Fuzzy Representation Research Articles

Three-way decision-based Takagi–Sugeno–Kang fuzzy classifier for partially labeled data

The salient features of Takagi–Sugeno–Kang (TSK) fuzzy classifiers are their superior nonlinear fitting capability and better interpretability, rendering them widely applicable in the domains of data mining and machine learning. However, using TSK fuzzy classifiers for partially labeled data has received little attention. Based on the three-way decision (TWD) theory, this study proposed a TSK fuzzy model to learn from partially labeled data. First, an adaptive sample weight strategy is introduced for the fuzzy partition of the antecedent part and the cross-entropy loss of the consequent part, respectively. Subsequently, a prototype-based firing strength loss mechanism is proposed to constrain the optimization of the model in the fuzzy representation space. It employs a TWD strategy based on the entropy criterion to classify samples as useful, useless, and uncertain, where the proposed model enhances the performance by iteratively utilizing a certain number of useful pseudo-labeled samples. Finally, the validity of the model is theoretically analyzed based on the principle of noise learning. The experimental results on UCI datasets demonstrate that the proposed model exhibits superior performance compared with classical semi-supervised methods, even attaining a performance comparable to that of the model trained on all data with ground-truth labels.

Sample-efficient reinforcement learning with knowledge-embedded hybrid model for optimal control of mining industry

The froth flotation process is a cost-effective and widely employed method for mineral separation. A core challenge is to maximize mineral recovery while maintaining a specified minimum concentrate grade. This requires precise control of aeration and slurry level and overcoming disturbances. The rapid advancements in reinforcement learning present a promising approach for controlling froth flotation. However, reinforcement learning suffers from sample inefficiency, which significantly hampers its application to real-world problems. In this research, we proposed an innovative sample-efficient model-based reinforcement learning algorithm to enhance flotation performance by directly leveraging the dynamics of the slurry phase. Our proposed algorithm involves the construction of a hybrid model, comprising a physical model and a data residual model, which effectively learns the underlying dynamics of the flotation process during the interaction between the reinforcement learning agent and process. The physical model integrates domain knowledge into the hybrid model to expedite the training process and enhance the interpretability and generalizability of the hybrid model. To capture uncertainty and address unmodeled aspects of the physical model, we employ an ensemble data residual model. Actor and critic are augmented with fuzzy representation modules based on fuzzy logic inference to improve the learning capacity of the networks and the multi-head critic is applied to reduce overestimation biases and enhance training stability. Case studies demonstrate that, compared to the baseline algorithm, our proposed algorithm requires merely 86.8% of the samples employed by conventional model-based reinforcement learning algorithm and improves the long-term return by at least 12.0%, underscoring the role of domain knowledge in facilitating efficient reinforcement learning.

A Confidence and Conflict-Based Consensus Reaching Process for Large-Scale Group Decision-Making Problems With Intuitionistic Fuzzy Representations

A Confidence and Conflict-Based Consensus Reaching Process for Large-Scale Group Decision-Making Problems With Intuitionistic Fuzzy Representations

About defuzzification methods influence on fuzzy traveling salesman problem’s solving

The article investigates the approach to using fuzzy numbers and the method of dynamic programming to find solutions to the traveling salesman problem, considering the fuzzy representation of time in real travel conditions. This allows for formulating a fuzzy optimization problem to find the best value of the objective function, which is determined by the amount of time required to travel between cities. The traveling salesman problem (TSP) is a classic problem of combinatorial optimization, which involves finding the shortest or fastest route among a set of cities. Fuzzy numbers are used to formalize the uncertainty and imprecision of input data, associated with the subjectivity in estimates of the duration of necessary travel intervals. For operating with fuzzy numbers, their transformation into a special form is proposed, and the formalization of the obtained fuzzy results into a crisp representation is carried out based on the center of gravity (CoG) method. A comparison of the results obtained based on solving the deterministic traveling salesman problem using defuzzified time distances and the defuzzification of the solution to the fuzzy traveling salesman problem was conducted. The results confirmed the dependency of the solution on the method of defuzzification. A program was developed that was used to compare the results of the traveling salesman problem using crisp and fuzzy numbers based on the dynamic method. A conclusion is drawn, indicating that the use of trapezoidal fuzzy numbers with the dynamic programming method leads to improved results of the problem compared to using crisp numbers based on the defuzzification of fuzzy distances. Methods of implementation and problematic areas of application of the computation results are presented and analyzed, demonstrating the constructiveness of the proposed approach for studying real processes.

