Search

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. In large-scale multiobjective optimization, too many decision variables hinder the convergence search of evolutionary algorithms. Reducing the search range of the decision space will significantly alleviate this puzzle. With this in mind, this paper proposes a fuzzy decision variables framework for largescale multiobjective optimization. The framework divides the entire evolutionary process into two main stages: fuzzy evolution and precise evolution. In fuzzy evolution, we blur the decision variables of the original solution to reduce the search range of the evolutionary algorithm in the decision space so that the evolutionary population can quickly converge. The degree of fuzzification gradually decreases with the evolutionary process. Once the population approximately converges, the framework will turn to precise evolution. In precise evolution, the actual decision variables of the solution are directly optimized to increase the diversity of the population so as to be closer to the true Pareto optimal front. Finally, this paper embeds some representative algorithms into the proposed framework and verifies the framework’s effectiveness through comparative experiments on various large-scale multiobjective problems with 500 to 5000 decision variables. Experimental results show that in large-scale multiobjective optimization, the framework proposed in this paper can significantly improve the performance and computational efficiency of multiobjective optimization algorithms.

Privacy concerns of users threaten the usage of online social networks (OSN). In this regard, privacy preserving of OSN emerged as a convincing solution for preserving the privacy of users and uncovering useful insights from the social network data. In this article, we propose a novel algorithm based on the fuzzy sets and rewiring algorithm for preserving the privacy of users. This article presents the algorithm called privacy-preserving rewiring algorithm (PPRA), which can be used for anonymizing the social network data. The algorithm is validated by showing its effectiveness on four real-world datasets across three major graph mining tasks. The proposed PPRA algorithm will help in preserving the privacy of users in the OSN graph while simultaneously maintaining the utility that can be generated from the OSN graph structure.

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.

With the rise of emerging technology in the fourth industrial revolution, modern agricultural technologies are gradually adopted to increase the yield and efficiency. Meanwhile, they also may bring the negative effect to social and environment sustainable development. Ignoring the requirement of sustainability will have an impact on the development of the country and society. Besides, the uncertainty and multistakeholder on sustainable modern agricultural technology assessment (SMATA) have made this appraisal much more complex, including their entanglement with rapidly changing cultural norms and social relations. Thus, in order to address these concerns, this article develops a holistic multistakeholder transdisciplinary approach with supporting SMATA. More precisely, due to the uncertainty of environment and vague knowledge possessed by stakeholders, we first investigate the evaluation measure of SMATA by introducing $q$ -rung orthopair fuzzy set ( $q$ -ROFS). Second, group opinion of stakeholders is fused by developing a new transdisciplinary evaluation aggregation operator. Third, to achieve more robust weights of key factors, three extended best worst method models from three different comparative perspectives of $q$ -ROFS are established. The final weight of key factors is further obtained by utilizing the variable entropy method. Fourth, we design a new decision approach of SMATA by improving evaluation based on distance from average solution method. Finally, a modern agricultural project base of Xichang city in China is used to demonstrate the effectiveness and rationality of our proposed SMATA method, including the simulation experiments on sensitivity analysis and comparative analysis. These results provide some exploratory insight and guidelines of SMATA for government and organization.

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.

Fuzzy sets introduced to overthrow the uncertainty of an object. Interval valued intuitionistic fuzzy sets in topological structure space is an extension of fuzzy sets. Interval-valued intuitionistic multi fuzzy set theory is a capable tool for commerce with ambivalence of expertise in information systems. The motive of this paper is to present interval valued intuitionistic multi fuzzy completely generalized semiprecontinuous mappings and provide some of their properties. Also we proved the relation between various types of interval valued intuitionistic multi fuzzy continuous mappings. AMS Subject Classification (2010): 54A40.

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.

The various extensions of the fuzzy set are considerably applied in many complex problems of real world to describes the improper information. The PFS (pythagorean fuzzy set) which is the expanded form of IFS (intuitionistic fuzzy set) is more applicable and precise to measure the uncertainty. The research work presents the novel entropy measure defined on PFS which satisfied axioms of the entropy. The entropy measure is determined the uncertainty that defined the fuzziness degree on the fuzzy set. The applicability of the entropy is verified in selection of the advertising company and results compared to the existing entropies defined on PFS. The outcomes of the illustrative example show that the new entropy measure is more precise, simpler, and consistent as compare to existing entropies on PFS.

