Fuzzy Relations Research Articles

Analytical-solution-based interval fuzzy utility acquisition and decision making with interval-valued fuzzy preference relations based on additive consistency

Acquiring an analytical solution of interval fuzzy utility vectors (IFUVs) from interval-valued fuzzy preference relations (IVFPRs) plays a key role in improving the efficiency and performance of decision making with IVFPRs. This study devises formulas to compute uncertainty indices of interval-valued fuzzy assessments and IVFPRs, and builds uncertainty constraints among fuzzy assessments in an additively consistent IVFPR. By dividing all IVFPRs with the same size into two categories, least square models with constraints of uncertainty indices are set up and their analytical solutions are found to respectively acquire normalized IFUVs from the two categories of IVFPRs. The analytical solutions are then integrated into unified computational formulas acquiring normalized IFUVs from IVFPRs. On the basis of analytical-solution-based IFUVs, a distance based additive consistency index is devised and a novel acceptability concept is presented by taking both additive inconsistency acceptability and uncertainty acceptability into account. Subsequently, this paper proposes a multi-criteria decision making method with highlighting individual characteristics of alternatives. An illustration with one consistent IVFPR and three inconsistent IVFPRs is offered and a comparative study is implemented to validate the models presented. An annual-performance-evaluation-based outstanding teacher recommendation problem is utilized to show the practicality of the decision method proposed.

A preference group consensus method with three-way decisions and regret theory under multi-scale information systems

The foundation of intelligent computing and expert systems relies on the data processing conducted within the realm of multi-scale information systems (MSISs). Data processing within MSISs caters to diverse analytical needs, where the preference hierarchy among various factors plays a vital role in the consensus reaching process (CRP). Additionally, the three-way decisions (TWD) theory serves as an efficient tool, while regret theory (RT) quantifies decision-makers' risk inclinations associated with various psychological behaviors. Thus, the paper aims to introduce an innovative approach known as the CRP-TWD-RT-MSIS method. The study draws inspiration from spatial geometry, incorporating concepts like points, lines, surfaces, and bodies to create MSISs. This process generates a matrix of fuzzy preference relations (FPRs) among distinct decision-makers through data preprocessing. In addition, the paper explores feedback mechanisms based on identification and directional rules, as well as those rooted in minimal adjustments or cost considerations. Simultaneously, it takes negotiation and discussion time into account, culminating in the development of a personalized adjustment optimization model that focuses on minimizing time costs. In the end, the method's effectiveness and superiority are validated through a case study and a comparative analysis of real data from the Chinese Weather and Meteorological Bureau's website.

Evaluation and ranking of fuzzy sets under equivalence fuzzy relations as [formula omitted]certainty and [formula omitted]possibility

In this paper, we deal with a finite collection of fuzzy sets that are used to represent a given linguistic variable in real-world problems. These fuzzy sets are usually represented as fuzzy singletons, fuzzy numbers, or fuzzy G-numbers. In many cases, there are significant interactions between elements of a given set, so it is useful to evaluate and rank elements while taking the degree of interactions into consideration. To find the degree of interaction, we develop a fuzzy equivalence relation based on a similarity function and a triangular norm operator. The compositions of the (max -(T-norm)) and (min -(S-norm)) cause the membership function to change from the minimum values (certainty version) to the maximum values (possibility version). These concepts are also useful for improving fuzzy data mining, rough fuzzy set theory, etc. Furthermore, two indices, α and β, are introduced to determine the degree of certainty (α-certainty) and degree of possibility (β-possibility). Examples are provided to compare the proposed method with the existing method. After comparing the experimental results, it can be concluded that the proposed approach is satisfactory for many situations. Finally, we apply the proposed methodology to evaluate the results of a hospital efficiency study conducted for the Office of Inspector General(OIG)-Eastern Virginia Department of Health and Human Services.