A Systematic Overview of Fuzzy Extended Entity Relationship (Fuzzy EER) Model Using Practical Examples

Most real-world data are vague and imprecise, so traditional relational databases cannot represent, integrate, and manage them effectively. In this research, we gave an overview of the application of fuzzy logic to the conceptual modeling facet of database design, which is an enhancement of the Extended Entity Relationship (EER) model. This is done to give a clearer picture of how imprecise and vague data are represented and managed, especially in multiple-criteria decision-making database systems. To achieve this, an overview of fuzzy attributes, fuzzy values in the attributes, notation for fuzzy representations, fuzzy degree in each value of an attribute, fuzzy degree in a set of values of different attributes, fuzzy degree with its own meaning and fuzzy degree to the model was carried out with practical examples.

Fuzzy Representation Learning on Dynamic Graphs

Fuzzy Representation Learning on Dynamic Graphs

$\mathbb{T}-$Relative Fuzzy Linear Programming for $\mathbb{T}-$Relative Fuzzy Target Coverage Problems

Optimal set covering problems are commonplace in communication, remote sensing, logistics, image processing, and network fields [3]. Thus, studies on determining optimal covering sets (sensors) of points (targets) in a region have emerged recently. One characteristic of these studies is the consideration of cases where a target is considered fully covered when it falls within a coverage area ("Boolean" coverage). Consequently, optimality solutions/methods/algorithms founded on this coverage scheme are usually too restrictive and (or) precise and so are not suitable for many complex and real life situations, which are most times plagued with ambiguity, vagueness, imprecision and approximate membership of points and (or) covering sets. Fuzzy structures have proven to be suitable for the representation and analysis of such complex systems with many successful applications. Although fuzzy sets generalizes a set, a more recent generalization for both and its related concepts is the Relative fuzzy set [1] which gives a dynamic fuzzy representation to sets. $\mathbb{T}-$Relative Fuzzy fixed points results of $\mathbb{T}-$Relative fuzzy maps were studied in [5] and recently, the concept of $\mathbb{T}-$Relative fuzzy linear programming [6] was introduced as a generalization of fuzzy linear programming. The results were applied to generalize the Boolean set based covering problems in literature to a $\mathbb{T}-$Relative fuzzy Boolean coverage one. Although, Shan et al. in [15] and others [16] - [21] have given a probabilistic coverage consideration but this lacks subjectivity in representing vagueness and imprecision inherent in most systems. In this present article the Linear Programming (LP) formulation of “A Computational Physics-based Algorithm for Target Coverage Problems" by Jordan Barry and Christopher Thron is generalized by considering a fuzzy and relative fuzzy target coverage instead of the crisp set Boolean coverage. Also we introduce the Fuzzy Linear Programming (FLP) and the $\mathbb{T}-$Relative Fuzzy Linear Programming (RFLP) for the set coverage problem which allows for ascertaining dynamic optimality with aspiration levels.

A study on fuzzy representations and algebraic structures

A study on fuzzy representations and algebraic structures

Probabilistic Intersection-Over-Union for Training and Evaluation of Oriented Object Detectors.

Oriented object detection is a challenging and relatively new problem. Most existing approaches are based on deep learning and explore Oriented Bounding Boxes (OBBs) to represent the objects. They are typically based on adaptations of traditional detectors that work with Horizontal Bounding Boxes (HBBs), which have been exploring IoU-like loss functions to regress the HBBs. However, extending this idea for OBBs is challenging due to complex formulations or requirement for customized backpropagation implementations. Furthermore, using OBBs presents limitations for irregular or roughly circular objects, since the definition of the ideal OBB is an ambiguous and ill-posed problem. In this work, we jointly tackle the problem of training, representing, and evaluating oriented detectors. We explore Gaussian distributions-called Gaussian Bounding Boxes (GBBs)-as fuzzy representations for oriented objects and propose using a similarity metric between two GBBs based on the Hellinger distance. We show that this metric leads to a differentiable closed-form expression that can be directly used as a localization loss term to train OBB object detectors. We also show that GBBs present a natural representation as elliptical regions (called EBBs), which inherently mitigate ambiguity representation for circular objects. Finally, we empirically show that the proposed similarity metric computed between two GBBs strongly correlates with the IoU between the corresponding EBBs, motivating the name Probabilistic Intersection-over-Union (ProbIoU). Our experiments show that results using ProbIoU as a regression loss are competitive with state-of-the-art alternatives without requiring additional hyperparameters or customized implementations, and that ProbIoU is a promising alternative to evaluate oriented object detectors. Our code is available at https://github.com/ProbIOU/.

