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The assignment problem is a famous problem in combinatorial optimization where several objects (tasks) are assigned to different entities (workers) with the goal of minimizing the total assignment cost. In real life, this problem often arises in many practical applications with uncertain data. Hence, this data (the assignment cost) is usually presented as fuzzy numbers. In this paper, the assignment problem is considered with trapezoidal fuzzy parameters and solved using the novel Dhouib-Matrix-AP1 (DM-AP1) heuristic. In fact, this research work presents the first application of the DM-AP1 heuristic to the fuzzy assignment problem, and a step-by-step application of DM-AP1 is detailed for more clarity. DM-AP1 is composed of three simple steps and repeated only once in n iterations. Moreover, DM-AP1 is enhanced with two techniques: a ranking function to order the trapezoidal fuzzy numbers and the min descriptive statistical metric to navigate through the research space. DM-AP1 is developed under the Python programming language and generates a convivial assignment network diagram plan.

Spreadsheet-based tools provide a simple yet effective way of calculating values, which makes them the number-one choice for building and formalizing simple models for budget planning and many other applications.A cell in a spreadsheet holds one specific value and gives a discrete, overprecise view of the underlying model. Therefore, spreadsheets are of limited use when investigating the immanent uncertainties of such models and answering what-if questions. Existing extensions typically require a complex modeling process that cannot be smoothly embedded in a tabular layout.In Fuzzy Spreadsheet, a cell can hold and display the distribution of values. This integrated uncertainty handling immediately conveys sensitivity and robustness information. The fuzzification of the cells enables calculations not only with precise values but with distributions, and probabilities. We conservatively added and carefully crafted visuals to maintain the look and feel of a traditional spreadsheet while facilitating what-if analyses.Given a user-specified reference cell, Fuzzy Spreadsheet automatically extracts and visualizes contextually relevant information, such as impact, uncertainty, and degree of neighborhood, for the selected and related cells.To evaluate its usability and the perceived mental effort required, we conducted a user study.The results show that our approach outperforms traditional spreadsheets in terms of answer correctness, response time, and perceived mental effort for almost all tasks tested.

The Picture Fuzzy Set (PFS) is a broadening of the fuzzy set and intuitionistic fuzzy set. Pattern recognition, picture segmentation, and decision-making are some of the applications of PFS. The dissimilarity measure technique is used to illustrate a decision-making issue on an image fuzzy set in this article. Decision-making is a technique that enables a computer to think like a person, and it is critical for machine learning and the application of artificial intelligence to machines. These aids robots in thinking like humans. Finally, the suggested approach is presented in this article using a case study based on a survey of 100 consumers performed at a two-wheeler showroom.

In recent years, Botnet has become one of the most dreadful type of malicious entity. Because of the hidden and carrying capacity of Botnet, the detection task has become a real challenge. Different methodologies have been applied for finding the source of Botnet at an early stage. Machine Learning and Deep Learning have greatly impacted these Botnet detection methodologies. But still, it is a difficult task because of the lesser number of features available in the Botnet datasets. In this paper, we have proposed a Fuzzy Logic based feature engineering method. The proposed method first identifies the fuzzy elements in the dataset and then generates fuzzy sets. The features generated using this method is used by an Artificial Neural Network for classification of Botnet. To train and evaluate the ANN model, we have used the CTU-13 dataset. The proposed feature engineering method and Botnet classification method has performed well with an accuracy of 99.94%. Still this method needs to be tested on different datasets. In future, new fuzzy rules can also be made to generate a new set of features as well as these rules can be used to generate features from other datasets.

We consider calculation of the mode of compositional data, the data related to each other through a linear constraint. Compositional data arises in various extensions of the fuzzy sets theory (type-2 interval-valued, intuitionistic, hesitant fuzzy sets), biomedicine (relative abundance, genome sequencing, activity recognition), and data analytics (various wealth indices, interval-valued observations, traffic congestion, etc.). Mode is a pre-aggregation function in the case of single variable, used as a classical estimator robust to outliers, but its multivariate extensions face the challenges of high computational complexity and potential oversmoothing. In this work we present several novel techniques for mode estimation on the unit k-simplex representing compositional, interval-valued, and general vector-valued data. We highlight the re-weighted k-nearest neighbours algorithm based on the Choquet integral with respect to a 2-additive fuzzy measure, compare its performance against other approaches based on spatial partitioning, and illustrate its applications to aggregation of real-world interval-valued data sets.