Preschool Teachers Teaching Quality Evaluation Based on Neural Network Algorithms

Based on the current teaching situation of preschool teachers, in order to comprehensively evaluate the effectiveness of early childhood teaching, research have constructed a teaching quality evaluation model using fuzzy synthesis method and expert method. This model can handle the fuzzy relationship between evaluation indicators and achieve the evaluation of teaching quality. Considering that the teaching evaluation is influenced by many factors, the Genetic Algorithm back propagation (GA-BP) neural network algorithm is chosen for the solution model construction of the preschool teacher teaching quality. The entropy method chosen for the data calculation is to complete the preschool teaching quality evaluation. In the mean square error test for solving the model, the improved GA-BP model converged after 40 iterations with the model convergence speed increased by 34.65%. In the evaluation and prediction of preschool teacher indicators, the improved GA-BP model accurately evaluated the teacher classroom teaching indicators. In sample 3, sample 6, and sample 9, the improved GA-BP model scored 91, 89, and 88 points, respectively, close to the true scoring results. The improved model’s accuracy was high as 90% in teacher skills, personality charm, and academic research evaluation. The improved model also effected better in the application of the preschool teaching quality evaluation. The application effect of this model in teaching effectiveness evaluation and teacher quality evaluation is good, providing valuable reference for the establishment of early childhood education evaluation system.

Constructing Symmetric Equality Algebras

In this paper, we introduce the notion of strong fuzzy filter on hyper equality algebras and investigate some equivalence definitions of it. Then by using this notion we constructed a symmetric equality algebra and define a special form of classes. By using these, we define the concept of a fuzzy hyper congruence relation on hyper equality algebra and we prove that the quotient is made by it is an equality algebra. Also, by using a fuzzy equivalence relation on hyper equality, we introduce a fuzzy hyper congruence relation and prove that this fuzzy hyper congruence is regular and finally we prove that the quotient structure that is made by it is a symmetric hyper equality algebra.

MCClusteringSM: An approach for the multicriteria clustering problem based on a credibility similarity measure

Multicriteria clustering problem has been studied and applied scarcely. When a multicriteria clustering problem is tackled with an outranking approach, it is necessary to include preferences of decision makers on the raw dataset, e.g., weights and thresholds of the evaluation criteria. Then, it is necessary to conduct a process to obtain a comprehensive model of preferences represented in a fuzzy or crisp outranking relation. Subsequently, the model can be exploited to derive a multicriteria clustering. This work presents an exhaustive search approach using a credibility similarity measure to exploit a fuzzy outranking relation to derive a multicriteria clustering. The work includes two experimental designs to evaluate the performance of the algorithm. Results show that the proposed method has good performance exploiting fuzzy outranking relations to create the clusterings.

Research on network-aware data fusion algorithm based on fuzzy time series

Abstract The traditional adaptive weighted fusion algorithm ignores the spatial correlation between the network sensing data and has high fusion bias, significantly reducing network data transmission quality. The network perception data fusion algorithm based on fuzzy time series is proposed, and the network perception data prediction algorithm based on fuzzy time series is used. The network data value is calculated using first and two-order fuzzy relations during the training stage, and the trend value of the network data is obtained. The trend value in the prediction stage dynamically obtains the network sense. Based on the relationship, the fuzzy relation of knowledge data is used to predict the network perception data for the next time series. The network sensing data fusion algorithm based on the confidence matrix is used to fuse the data by predicting the spatial correlation between the data and filtering the noise of the abnormal data to the fusion results. The proposed algorithm’s high fusion accuracy and improved quality of network data transmission are demonstrated by experimental results.

A Novel Approach to Roughness of Linear Diophantine Fuzzy Sets by Fuzzy Relations and its Application towards Multi-Criteria Group Decision-Making

A Novel Approach to Roughness of Linear Diophantine Fuzzy Sets by Fuzzy Relations and its Application towards Multi-Criteria Group Decision-Making

Deriving fuzzy topological relations from incomplete observations

Deriving fuzzy topological relations from incomplete observations

An assessment of fertilizer spraying drones based on hesitancy fuzzy similarity measures for sustainable green development

This research proposes a new similarity measure on hesitancy fuzzy graphs. The similarity measures are crucial concepts to explore the closeness between fuzzy graphs. The available imprecise and inconsistent data were more effectively handled by fuzzy similarity measures and intuitionistic fuzzy similarity measures. With time in decision-making theory, a complex frame of the background that occurs cannot be specified entirely by these fuzzy graphs but generalized fuzzy graphs like the hesitancy fuzzy graph can handle such a situation efficiently. The applicability of Hesitancy Fuzzy Graph (HFG) attracted the researchers to generalize ranking order based on the working procedures I, II of Xu’s approach and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) approach. For this purpose, we first define hesitancy fuzzy preference relations, Laplacian energy, and similarity measures in these HFG. The decision-making technique is then proposed in which a weighting technique is developed by building an optimal model based on the proposed Laplacian energy and similarity measure under a hesitancy fuzzy environment. This research studies the decision-making problem in which the preference information given by the experts takes the form of Hesitancy Fuzzy Preference Relations (HFPRs) and the information about experts’ weights are completely unknown. This research utilizes the hesitancy fuzzy weighted averaging operator to aggregate all individual HFPRs into a collective HFPR. Then, based on the degree of similarity between the individual HFPRs and the collective ones, we develop an approach to determine the experts’ weights. Moreover, based on HFPRs, in which the similarity measures between the collective preference relation and hesitancy fuzzy ideal solution are used to rank the given alternatives. We provide an illustrative numerical example to illustrate the mentioned approach and also we compare the aggregate results of the two techniques.