Stochastic EV Charging Dispatch in Unbalanced Three-phase Networks Based on Interpretable Fuzzy Representation of User Preferences

Stochastic EV Charging Dispatch in Unbalanced Three-phase Networks Based on Interpretable Fuzzy Representation of User Preferences

Personalized fuzzy semantic model of PHFLTS: Application to linguistic group decision making

The proportional hesitant fuzzy linguistic term set (PHFLTS) has been effectively employed in analyzing the group’s hesitancy in linguistic group decision making (LGDM). The application of PHFLTS assists in capturing the individual’s hesitancy across diverse time periods. It is acknowledged that a single word could potentially convey various meanings to different decision makers, such differences can be proficiently managed by utilizing personalized individual semantic (PIS) models. Previous approaches for calculating PIS failed to incorporate the individual’s updating preference information over time, which increases the risk that the computation of PIS is affected by random factors in a specific moment. In our current research, individual linguistic preference gathered over a time period are leveraged to form the PHFLTS. Additionally, a consistency driven optimization model based on PHFLTS is formulated to obtain PIS of linguistic terms. Subsequently, a fuzzy representation model termed as the fuzzy envelope of PHFLTS is introduced to facilitate the computation with words processes, integrating PHFLTS in LGDM. The practicality and legitimacy of these proposed models are evaluated through a comparative analysis. Lastly, these proposed models are tested and applied in a dedicated case study to further prove their usefulness and efficacy.

A comparative study on precision of pairwise comparison matrices

Pairwise comparisons have been a long-standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision-making methods such as the Analytic Hierarchy/Network Process (AHP/ANP), the Best-Worst method (BWM), PROMETHEE and many others. Pairwise comparisons can be performed within several frameworks such as multiplicative, additive and fuzzy representations of preferences, which are particular instances of a more general framework based on Abelian linearly ordered groups. Though multiplicative, additive and fuzzy representations of preferences are widely used in practice, it is unknown whether decision makers are equally precise in the three aforementioned representations when they measure objective data. Therefore, the aim of this paper is to design, carry out and analyse an experiment with over 200 respondents (undergraduate university students) from two countries, Czechia and Italy, to compare precision of the respondents in all three representations. In the experiment, respondents pairwise compared (by approximation) the areas of four geometric figures and then, the imprecision of their assessments was measured by computing the distance with the exact pairwise comparisons. We grouped the respondents in such a way that each participant was allowed to deal with a unique type of representation. The outcomes of the experiment indicate that the multiplicative approach is the most precise.

Interval Type-2 Fuzzy Relation Matrix Model via Semitensor Product

A new modeling idea of interval type-2 fuzzy logic system (IT2 FLS) is proposed on the basis of matrix semi-tensor product (STP) fuzzy representation technique, to construct an interval type-2 fuzzy relationship matrix (IT2 FRM) model. The model naturally inherits the advantages of STP theory, which enables the fuzzy logic reasoning process to be translated into algebraic form for computation. In most cases, the fuzzy rules in the IT2 FRM are generally unknown. To address the above situation, the parameters of this model can be trained with observed data pairs. Firstly, the fuzzy rules are generated by the space division method, and the initial parameters of the model are determined. Secondly, the parameters in the model are trained using the steepest descent algorithm. Finally, the IT2 FRM model is validated by simulation, and the results demonstrate that the IT2 FLS can be designed using the STP method.