Three-way decision is consistent with human cognitive processes and applied to different information systems. However, since the real world is more imprecision, hesitation and ambiguity, experts can select interval fuzzy information to represent their evaluations. In the evaluation process, experts sometimes may not guarantee the interval fuzzy information satisfy the constraint between membership and non-membership and further impact make decisions. Interval-valued q-rung Orthopair fuzzy set (IVq-ROFS) are proposed to improve the fault-tolerant ability and ensure the experts' evaluation make sense. In this case, this paper generalizes IVq-ROFS to three-way decision, which consists of the construction of three-way decision and the aggregation of interval continuity of IVq-ROFS. For considering the aggregation of interval continuity of IVq-ROFS, we firstly investigate the IVq-ROFS integral to aggregate continuous IVq-ROFSs by developing simplified interval-valued q-rung Orthopair fuzzy set (SIVq-ROFS). Particularly, in order to obtain integrable region, we design $\varepsilon$ -amendment to amend integral region of IVq-ROFS for removing unmeaning point in advance. To simplify the calculation, we further utilize Taylor series of the integral function to replace the complicated integral function. Secondly, a new equivalence class method is constructed to support three-way decision. Thirdly, with the aid of the integral of IVq-ROFS and equivalence class method, we availably fuse the loss functions of the equivalence class and obtain the classifying rules of three-way decision by comparing the expected losses. Finally, we elaborate three-way decision by using a case of medical diagnosis about nephropathy and prove the validity of the investigated model.

Although there have been many fuzzy or probabilistic relational database models proposed for representing and handling imprecise and uncertain information of objects in real-world applications, models combining the relevance and strength of both fuzzy set theory and probability theory appear sporadic. In this paper, we propose a new fuzzy and probabilistic relational database model where the imprecision of an attribute value is represented by a fuzzy set and the uncertainty of a relational tuple is represented by a probability interval. The mass assignment theory is employed to deal with the challenge of integration and computation of both fuzzy sets and probabilities in the same model. The conjunction and disjunction strategies to combine imprecise and uncertain information are introduced. Then the fundamental concepts of the classical relational database model are extended and generalized in this new model. The syntax and semantics of the selection operation are formally defined. Finally, the other important algebraic operations on imprecise attributes and uncertain tuples are developed.

The aim of this paper is to extend closure systems from being crisp sets with certain fuzzy properties to proper fuzzy sets. The presentation of the paper shows a thorough discussion on the different alternatives that could be taken to define the desired fuzzy closure systems. These plausible alternatives are discarded if they are proven impossible to be in a bijective correspondence with closure operators. Finally, a definition of fuzzy closure system is established and a one-to-one relation with closure operators is proved. The aim of this paper is to extend closure systems from being crisp sets with certain fuzzy properties to proper fuzzy sets. The presentation of the paper shows a thorough discussion on the different alternatives that could be taken to define the desired fuzzy closure systems. These plausible alternatives are discarded if they are proven impossible to be in a bijective correspondence with closure operators. Finally, a definition of fuzzy closure system is established and a one-to-one relation with closure operators is proved. Funding for open access charge: Universidad de Málaga / CBUA

Faced with any decision-making problems with fuzzy multi-criteria information, decision-makers generally set a minimum requirement on each criterion for satisfying their own preferences, thereby forming a fuzzy set on the criterion universe, which is called the criterion fuzzy set. From the perspective of realistic decision, the final decision of all alternatives should be determined according to this criterion fuzzy set. In view of this, this paper proposes the criterion-oriented three-way ranking and clustering strategies, which can solve the qualitative clustering and ranking problems of all alternatives from the perspective of criterion fuzzy sets. Firstly, we define a criterion fuzzy set as a criterion-oriented fuzzy concept and propose a criterionoriented relative risk loss model and discuss related properties accordingly. Meanwhile, we use the generalized fuzzy rough lower (upper) approximation to estimate the absolute (relative) conditional probability between the binary fuzzy class of the alternative and the criterion-oriented fuzzy concept. Then, a criterion-oriented absolute (relative) three-way clustering strategy is proposed, which can perform qualitative analysis on all alternatives. Furthermore, based on the three-way semantics and global cost function, we recommend a criterion-oriented absolute (relative) three-way ranking strategy, which can rank all alternatives. Finally, through numerical example, comparative analysis and sensitivity analysis, we test the feasibility and effectiveness of the proposed criterion-oriented three-way ranking and clustering strategies.