Firm survival in dynamic software markets depends on collaboration with ecosystem complementors and exploitative and/or explorative innovation. Such activities have been widely accepted as crucial antecedents for collaboration success, but few studies have analyzed the configurational effects of collaborative modes effect on firm performance. Based on a sample of 224 software firms and fuzzy set qualitative comparative analysis, results show that four causal configurations equivalently explain high innovation performance, in which exploitation, exploration, and collaboration with academic and governmental institutes are proven to be core causal conditions. Theoretically, this article contributes to the literature on collaborative innovation in terms of causality research and collaborative pathways but also enriches the literature on software ecosystems regarding partnerships and collaborative processes. Practical guidance and flexible choices for software firms to achieve high innovation performance are provided by offering four equivalent configurations.

This research presents and compares the outcomes of experimental implementations of different fuzzy logic control structures for a proton exchange membrane fuel cell (PEMFC). These devices are well known for their capability to transform chemical energy into electrical with low emissions. Commonly, a PEMFC has a linkage with a boost converter which allows a suitable end-user voltage through a nonlinear control law. Hence, the contribution in this sense is the experimental comparison of two fuzzy logic strategies known as type-1 and type-2 that were implemented in a PEMFC system. The approaches were embedded in a control board dSPACE 1102 which also has the capability to acquire data. The contrast of results showed capabilities improvement against disturbances in terms of error reduction, control signal, and robustness. The authors wish to express their gratitude to the Basque Government, through the project EKOHEGAZ (ELKARTEK KK-2021/00092), to the Diputación Foral de Álava (DFA), through the project CONAVANTER, and to the UPV/EHU, through the project GIU20/063, for supporting this work.

For a regular investor, it is necessary to identify the stocks with the strong fundamentals that yield good returns. An individual can check few such stocks manually but cannot do so for whole of the stock market listing. Thus, it is desirable to devise a mechanism that is able to assess the intrinsic health of the stock, across the whole of stock market scenario, in an automated manner and provide credible advice(s). The proposed work is an effort in this direction wherein on the basis of expert advice; a regression based supervised learning model has been created using feature extraction from the raw data. The regressive output of the learning model provides a stock health index that has been classified into fuzzy sets. A fuzzy rule base was created that generates the requisite advice on the basis of stock health index. The paper concludes with the identification of some fundamentally good stocks and validates the results through their quantified performance.

The hyperspectral images have so far been widely utilized in monitoring and detecting the changes in a broad range of environmentally related matters. The hyperspectral image analysis yields maps that show spatial dispersion of physical and ecological characteristics of the terrain. Within the scope of the current study, an integrated Fuzzy-MCDM in a Geographic Information Systems (GIS) platform was used to map the health condition of Ramsar forest. Spectral indices can provide different methods for identifying vegetation coverings. For forest health analysis, spectral indices such as NDWI, CRI1, PSRI, PRI, and NDVI were used to infer the causative factors of forest health. The findings highlight the suitability of the used methodology in identifying potential forest statuses, where forest health protection measures can be taken in advance. The results also suggest that the southern and the western aspects of the study area are of “very low” to “low” forest health. Furthermore, the results indicate a high potentiality for applying the spatial MCDM techniques as an effective tool for the forest health investigation.

For practical multiple attribute decision making problems, it is common to involve heterogeneous attribute information and a rational choice may be distorted by the judgments of decision-makers due to their limited personal cognition. In this regard, this article puts forward an integrated model to solve multiple attribute decision-making problems considering the interaction among heterogeneous attributes based on the regret theory. First, a target-based utility function that is in line with people's perceptions is developed. Based on this function, the specific utilities of different forms of performance scores, including crisp numbers, interval numbers, and hesitant fuzzy sets, are given. Then, the regret theory is used to identify the partial perceived utilities of alternatives on each attribute, which include the utility, regret, and rejoicing values of decision-makers. In addition, to address both positive and negative interactions among attributes, the Choquet integral is employed to derive the global utilities of alternatives. An application to determine the optimal provider of waste classification service in multiattribute reverse auction is given, and the corresponding comparative and sensitive analyses verify the applicability and effectiveness of the proposed method.

In this article, a deterministic model for the selection and ranking of commercial off-the-shelf (COTS) components is developed on the basis of fuzzy modified distance-based approach (FMDBA). The COTS selection and ranking problem is modeled as multicriteria decision making problem due to the involvement of multiple ranking criteria like functionality, reliability, compatibility, etc. FMDBA is the combination of the fuzzy set theory and the modified distance-based approach. To show the working of the developed ranking model, a case study of the e-payment system is demonstrated which aims on the selection and ranking of eight COTS components over four major categories of ranking criteria. FMDBA provides a comprehensive ranking of the components based on their calculated composite distance values. To depict the docility of FMDBA method, the results obtained are also compared with the existing decision-making methodologies.