Fuzzy Representation Learning on Graph

Recent years have witnessed a drastic surge in graph representation learning, which usually produces low-dimensional and crisp representations from graph topology and high-dimensional node attributes. Nevertheless, a crisp representation of a node or graph actually conceals the uncertainty and interpretability of features. In citation networks, for example, the reference between two papers is always involved with fuzziness denoting the correlation degrees, that is, one connection may simultaneously belong to strong and weak references in different beliefs. The uncertainty in node connections and attributes inspires us to delve into fuzzy representations. This paper, for the first time, proposes an unsupervised fuzzy representation learning model for graphs and networks to improve their expressiveness by making crisp representations fuzzy. Specifically, we develop a fuzzy graph convolution neural network (FGCNN), which could aggregate high-level fuzzy features, leveraging fuzzy logic to fully excavate feature-level uncertainties, and finally generate fuzzy representations. The corresponding hierarchical model composed of multiple FGCNNs, called deep fuzzy graph convolution neural network (DFGCNN), is able to generate fuzzy node representations which are more expressive than crisp ones. Experimental results of multiple network analysis tasks validate that the proposed fuzzy representation models have strong competitiveness against the state-of-the-art baselines over several real-world datasets.

Promoting Green Supply Chain Management With Optimal Selection Of Packaging Materials Using Integrated Fuzzy MCDM and Rl Model

Green supply chain management is highly significant to maintain environmental sustainability. The agglomeration of green components enhances and supports the business activities to practice green supply chain more effectively. Utilizing sustainable packaging materials in logistics is a step towards promoting business eco sustainability. This research work attempts to develop a hybrid decision making model by integrating techniques of fuzzy multi criteria decision making (MCDM) and Reinforcement Learning (RL). This research work proposes a decision-making method of IDOCRIW (Integrated Determination of Objective Criteria Weights) under fuzzy environment with linguistic representations to determine the criterion weights of material selection and applies the RL method of Q learning in ranking the packaging materials for promoting green sustainability. The proposed fuzzy based MCDM method resolves the problems of conflict of uncertainty. The ranking results obtained using this method are compared with the non-integrated MCDM method. The proposed combined model shall be discussed under various other extended fuzzy representations. The decision-making problem on optimal selection of packaging materials addressed in this research work benefits the business decision makers to make right choices. This hybrid model will certainly make the logistic environment more robust and also it will upscale the smart framework of supply chain management.

A novel interval valued circular intuitionistic fuzzy AHP methodology: Application in digital transformation project selection

Since its first introduction, ordinary fuzzy sets have been extended to new types of fuzzy sets as a tool of artificial intelligence techniques. One of the recently introduced fuzzy sets, “Circular Intuitionistic Fuzzy (CIF)” sets enable us to take into account instability of the membership and non-membership degrees with a circular area & its radius. In this study, we first introduce Interval Valued CIF (IVCIF) sets and their arithmetic operations to better incorporate the uncertainty and cover a broader domain. Then, we introduce a novel IVCIF Analytic Hierarchy Process (AHP) method and apply it to evaluate Digital Transformation (DT) projects with complex nature. DT projects requiring fundamental changes in processes, business models and cultures of the companies, contribute a significant value to the companies and increase their market shares; so that they can achieve long term success and competitive advantage. On the other hand, DT problems which are usually ill-defined and include incomplete information based on human judgments, necessitate fuzzy representation. For the success of a digital transformation and to contribute excellence in engineering applications, DT projects should be carefully analyzed. For these reasons, we focus on DT project evaluation problem in application. Also, sensitivity & comparative analyses are performed.

Fuzzy Taxonomy Based Optimal Decision Making on Construction Materials

Decision making on material selection is quite an inevitable task in the construction industry. This research work discusses the taxonomy method of decision making under a fuzzy environment. A decision-making model is developed to make optimal selection of construction materials based on five core criteria. The representations using fuzzy facilitates flexible decision making in material selection-based problems. A decision matrix with linguistic values representing the criterion satisfaction of the alternatives is subjected to the proposed method of fuzzy taxonomy to derive the optimal ranking results of the construction materials that are considered as the alternatives. The consistency of the ranking results using fuzzy taxonomy is found to be more consistent when compared with other fuzzy based decision-making methods. The efficiency of fuzzy representations is more promising and this will definitely support the decision makers to endure the hurdles and commotions in material selection.