Weighted minimax programming subject to the max-min fuzzy relation inequalities

<abstract><p>Recently, max-min fuzzy relation inequalities (FRIs) have been used to model a (peer-to-peer) P2P network system. Any feasible scheme in the P2P network system is reflected by a solution of the max-min FRIs. One of the objectives of system managers is to decrease network congestion. To satisfy this objective, we attempt to minimize a weighted minimax function motivated by existing research. As a consequence, we establish a weighted minimax programming model in which the constraint is the max-min FRIs. Our goal in this work is to develop an effective algorithm to obtain the optimal solution of the optimization model. The so-called SCP-based algorithm is proposed to find the optimal solution. A numerical example shows the efficiency of our proposed SCP-based algorithm.</p></abstract>

Using the Degree r ∈ [0, 1] in Defining Rough Fuzzy Sets

This paper introduced a new definition of rough fuzzy sets based on a fuzzy ideal defined on a fuzzy approximation space (X, R). This definition considered the degree r ∈ [0, 1] in defining the after sets and the before sets of the arbitrary fuzzy relation R on the finite set of objects X. It is shown that this new type of roughness is a generalization to many of previous definitions in the fuzzy case and also in the ordinary case. As an application, it is given a rough fuzzy‐connected set notion depending on some degree r ∈ [0, 1].

Algebraic structures of q-rung orthopair fuzzy relations with applications in decision-making

Algebraic structures of q-rung orthopair fuzzy relations with applications in decision-making

Decision-making Model Construction of Enterprise Marketing Outlet Resource Allocation by Integrating Fuzzy Logic

Abstract In the tide of modern business competition, how to efficiently utilize limited resources to obtain the best economic benefits is the core issue that determines the survival and development of enterprises. This paper integrates fuzzy logic theory with resource allocation and proposes the direction of channel integration of marketing resources. The concept of affiliation degree is introduced in fuzzy logic to describe the relationship between things and form the fuzzy relationship in the fuzzy set, which indicates the degree of association between elements in the fuzzy set. The linguistic rule representation method is used to implement the control strategy for decision-making in enterprise marketing outlets. Improve the construction of the optimization model for enterprise outlets’ marketing resources by establishing a two-layer planning model. The research enterprise’s outlet marketing resources allocation situation is examined by combining actual and simulation, based on the principle of outlet marketing resources allocation. From the point of view of outlet affiliation, the central region with a “suitable” resource allocation level includes Hunan Province, with an affiliation degree of 0.4655, and the affiliation degrees of some western regions and northeastern regions range from 0.3896 to 0.5663. The fuzzy logic model generates six resource allocation strategies, and they are tested one by one using simulation experiments to determine the best allocation strategy.

The Promoting Role of Green Finance Reform and Innovation on the Sustainable Development of Low-Carbon Enterprises - An Analysis Based on Recursive Neural Networks

Abstract The government has introduced a series of green financial support policies to support the low-carbon technological innovation of enterprises, and it has become an inevitable trend to take the road of high-quality development with clean, low-carbon efficiency and safety. In this paper, in order to further realize the quantitative analysis of green financial reform on the sustainable development of low-carbon enterprises, based on the principles of the evaluation index system construction on the sustainable development of low-carbon enterprises evaluation index system design, to determine the evaluation index level thesis domain, its data dimensionless processing, so that its evaluation indexes are composed of fuzzy relationship matrix. With the help of a recursive neural network, we analyze the low-carbon sustainable development of enterprises in the context of green financial reform. It is found that the squared error of the mean value of the enterprise low carbon sustainable development ability index based on a recursive neural network is 0.044. During the implementation of the green financial reform policy, the low carbon sustainable development ability of the sample enterprises has been improved, among which the growth trend of enterprise D (0.50415-0.44039=0.06376) is more rapid, which strongly confirms that the green financial reform and innovation promote the sustainable development of the low carbon enterprises. The promotion of green financial reform and innovation has been confirmed to have a strong effect on the sustainable development of low-carbon enterprises.