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.

Because of COVID-19, factories are facing many difficulties, such as shortage of workers and social alienation. How to improve production performance under limited labor resources is an urgent problem for global manufacturing factories. This work studies an energy-efficient job-shop scheduling problem with limited workers. Those workers can have multiskills. A many-objective model with five objectives, that is: 1) makespan; 2) total tardiness; 3) total idle time; 4) total worker cost; and 5) total energy, is built. To solve this many-objective optimization problem (MaOP), a novel fitness evaluation mechanism (FEM) based on fuzzy correlation entropy (FCE) is adopted. Two construction methods for reference points are proposed to build the bridge between MaOP and a fuzzy set. Based on FCE and cluster methods, an environmental selection mechanism (ESM) is proposed to achieve a balance between solution convergence and diversity. With the proposed FEM and ESM, two many-objective evolutionary algorithms are proposed to solve MaOP. The effect of FCE-based FEM and ESM on the performance of algorithms is verified via experiments. The proposed algorithms are compared with four well-known peers to test their performance. The extensive experimental results show that they are very competitive for the considered many-objective scheduling problem.

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.

In this paper, we focus on combining the theories of picture fuzzy sets on rings and establishing a new framework for picture fuzzy sets on commutative rings. The aim of this manuscript is to apply picture fuzzy set for dealing with several kinds of theories in commutative rings. Moreover, we introduce the notions of picture fuzzy ideals on commutative rings and some properties of them are obtained. Finally, we give suitable definitions of the operations of picture fuzzy ideals over a commutative ring, as composition, product and intersection.

As a combination of fuzzy sets and covering rough sets, fuzzy β covering has attracted much attention in recent years. The fuzzy β neighborhood serves as the basic granulation unit of fuzzy β covering. In this article, a new discernibility measure with respect to the fuzzy β neighborhood is proposed to characterize the distinguishing ability of a fuzzy covering family. To this end, the parameterized fuzzy β neighborhood is introduced to describe the similarity between samples, where the distinguishing ability of a given fuzzy covering family can be evaluated. Some variants of the discernibility measure, such as the joint discernibility measure, conditional discernibility measure, and mutual discernibility measure, are then presented to reflect the change of distinguishing ability caused by different fuzzy covering families. These measures have similar properties as the Shannon entropy. Finally, to deal with knowledge reduction with fuzzy β covering, we formalize a new type of decision table, that is, fuzzy β covering decision tables. The data reduction of fuzzy covering decision tables is addressed from the viewpoint of maintaining the distinguishing ability of a fuzzy covering family, and a forward attribute reduction algorithm is designed to reduce redundant fuzzy coverings. Extensive experiments show that the proposed method can effectively evaluate the uncertainty of different types of datasets and exhibit better performance in attribute reduction compared with some existing algorithms.

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.

In this article, we apply a high-order control to a dynamical system with uncertainty. There are two characteristics. First, the uncertain part, which is time-varying but bounded, is described in a fuzzy aspect. Specifically, the uncertainty lies within a fuzzy set and the bound is regarded as a fuzzy number. Second, the systems are uniformly bounded and uniformly ultimately bounded with a deterministic controller based on the Lyapunov theory. To obtain better system performance and lower control input, we apply the noncooperative game theory to optimize the parameters by establishing a Nash game. Then, the D-operation is proposed for the uncertainty related to fuzzy numbers. Finally, we perform the numerical simulations of the steering-by-wire system for verification.

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.

There is uncertainty in the system, and we consider that uncertainty is (possibly fast) time varying, but with definite bound. Fuzzy set theory is used to describe the inexact boundary and then the problem of robust control of uncertain dynamical systems is studied. Based on two adjustable design parameters, a robust control method for general mechanical systems is proposed. The control is deterministic, not the conventional IF-THEN rule based. By using the Lyapunov minimax approach, it is proved that the proposed control can guarantee system performance to be uniformly bounded and uniformly ultimately bounded. In order to find the optimal solution in the prescribed range, a two-player cooperative game is used. To reduce costs while ensuring control performance, two performance indices are developed, each of which is controlled by an adjustable parameter (i.e., player). Both necessary and sufficient conditions for Pareto-optimality are established. Using these conditions, the Pareto-optimal solution can be obtained. The effectiveness of the control design is demonstrated by the simulation of the two-body pendulum.

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.

