximation operators in the proposed q-rung orthopair fuzzy decision-theoretic rough sets (q-ROFDTRSs) model. Thirdly, we use the proposed model to study a land-use conflict case in a metropolitan area to verify the feasibility. Finally, from sensitivity and comparative analysis, we verify the stability and validity of the q-ROFDTRSs model.

Risk assessment method for controlled flight into terrain of airlines based on QAR data

PurposeThe purpose of this paper is to assess the risk of controlled flight into terrain (CFIT) for airlines and to develop a practical method for evaluating and predicting CFIT risk to ensure safe and efficient airline operations.Design/methodology/approachIn accordance with the monitoring project specification issued by the Flight Standards Department of the Civil Aviation Administration of China (CAAC), a preliminary draft of evaluation indicators for CFIT risk was developed based on the literature review and semi-structured interviews. Fifteen aviation experts were then selected and invited to participate in a Delphi method to revise the draft. Analytic hierarchy process (AHP) and entropy weight method were used to determine the combined weight of the indicators. The variable fuzzy set model and quick access recorder (QAR) data were applied to evaluate the CFIT risk of an airline from 2007 to 2018, and the classification results were compared with actual operational data.FindingsThe research findings reveal that the six most significant monitoring items affecting CFIT risk are incorrect configuration settings during landing, loss of altitude during climbing, ground proximity warning, G/S deviation, flap extension delay during landing and incorrect takeoff configuration. The CFIT risk of airlines has shown an increasing trend since 2015. The values in 2010, 2017 and 2018 were greater than 2 and less than 2.5, indicating that the CFIT risk is at Level 2, close to Level 3, and the risk is low but approaching medium.Practical implicationsUsing the combination weight determined by AHP and entropy weight method to rank the weight of 15 monitoring items, airlines can take necessary measures (simulator training, knowledge training) to reduce the occurrence of monitoring items with high weight to reduce CFIT risk. This risk assessment method can quantitatively evaluate the CFIT risk of airlines and provide theoretical guidance and technical support for airlines to formulate safety management measures and flight training programs, enabling the interconnection between QAR data and flight quality.Originality/valueThe proposed method in this study differs from traditional approaches by offering a quantitative assessment of CFIT risk for airlines and enabling the interconnection between QAR data and flight quality.

Axiomatic characterizations of (𝔾, 𝕆)-fuzzy rough approximation operators via overlap and grouping functions on a complete lattice

Recently, Jiang, H. B., and B. Q. Hu. [2022. “On (O,G)-Fuzzy Rough Sets Based on Overlap and Grouping Functions Over Complete Lattices.” International Journal of Approximate Reasoning 144: 18–50. doi:10.1016/j.ijar.2022.01.012] constructed a -fuzzy rough set model with the logical connectives–a grouping function and an overlap function on a complete lattice, which provided a new constructive approach to fuzzy rough set theory. The axiomatic approach is as important as the constructive approach in rough set theory. In this paper, we continue to study axiomatic characterizations of -fuzzy rough set. Traditionally, the associativity of the logical connectives plays a vital role in the axiomatic research of existing fuzzy rough set models. However, a grouping function and an overlap function lack the associativity. So we explore a novel axiomatic approach to -upper and -lower fuzzy rough approximation operators without associativity. Further, we provide single axioms to characterize -upper and -lower fuzzy rough approximation operators instead of sets of axioms. Finally, we use single axioms to characterize fuzzy rough approximation operators generated by various kinds of fuzzy relations including serial, reflexive, symmetric, -transitive, -transitive fuzzy relations as well as their compositions.

Local fuzzy rough set model over two universes and its reduction

Local fuzzy rough set model over two universes and its reduction

Einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making.

The spherical fuzzy set (SFS) model is one of the newly developed extensions of fuzzy sets (FS) for the purpose of dealing with uncertainty or vagueness in decision making. The aim of this paper is to define new exponential and Einstein exponential operational laws for spherical fuzzy sets and their corresponding aggregation operators. We introduce the operational laws for exponential and Einstein exponential SFSs in which the base values are crisp numbers and the exponents (weights) are spherical fuzzy numbers. Some of the properties and characteristics of the proposed operations are then discussed. Based on these operational laws, some new aggregation operators for the SFS model, namely Spherical Fuzzy Weighted Exponential Averaging (SFWEA) and Spherical Fuzzy Einstein Weighted Exponential Averaging (SFEWEA) operators are introduced. Finally, a decision-making algorithm based on these newly introduced aggregation operators is proposed and applied to a multi-criteria decision making (MCDM) problem related to ranking different types of psychotherapy.

Global [formula omitted]-Commerce (G[formula omitted]C) theory by intuitionistic fuzzy [formula omitted]-submodule

Intuitionistic fuzzy set (IFS) theory can be applied for multi-aspect systems due to its capability to address uncertainty and incomplete information in terms of membership and non-membership degrees. Unfortunately, classical Γ-structures cannot handle fuzzy and imprecise information in real problems. In fact, there is no rigorous base to practically express the effectiveness of multi-attribute systems in IFS environment. Here, we develop a generalized IFS with the notion of Γ-module called intuitionistic fuzzy Γ-submodule (IFΓM) to establish a novel “Global electronic (e)-Commerce (GeC) Theory”. To simplify the analysis of parameters, (α,β)-cut representation is proposed in terms of comprehensive distribution of fuzzy number for the classification of components. On the other hand, Cartesian product is implemented to correspond the elements. Substantial properties of IFΓM including (α,β)-cut, Cartesian product and t-intuitionistic fuzzy Γ-submodule (t-IFΓM) are characterized with illustrative examples to extend the framework of IFΓM, where (α,β)-cut and support t-IFΓM are verified to be Γ-submodules based on the properties of IFΓM. Through Γ-module homomorphism, image and inverse image, the parametric connections between (α,β)-cuts are systematically investigated. In addition, a mathematical relationship between the Cartesian product and (α,β)-cut is determined. The overlapping intersection of a collection of t-IFΓM is proved to be t-IFΓM, and the image and inverse image are preserved under Γ-module homomorphism. As global e-trades are increasingly expanding after the recent coronavirus disease 2019 (COVID-19) hit, with the growth of 26.7-trillion dollars, businesses are required to transform their traditional functional natures to online (or blended) strategies for cost efficiency and self-survival in the present competitive environment. Therefore, compared to recent studies on IFS in the context of Γ-structures, the main contribution of this study is to provide a theoretical basis for the establishment of a new GeC Theory through the developed IFΓM method and Γ-module M which targets the purchasing rate of customers through e-commerce companies. In the end, the performance of the proposed method in terms of upper and lower cut, t-intuitionistic fuzzy set, support and IFΓM model, is analyzed in the developed GeC Theory. The proposed GeC Theory is validated using real datasets of e-commerce mega companies, i.e., Amazon, Alibaba, eBay, Shopify. They are characterized based on the amount of online shopping by samples (individuals). Compared to the existing methods, the GeC approach is an effective IFS-based method for complex systems with uncertainty.