Statistical depth functions provide a way to order the elements of a space by their centrality in a probability distribution. That has been very successful for generalizing non-parametric order-based statistical procedures from univariate to multivariate and (more recently) to functional spaces. We introduce two general definitions of statistical depth which are adapted to fuzzy data. For that purpose, two concepts of symmetric fuzzy random variables are introduced and studied. Furthermore, a generalization of Tukey's halfspace depth to the fuzzy setting is presented and proved to satisfy the above notions, through a detailed study of its properties. A. Nieto-Reyes and L. Gonzalez are supported by the Spanish Ministerio de Economía, Industria y Competitividad grant MTM2017-86061-C2-2-P. P. Terán is supported by the Ministerio de Economía y Competitividad grant MTM2015-63971-P, the Ministerio de Ciencia, Innovación y Universidades grant PID2019-104486GB-I00 and the Consejería de Empleo, Industria y Turismo del Principado de Asturias grant GRUPIN-IDI2018-000132.

Quantum computation is going to revolutionize the world of computing by enabling the design of massive parallel algorithms that solve hard problems in an efficient way, thanks to the exploitation of quantum mechanics effects, such as superposition, entanglement and interference. These computational improvements could strongly influence the way how fuzzy systems are designed and used in contexts, such as big data, where computational efficiency represents a non-negligible constraint to be taken into account. In order to pave the way towards this innovative scenario, this paper introduces a novel representation of fuzzy sets and operators based on Quadratic Unconstrained Binary Optimization (QUBO) problems, so as to enable the implementation of fuzzy inference engines on a type of quantum computers known as quantum annealers.

A fuzzy interval is a fuzzy set in R such that its α-level sets are bounded closed intervals in R . The purpose of this article is to generate fuzzy intervals using gradual intervals and gradual numbers by following the mathematical expression in decomposition theorem. On the other hand, the concepts of elements and subsets of fuzzy intervals are proposed on the basis of the concept of gradual numbers. Each gradual number can induce a corresponding fuzzy set in R . We also compare the fuzziness between the generated fuzzy interval and the fuzzy set generated by the corresponding gradual number.

Federated learning addresses the issue of machine learning realized under constraints of privacy and security. While there have been intensive studies on building and analyzing federated regression models, this topic has not been analyzed so far in the area of fuzzy systems. To narrow down this gap, in this study, we formulate and solve a problem of unsupervised federated learning by designing an original federated FCM (F-FCM) clustering which could serve as a basis towards building a spectrum of fuzzy set constructs including rule-based models. Following a general client-server structure where the local data residing with each client are not available globally and cannot be centralized (as commonly encountered in learning scenarios), the aim is to discover an overall structure across all data. The federated gradient-based optimization realized in the horizontal mode is developed. An overall learning process is derived, which is composed of communicating gradients coming from clients and providing updates of the prototypes at the server side and passing them on to the clients. It is also shown that the relevance of the globally constructed structure is conveniently assessed in terms of granular footprints of the prototypes constructed by the F-FCM. Some illustrative examples are covered to illustrate the efficiency of the developed federated algorithm.

This paper constructs a conjunction and a disjunction operator for type-2 fuzzy sets that cannot be expressed by the sup-t-norm extension principle applied to conjunction and disjunction of type-1 fuzzy sets by means of t-norms and t-conorms on the unit interval. This result answers affirmatively an open problem posed by Hernandez et al. in 2015. The duality between the set-theoretic operators for type-2 fuzzy sets is obtained from the duality of set-theoretic operations on type-1 fuzzy sets.