The Study of Max-Min Composition in Fuzzy Relation

One of the foundational concepts in both pure and applied mathematics is the notion of relations. Fuzzy relations extend this concept much like fuzzy sets generalize the fundamental idea of sets. This study provides a comprehensive overview of operations, compositions, and the various types inherent in fuzzy relations.

Non-uniform allocation of information granularity to improve consistency and consensus in multi-criteria group decision-making: Application to building refurbishment

If a decision depends on the views of a group of people, it is crucial that these views are consistent, in particular if they are represented in terms of fuzzy preference relations. Moreover, before making the decision, the agreement achieved must be as high as possible. In most cases, to achieve it, the initial viewpoint of each group member must be modified during the decision-making process, which causes an information loss. To handle this issue, some conditions have been added to the modification process. Concretely, some approaches have turned to an allocation of information granularity to control it. However, these approaches either allocate the information granularity in a uniform way or not consider the issues of consistency and consensus in a scenario of multi-criteria group decision-making. To enhance these approaches, we elaborate a novel granular-based approach composed of two processes. Firstly, an automatic process based upon a non-uniform allocation of information granularity is developed to maximize both the consensus and the consistency in multi-criteria group decision-making where fuzzy preference relations are used to model the group members’ views. Based upon it, secondly, an interactive process requiring the implication of the group members is introduced, which also intends to maximize both the consensus and the consistency. Some experimental studies are completed to show the essence of this new approach and to demonstrate its performance and flexibility. A case study on building refurbishment is also conducted to validate its effectiveness and feasibility in practical real-world problem-solving.

Noise-aware and correlation analysis-based for fuzzy-rough feature selection

Feature selection has gained significant attention, with a focus on removing redundant or irrelevant features to improve subsequent machine learning tasks. The fuzzy rough set is extensively utilized for feature selection because of its ability to manage uncertainty. The fuzzy dependency-based approach represents an effective branch within the domain of fuzzy rough set models. However, it has been revealed that fuzzy dependency function is not robust to noise data while the noise objects often occur. Furthermore, as the size of dataset increases, the computational complexity of evaluating metrics also tends to increase due to potentially unnecessary computational effort. Hence, to address both of these research issues simultaneously, we propose a fuzzy rough correlation-based feature selection algorithm, denoted as FRCB. The introduction of neighborhood radius constraints and granularity conditions aims to interpret and mitigate the impact of noisy data by partitioning objects into a Core-Boundary-Outlier structure. A more robust hybrid fuzzy relation and correlation-based fuzzy rough dependency is proposed by considering the representativeness and attractiveness of the core to other objects within the internal class, as well as the impacts on other objects in external classes. To minimize processing overhead and time complexity, redundant features are identified through correlation analysis, which involves evaluating, ranking, and grouping before proceeding to the next iteration. The experiments were conducted using eleven datasets. The analysis of the noise curves and the raw data curve indicates that the proposed correlation-based fuzzy rough dependency is more robust than other benchmarking methods. Moreover, the results of the classification and running time comparisons indicate that the FRCB algorithm proposed in this study exhibits superior performance compared to the baseline methods.

Selection of technological and organizational solutions for construction works with the use of a fuzzy relation of preferences

Selection of technological and organizational solutions for construction works with the use of a fuzzy relation of preferences

Depth-Bounded Fuzzy Bisimulation for Fuzzy Modal Logic

We introduce depth-bounded fuzzy bisimulation between fuzzy Kripke models. Roughly speaking, a depth-bounded fuzzy bisimulation is a decreasing sequence of fuzzy binary relations whose infimum is a fuzzy bisimulation. We provide logical characterizations of depth-bounded fuzzy bisimulations between fuzzy Kripke models w.r.t. a fuzzy multimodal logic over complete residuated lattices, including fuzzy invariance of formulas of with a modal depth bounded by under the th component of a depth-bounded fuzzy bisimulation, as well as the Hennessy-Milner property of depth-bounded fuzzy bisimulations. We also provide a polynomial-time algorithm for computing the th component of the greatest depth-bounded fuzzy bisimulation between two finite fuzzy Kripke models when the underlying complete residuated lattice is linear.