The Bandler-Kohout subproduct (BKS) method is one of the two widely acknowledged fuzzy relational inference (FRI) schemes. The previous works related to its stability and robustness mainly concentrated on how the output values were changed with perturbation parameters of input values. However, the works on estimating oscillation bounds of output values with regard to varying limits of input, are lacking. In this study, we investigate the oscillation-bound estimation of perturbations for BKS. First, the BKS output variation scopes are acquired for interval perturbation, where the R -implication, ( S, N )-implication, QL-implication, and t -norm implication are adopted. Second, in allusion to the more sophisticated problem of the fuzzy reasoning chain with BKS, the oscillation bounds of BKS output resulting from input interval perturbation are offered. Third, we construct the upper and lower bounds of BKS output deviation originated in the simple perturbation of the input fuzzy set, in which the situations of one rule and multiple rules are both dissected. Finally, the stable properties of all these BKS strategies are confirmed. It is emphasized that interval perturbation and simple perturbation are more general ways to give expression describing the robustness issue, and the obtained oscillation bounds also deliver more detailed characterization of the output deviation along with the input perturbation. This study further validates the sound properties of the BKS method.

A multivariable robust control design for aircraft engines is proposed. The engine is modeled as a fuzzy dynamic system (FDS), which is not the same as Takagi-Sugeno inference system, based on a series of state vector models in the flight envelope. The possible value of uncertainty is prescribed to be within fuzzy sets. The uncertainty is divided into the matched and the mismatched portions. While the matched uncertainty lies within the range space of the input matrix, the mismatched uncertainty falls outside, which poses a significant challenge for control design. A robust control, which is deterministic and is not IF-THEN fuzzy rule based, is designed. The control design parameter needs to be feasible, i.e., within a prescribed range. Some prescribed deterministic performances of the system are guaranteed under the control, regardless of the uncertainty. By taking the control cost and the performance threshold into consideration, which is under the influence of both matched and mismatched uncertainty, the optimal choice of the control parameter is explored. As a result, this control design delicately blends optimality with mismatched uncertainty. This design is applied to a turbofan engine. HIL (hardware-in-the-loop) laboratory testing in the flight envelope demonstrates the superiority of the control design.

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.

This study aims to analyse how memorable local gastronomic experiences and tourists' gastronomy-related traits influence destination loyalty and future intentions. A fuzzy set model is used to examine these intricate relationships using samples of US tourists who visited Europe and Asia. The findings reveal that dimensions of memorable local gastronomic experience and their influence on destination loyalty differ based on tourists' personal gastronomic traits. Hospitality explained destination loyalty well when combined with social interaction, neophilia, and local gastronomy tourism-induced wellbeing. Theoretical and practical insights are provided to aid destination planning and local food marketing efforts. info:eu-repo/semantics/publishedVersion

Buried natural gas pipelines are vulnerable to external corrosion because they are encased in a soil environment for a long time. Identifying the causes of external corrosion and taking specific maintenance measures is essential. In this work, a risk analysis and maintenance decision-making model for natural gas pipelines with external corrosion is proposed based on a Bayesian network. A fault tree model is first employed to identify the causes of external corrosion. The Bayesian network for risk analysis is determined accordingly. The maintenance strategies are then inserted into the Bayesian network to show a reduction of the risk. The costs of maintenance strategies and the reduced risk after maintenance are combined in an optimization function to build a decision-making model. Because of the limitations of historical data, some of the parameters in the Bayesian network are obtained from a probabilistic estimation model, which combines expert experience and fuzzy set theory. Finally, a case study is carried out to verify the feasibility of the maintenance decision model. This indicates that the method proposed in this work can be used to provide effective maintenance schemes for different pipeline external corrosion scenarios and to reduce the possible losses caused by external corrosion.

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 paper, an interval type-2 fuzzy disturbance observer (IT2FDO) is proposed for the trajectory tracking control of a flexible joint actuated by a pneumatic artificial muscle (PAM) and a torsion spring. Interval type-2 fuzzy sets are introduced into the fuzzy disturbance observer (FDO) to enhance fuzzy approximation capability. A novel adaptive law that updates all the parameters of the FDO, including the control representative values, the center vectors, and the width vectors, is developed. A new control strategy incorporating the proposed IT2FDO and T-S fuzzy model-based control is designed for the trajectory tracking task. With the newly designed adaptive law, the stability of the IT2FDO and that of the closed-loop system are guaranteed. Simulation studies verify the effectiveness of the proposed IT2FDO, and real-world experiments demonstrate the robustness of the proposed control strategy to the external disturbance.

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.