This paper presents a novel network, Contribution-Degree-based Spiking Neural Network (CDSNN), which combines ideas of spiking neural network (SNN) and fuzzy set theory. In this framework, two types of information, interval and instantaneous information conveyed by the membrane potential are described by two concepts such as area under membrane potential (AUM) and firing strength. Given that the neuron with large AUM or strong firing strength would enhance the frequency of action potentials of its postsynaptic neurons, the connection between the neuron and its postsynaptic neurons should be strengthened. Combined with an idea of membership function, three contribution degrees (E, S and ES) are defined to quantify the ability of a neuron to provide information for postsynaptic neurons. According to these three degrees, the corresponding SpikeProp learning algorithms, referred to as SPE, SPS and SPES, are developed. Experimental results obtained on ten benchmark datasets, one high-dimensional feature dataset, one big dataset and one time series dataset with some commonly used algorithms, networks and CDSNN demonstrate that CDSNN can achieve improved performance in terms of accuracy, generalization, precision, recall and F-measure. The study demonstrates that the mechanism by which interval-instantaneous information is simultaneously learned in a SNN is feasible.

Granular representations of crisp and fuzzy sets play an important role in rule induction algorithms based on rough set theory. In particular, arbitrary fuzzy sets can be approximated using unions of simple fuzzy sets called granules. These granules, in turn, have a straightforward interpretation in terms of human-readable fuzzy “if..., then...” rules. In this paper, we are considering a fuzzy rough set model based on ordered weighted average (OWA) aggregation over considered values. We show that this robust extension of the classical fuzzy rough set model, which has been applied successfully in various machine learning tasks, also allows for a granular representation. In particular, we prove that when approximations are defined using a directionally convex t-norm and its residual implicator, the OWA-based lower and upper approximations are definable as unions of fuzzy granules. This result has practical implications for rule induction from such fuzzy rough approximations.

Many valued topologies on L-sets, providing a common framework for fuzzy topologies on fuzzy sets and the fixed-basis lattice-valued topologies on ordinary sets, are the main subject of the present study. In this paper, we have introduced many valued topological L-set-spaces, referring to L-sets equipped with many valued topologies, in an axiomatic way and focused on the vindication of their axiomatization in a categorical framework. In order to attain this objective, we apply the theory of Hohle of topological space objects formulated in terms of a partially ordered monad on an abstract category, and show that the category of many valued topological L-set-spaces is isomorphic to the category of topological space objects with respect to a partially ordered monad on a category of L-sets.

In this article, we present a semantic semisupervised learning (Semantic SSL) approach targeted at unifying two machine-learning paradigms in a mutually beneficial way, where the classical support vector machine (SVM) learns to reveal primitive logic facts from data, while axiomatic fuzzy set (AFS) theory is utilized to exploit semantic knowledge and correct the wrongly perceived facts for improving the machine-learning model. This novel semisupervised method can easily produce interpretable semantic descriptions to outline different categories by forming a fuzzy set with semantic explanations realized on the basis of the AFS theory. Besides, it is known that disagreement-based semisupervised learning (SSL) can be viewed as an excellent schema so that a co-training approach with SVM and the AFS theory can be utilized to improve the resulting learning performance. Furthermore, an evaluation index is used to prune descriptions to deliver promising performance. Compared with other semisupervised approaches, the proposed approach can build a structure to reflect data-distributed information with unlabeled data and labeled data, so that the hidden information embedded in both labeled and unlabeled data can be sufficiently utilized and can potentially be applied to achieve good descriptions of each category. Experimental results demonstrate that this approach can offer a concise, comprehensible, and precise SSL frame, which strikes a balance between the interpretability and the accuracy.

Uncertainty is a major concern in vehicle path tracking control design. The coefficients of the uncertainty bound are unknown. They are assumed to lie within prescribed fuzzy sets. First, based on the path tracking kinematic model, this paper innovatively formulates the vehicle path tracking task as a constraint-following problem. Second, we put forward a deterministic adaptive robust control law with a tunable parameter to ensure the uniform boundedness and ultimate uniform boundedness of the closed-loop system. Third, an optimal scheme for the tunable parameter is proposed based on the fuzzy uncertainty. The resulting optimal robust control (ORC) minimizes a comprehensive fuzzy performance index that involves the fuzzy system performance and the control cost. The results of the CarSim-Simulink co-simulation and the Hardware-in-loop (HIL) experiment together show that the proposed optimal robust control exhibits a superior path tracking performance.