De-identified Bayesian personal identity matching for privacy-preserving record linkage despite errors: development and validation

BackgroundEpidemiological research may require linkage of information from multiple organizations. This can bring two problems: (1) the information governance desirability of linkage without sharing direct identifiers, and (2) a requirement to link databases without a common person-unique identifier.MethodsWe develop a Bayesian matching technique to solve both. We provide an open-source software implementation capable of de-identified probabilistic matching despite discrepancies, via fuzzy representations and complete mismatches, plus de-identified deterministic matching if required. We validate the technique by testing linkage between multiple medical records systems in a UK National Health Service Trust, examining the effects of decision thresholds on linkage accuracy. We report demographic factors associated with correct linkage.ResultsThe system supports dates of birth (DOBs), forenames, surnames, three-state gender, and UK postcodes. Fuzzy representations are supported for all except gender, and there is support for additional transformations, such as accent misrepresentation, variation for multi-part surnames, and name re-ordering. Calculated log odds predicted a proband’s presence in the sample database with an area under the receiver operating curve of 0.997–0.999 for non-self database comparisons. Log odds were converted to a decision via a consideration threshold θ and a leader advantage threshold δ. Defaults were chosen to penalize misidentification 20-fold versus linkage failure. By default, complete DOB mismatches were disallowed for computational efficiency. At these settings, for non-self database comparisons, the mean probability of a proband being correctly declared to be in the sample was 0.965 (range 0.931–0.994), and the misidentification rate was 0.00249 (range 0.00123–0.00429). Correct linkage was positively associated with male gender, Black or mixed ethnicity, and the presence of diagnostic codes for severe mental illnesses or other mental disorders, and negatively associated with birth year, unknown ethnicity, residential area deprivation, and presence of a pseudopostcode (e.g. indicating homelessness). Accuracy rates would be improved further if person-unique identifiers were also used, as supported by the software. Our two largest databases were linked in 44 min via an interpreted programming language.ConclusionsFully de-identified matching with high accuracy is feasible without a person-unique identifier and appropriate software is freely available.

Fuzzy encoding and decoding approaches for 2-TCLE and their applications in multi-criteria decision making

In order to incorporate linguistic information into decision making, it is necessary to apply computing with words (CW) techniques. Traditional CW models use only single and simple linguistic terms to represent both input and output, which limits the flexibility in information processing. Recent researches on computing with comparative linguistic expression, including extension models, has partially overcome this limitation. Nonetheless, the flexibility of linguistic information expression remains limited due to the discrete distributions of primary terms. A complete CW framework should include both encoding and decoding technologies for linguistic information, but previous researches have primarily focused on fuzzy encoding approaches, while ignoring fuzzy decoding techniques for linguistic expressions. To improve the accuracy and interpretability of CW in dealing with linguistic expressions, this research proposes a novel model called 2-tuple comparative linguistic expression (2-TCLE). To establish a framework for studying fuzzy representations of linguistic expressions, both fuzzy encoding and decoding approaches for 2-TCLE will be presented in a systematic manner that are performed to match each other. A novel linguistic computational model for dealing with 2-TCLE is presented and then applied to solve a multi-criteria group decision making case study.

Centroid for Solving Bi-Level Linear Fractional Programming Problems with Fuzzy Interval Coefficients by Utilizing MO-Technique

This paper presents an efficient and straightforward methodology with less computational complexities to title the bi-level objective linear fractional programming problem with fuzzy interval coefficients (BILOLFPP with FIC). To construct the methodology, the concept of mean technique is utilized to tackle the fuzzy numbers in addition to adding to α = [mean (ai) , mean (bi)] , i = 1, …, n, then. Accordingly, the fuzzy programming issue is converted into a single objective linear fractional programming problem (SOLFPP with FIC) by the utilize of weight function. The fuzzy technique has significant structural transform metamorphosis during the recent decades. Numerous to mention introduced have been undertaken to explanation fuzzy methodology for linear, non-linear programming issues. While, the previous finding that introduced have been conflicting, recent studies of competitive situations indicate that LFPP with fuzzy interval coefficients (LFPP with FIC) has an advantageous effect mostly on comparison situation. One of the suggestions which we found is interval approximations, closed interval approximation of sequential fuzzy number for resolving fuzzy number LFPP without changing it to a crisp issue. A new variant of modified simplex methodology is studied here just for resolving fuzzy number LFPP utilizing fuzzy arithmetic. Consequently, fuzzy representation of some important theories of fuzzy LFPP has been reproved. A fuzzy LFPP with FIC is worked out as numerical examples illustrate to the suggested methodology. On iterative processes, it decreases the overall processing time to explain, the modified simplex methodology for solving BILLFPP with FIC with out to crisp by taking numerical examples and compare with Nasseri, Verdegay and Mahmoudi methodology changing it to a crisp issue [9].