The water, energy, and food (WEF) nexus has gained particular attention in the sustainable development community. Making effective decisions in this environment is difficult. Entwinement from multiple sustainability dimensions and various stakeholder perspectives contribute to this difficulty. Stakeholders have differing goals, interests, and preferences for potential technological and developmental solutions that address WEF nexus concerns. A holistic sustainable management approach with supporting decision support can address these concerns. This article introduces such a holistic framework to address WEF-sustainability (WEFS) concerns. Using a joint neighborhood rough set, interval-valued hesitant fuzzy set, and regret theory technique, this article introduces a multistakeholder transdisciplinary method to support WEFS nexus decisions. An illustrative example integrates the multiple stakeholder and WEFS nexus factors. The illustrative example provides insights into the modeling effort and data requirements. Research, practical implications, along with limitations of the study—which are all discussed—provide a foundation for future research directions in this socio-environmentally important field.

This paper develops a distributed cooperative energy management system with two distributed control layers for speed-coupling plug-in hybrid electric vehicles. By introducing personalized non-stationary inference, this system can fuse driving behavior and vehicle state information to adaptively adjust power-split control parameters for the improvement of vehicle energy economy. In the on-board control layer, five sets of personalized control parameters are optimized offline by using chaos-enhanced accelerated particle swarm optimization. In the distributed control layer, interval type-2 fuzzy sets are applied to develop a real-time driving style recognition function. Driving behavior is detected remotely, via the vehicle to everything network, and downloaded to adaptively adjust power-split control parameters in the on-board vehicle controller. Hardware-in-the-loop testing is carried out based on the four laboratory driving cycles and four personal driving cycles. The proposed system has been demonstrated with strong robustness that saves energy by up to 5.25% over the equivalent consumption minimization strategy (ECMS), especially for gentle drivers. Even under harsh communication conditions (with signal loss 80+%), it still performs better than the ECMS (by 0.57%) and the series-parallel control strategy (by 2.66%).

Now-a-days, a large volume of biomedical data are continuously generated from various biomedical devices and experiments due to the rapid technological advancement in medical science. The effective analysis of these biomedical data such as extracting the significant features biologically and diagnostically is really a challenging task. This paper proposes a Neuro-Fuzzy model with post-feature reduction to analyze these complex biomedical data. The proposed Neuro-Fuzzy approach uses class belongingness fuzzification of input patterns to handle uncertainty issues. However, the complexity of the model increases due to this fuzzy expansion of input patterns. On the other hand, all the expanded fuzzified patterns may not always be significant for model identification. To address this issue, post-feature reduction has been employed on fuzzified patterns to filter out the irrelevant, redundant and noisy features. Unlike pre-feature reduction, this allows all the features to be participated in the fuzzification process and then identify irrelevant features from the fuzzified patterns. Further, this approach allows exploring potential fuzzified features from the strong as well as weak feature set. The effectiveness of this proposed model has been tested and validated with a variety of benchmark biomedical data collected from various domains.

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.

Commonly used GIS combination operators such as Boolean conjunction/disjunction and weighted linear combination can be generalized to the ordered weighted averaging (OWA) family of operators. This multicriteria evaluation method allows decision-makers to define a decision strategy on a continuum between pessimistic and optimistic strategies. Recently, OWA has been introduced to GIS-based decision support systems. We propose to extend a previous implementation of OWA with linguistic quantifiers to simplify the definition of decision strategies and to facilitate an exploratory analysis of multiple criteria. The linguistic quantifier-guided OWA procedure is illustrated using a dataset for evaluating residential quality of neighborhoods in London, Ontario. This is a post-peer-review, pre-copyedit version of an article published in Journal of Geographical Systems. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10109-005-0159-2

Fuzzy sets are a major oversimplification and extension of classical sets. Fuzzy sets have become a recognized research topic in many fields. This paper proposes a new type of set theory is Neutrosophic set. As a novel study field, new hybrid sets created from Neutrosophic sets are gaining prominence. The Neutrosophic set is used to describe indeterminacy and uncertainty in any information. The Neutrosophic set extension has been explored by many researchers. Here we introduce properties of Neutrosophic Fuzzy (NF) ideals in Γ Rings. Some new Neutrosophic operations are explored.

In this paper, we introduce the notion of bipolar-valued neutrosophic subbisemiring (BVNSBS), level sets of BVNSBS, and bipolar valued neutrosophic normal subbisemiring (BVNNSBS) of a bisemiring. The concept of BVNSBS is a new generalization of subbisemiring over bisemirings. We discussed the theory of (ξ, τ )- BVNSBS and (ξ, τ )-BVNNSBS over bisemirings and presented several illustrative examples to demonstrate the sufficiency and validity of the proposed theorems, lemmas, and propositions

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.