This article proposes a data-driven multiobjective evolutionary interval type-2 fuzzy-logic system (IT2FLS) learning approach that considers both system performance and rule interpretability. One characteristic of the evolutionary learning framework is that the IT2FLS structure is incrementally generated instead of searching from an initially huge grid-type rule base, which significantly reduces the parameter search space. Another one is that a new constrained objective function is proposed to improve the distinguishability of the generated interval type-2 fuzzy sets (FSs) without restricting them to be evenly distributed. Because of the tradeoff between system performance and interpretability, a new multiobjective ant colony optimization (ACO) algorithm is proposed to optimize the IT2FLS parameters and improve optimization performance. The evolutionary IT2FLS learning approach is applied to control a real wall-following hexapod robot. The approach shows the advantages of model-free design and interpretability and robustness to noise in the evolved type-2 fuzzy rules. Simulations with performance comparisons and experiments in controlling a real robot show the advantages of the learning approach.

The centroid is one of the most important methods for type–reduction of Type–2 fuzzy sets/numbers and it is also a popular expectation measure, but available methods to compute it are iterative/algorithmic which is an important issue for real–world implementations. This paper presents some theoretical results about the Chebyshev integral inequality for a class of Interval Type–2 fuzzy numbers which leads to obtain non–iterative closed forms of the centroid and its bounds for Type–1 and interval Type–2 fuzzy numbers (by extension). An analysis of the obtained results and a comparison to four well known type–reduction methods: the Karnik–Mendel, Yager Index, Mitchell and Nie–Tan methods are provided where the experimental evidence shows that the proposed method is equivalent to the K–M algorithms.

Fuzzification of real-valued functions using the extension principle is frequently used to study engineering and economic problems when fuzzy data are taken into account. In this article, we generate a fuzzy function by fuzzifying a vector-valued function using the extension principle. On the other hand, it is also well known that the membership function of each fuzzy set can be expressed in terms of its α-level sets. Roughly speaking, each fuzzy set can be decomposed into its α-level sets. Therefore, we generate another fuzzy function by fuzzifying a vector-valued function on the basis of the decomposition form. The main focus is to establish their equivalence under some suitable conditions. Without extra conditions, we have difficulty to establish their equivalence. However, their relationship can be realized on the basis of the degree of fuzzy uncertainty. In these settings, we suggest the use of the decomposition form rather than the extension principle to fuzzify vector-valued functions.

The law of importation, given by the equality (x^y)→z ≈ (x→(y→z)), is a tautology in classical logic and has been proved to be widely used in approximate reasoning and image processing. Some open problems of fuzzy implication dealing with the law of importation were suggested on 8th international conference on Fuzzy Set Theory and Applications (FSTA 2006). In this paper, we partially solve one open problem associated with this property. Specifically, we mainly devote ourselves to solving the general form of the law of importation I(U(x, y), z) = I(x, I(y, z)), where I is a fuzzy implication and U is a conjunctive uninorm with a continuous underlying tnorm and a continuous underlying t-conorm. Along this study, given a fixed uninorm with continuous underlying operators, all fuzzy implications that satisfy the law of importation with respect to this uninorm, and having an α-section that is a continuous negation, are characterized.

Range query processing is a common edge computing and service in the Internet of Things, which can extract user-interest information from distributed edge devices. How to design lightweight privacy-preserving range query processing methods remains a challenging task. Existing secure range query approaches suffer from both high communication cost and long response time, which makes them unsuitable for edge computing over resource-constrained edge devices. In this paper, we propose two privacy-aware fuzzy query processing schemes based on fuzzy theory. Linguistic range variables, fuzzy overlap information and its recovery mechanism are introduced respectively. In addition, two distributed privacy-aware fuzzy range query processing algorithms are devised. Our approaches not only serve for privacy protection, but also aim to provide other optimal performances in terms of reliability, energy efficiency, and real-time response. Theoretical analysis and experimental evaluations based on real-world data sets validated our motivation.

This manuscript has been partially supported by Junta de Andalucía by Project FQM-365 of the Andalusian CICYE, and also by Projects PID2020-119478GB-I00 and PID2019-108392GB-I00 ( AEI/10.13039/501100011033 , Ministerio de Ciencia e Innovación )., In this paper we introduce a novel methodology to face the problem of finding, for every fuzzy set of the real line, a fuzzy number which can be considered as an approximation of the first one in some reasonable sense. This methodology depends on a wide variety of initial parameters that each researcher may set depending on his/her own interests. The main objective of this new methodology is to ensure that many of the techniques that are currently available for fuzzy numbers can also be extended to the setting of fuzzy sets of the real line which are, in many ways, much more enriching. To do this, we carry out a study of the families of nested sets that can determine fuzzy numbers through their level sets. Next, we describe some of the main properties that this approximation methodology verifies and we show some examples to illustrate how the initial parameters influence the result of the approximation., Andalusian CICYE AEI/10.13039/501100011033, PID2019-108392GB-I00, PID2020-119478GB-I00, Ministerio de Ciencia e Innovación

In this paper, we present a new approach to the Mandelbrot set via fuzzy set theory. We introduce and characterize the fuzzy Mandelbrot set by describing its membership function that determines the degrees of belonging of the points to this set under the iteration even if the orbit of the point is not limited. Then we investigate the basic topological properties of the fuzzy Mandelbrot set and its strong α-cut such as closedness, openness, boundness, connectedness and simply connectedness.

This study first surveys fuzzy linearization approaches for solving multi-objective linear fractional programming (MOLFP) problems. In particular, we review different existing methods dealing with fuzzy objectives on a crisp constraint set. Those methods transform the given MOLFP problem into a linear or a multi-objective linear programming (LP or MOLP) problem and obtain one efficient or weakly efficient solution of the main MOLFP problem. We show that one of these popular existing methods has shortcomings, and we modify it to be able to find efficient solutions. The main idea of LP-based methods is optimizing a weighted sum of numerators and the negative form of denominators of the given fractional objective function over the feasible set. We prove there is no weight region to guarantee the efficiency of the optimal solutions of such LP-based methods whenever the interior of the feasible set is nonempty. Moreover, MOLP-based methods obtain an equivalent MOLP problem to the main MOLFP problem using fuzzy set techniques. We prove MOLFP problems with a non-closed efficient set are not equivalent to MOLP ones whenever the equivalency mapping is continuous.

The architecture of AND/OR fuzzy neural networks exhibits outstanding learning abilities and significant interpretation capabilities. However, AND/OR networks suffer from structure-related problems namely low efficiency and slow convergence of learning due to several reasons such as high dimensionality and gradient-based learning algorithms which lead to a visible computing overhead. In this paper, we present a two-phase fuzzy logic-oriented network design that is composed of AND/OR neurons. This design takes advantages of Randomized Neural Network (RNN) to achieve higher convergence while exhibiting good nonlinear approximation capabilities. A gradient–based learning algorithm is implemented in the second phase of the design to further reduce values of performance index. The quality of the proposed design and resulting architecture is quantified through the use of numeric data along with fuzzy sets (information granules). Experimental results meet the research’s objectives and the proposed design methodology opens up new future directions for proceeding with more improvements.

This paper investigates the dissipativity-based filtering problem for the nonlinear systems subject to both uncertainties and time-varying delay in the time-delay interval type-2 (IT2) polynomial fuzzy framework. Filter design is a challenging issue for complex nonlinear systems especially when uncertainties and time delay exist. IT2 polynomial fuzzy model is an effective and powerful approach to analyze and synthesize uncertain nonlinear systems. This is the first attempt to design both the full-order and reduced-order IT2 polynomial fuzzy filter to ensure that the filtering error system is asymptotically stable under the dissipativity constraint. The design of filtering is based on the imperfect premise matching scheme where the number of fuzzy rules and shapes of membership functions of the designed fuzzy filter can differ from those of IT2 polynomial fuzzy model, to provide greater design flexibility and lower implementation burden. By utilizing the Lyapunov-Krasovskii functional based approach, the information of membership functions, time delay and system states is taken into account in the design process to develop the relaxed membership-function-dependent (MFD) and delay-dependent filtering existence criteria. Finally, simulation results are presented to illustrate the effectiveness of the filtering algorithm reported in this paper.

To simultaneously monitor some electrical or mechanical faults of an in-wheel motor and intelligently evaluate the operation safety, a fuzzy system of operation safety assessment (OSA) is proposed. This method firstly uses many symptom parameters (SPs) such as root mean square, crest factor, temperature rise and current covariance to express the features of the electrical and mechanical faults from different perspectives such as vibration, noise, temperature, current and voltage, possibility theory is employed to translate the probability density function of each SP into the possibility function, and sample data are gradually updated to optimize the possibility function for obtaining the SPs’ membership functions that are evaluation models. Secondly, the probabilities of the current operation state that is safety, attention or danger are obtained from each evaluation model in a stage. Picture fuzzy set (PFS) is used to define a basic picture fuzzy number (PFN), then many PFNs from multiple models and multiple stages are used to establish an OSA's decision matrix. Thirdly, Mahalanobis distance is reintegrated into PFS's theory for objectively judging the real-time evaluation information, and best-worst method is used to estimate subjectively the initial evaluation experience, then the multi-model linkage mechanism is designed. Finally, TODIM is modified to define the relative safety ratio, and prospect theory is employed to structure the global index for formulating the multi-stage collaboration approach, then a fuzzy OSA's system is established. The effectiveness of the proposed method was verified by experimental analysis for the operation safety of in-wheel motor with electrical and mechanical faults.

Magnetic resonance imaging (MRI) is a prevailing method of modal infant brain tissue analysis that precisely segments brain tissue and is vitally important for diagnosis, remediation, and analysis of early brain development. To achieve such segmentation is challenging, particularly for the brain of a six-month-old, owing to several factors: 1) poor image quality; 2) isointense contrast between white and gray matter and the simple incomplete volume consequence of a tiny brain size; and 3) discrepancies in brain tissues, illumination settings, and the vagarious region. This paper addresses these challenges with a fuzzy-informed deep learning segmentation (FI-DL-Seg) network that takes T1- and T2-weighted MRIs as inputs. First, a fuzzy logic layer encodes input to the fuzzy domain. Second, A volumetric fuzzy pooling (VFP) layer models the local fuzziness of the volumetric convolutional maps by applying fuzzification, accumulation, and defuzzification on the adjacency feature map neighborhoods. Third, the VFP layer is employed to design the fuzzy-enabled multiscale feature learning (F-MFL) module to enable the extraction of brain features in different receptive fields. Finally, we redesign the Project & Excite module using the VPF layer to enable modeling uncertainty during feature recalibration, and a comprehensive training paradigm is used to learn the ideal parameters of every building block. Extensive experimental comparative studies substantiate the efficiency and accuracy of the proposed model in terms of different evaluation metrics to solve multimodal infant brain segmentation problems on the iSeg-2017 dataset.

In this paper, we propose a series of fuzzy temporal protoforms in the framework of the automatic generation of quantitative and qualitative natural language descriptions of processes. The model includes temporal and causal information from processes and attributes, quantifies attributes in time during the process life-span and recalls causal relations and temporal distances between events, among other features. Through integrating process mining techniques and fuzzy sets within the usual Data-to-Text architecture, our framework is able to extract relevant quantitative temporal as well as structural information from a process and describe it in natural language involving uncertain terms. A real use-case in the cardiology domain is presented, showing the potential of our model for providing natural language explanations addressed to domain experts., Comment: Accepted and published in FUZZ-IEEE 2021: https://doi.org/10.1109/FUZZ45933.2021.9494444 Cite as: Y. Fontenla-Seco, A. Bugarin and M. Lama, "Fuzzy Temporal Protoforms for the Quantitative Description of Processes in Natural Language," 2021 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Luxembourg, Luxembourg, 2021, pp. 1-6, doi: 10.1109/FUZZ45933.2021.9494444