General Fuzzy Research Articles

Improved Extended Dissipativity Results for T-S Fuzzy Generalized Neural Networks With Mixed Interval Time-Varying Delays

The asymptotic stability and extended dissipativity performance of T-S fuzzy generalized neural networks (GNNs) with mixed interval time-varying delays are investigated in this paper. It is noted that this is the first time that extended dissipativity performance in the T-S fuzzy GNNs has been studied. To obtain the improved results, we construct the Lyapunov-Krasovskii functional (LKF), which consists of single, double, triple, and quadruple integral terms containing full information of the delays and a state variable. Moreover, an improved Wirtinger inequality, a new triple integral inequality, and zero equation, along with a convex combination approach, are used to deal with the derivative of the LKF. By using Matlab’s LMI toolbox and the above methods, the new asymptotic stability and extended dissipativity conditions are gained in the form of linear matrix inequalities (LMIs), which include passivity, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{2}-L_{\infty }$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> , and dissipativity performance. Finally, numerical examples that are less conservative than previous results are presented. Furthermore, we give numerical examples to demonstrate the correctness and efficacy of the proposed method for asymptotic stability and extended dissipativity performance of the T-S fuzzy GNNs, including a particular case of the T-S fuzzy GNNs.

Novel Generalized Divergence Measure and Aggregation Operators With Applications for Simplified Neutrosophic Sets

The amount of information on which researchers work increases continuously due to the new developments around the world. This information contains data which is uncertain, incomplete and cannot be fully expressed using crisp numbers. To manage such information, the theory of fuzzy sets, intuitionistic fuzzy sets and neutrosophic sets are used. Neutrosophic sets were introduced as the generalization of fuzzy and intuitionistic fuzzy sets to show incomplete, imprecise, inconsistent and uncertain information that exists in real situations. In this paper, a generalized neutrosophic divergence measure is proposed along with the proof of its validity and neutrosophic aggregation operators are discussed. The proposed measure is applied in decision-making for simplified neutrosophic sets. An illustrative example is provided to demonstrate the application and effectiveness of the developed approach and to test its practicality and legitimacy.

Single axiomatic characterization of a hesitant fuzzy generalization of rough approximation operators

Single axiomatic characterization of a hesitant fuzzy generalization of rough approximation operators

Solving Higher-Order Fractional Differential Equations by the Fuzzy Generalized Conformable Derivatives

In this paper, the generalized concept of conformable fractional derivatives of order q ∈ n , n + 1 for fuzzy functions is introduced. We presented the definition and proved properties and theorems of these derivatives. The fuzzy conformable fractional differential equations and the properties of the fuzzy solution are investigated, developed, and proved. Some examples are provided for both the new solutions.

Some Studies on Fuzzy Generalized Open Sets

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An optimal solution of energy scheduling problem based on chance-constraint programming model using Interval-valued neutrosophic constraints

Neutrosophic sets have been commenced as a generalization of crisp, fuzzy and intuitionistic fuzzy sets to depict vague, incompatible and deficient information about a real world dilemma. Interval-valued fuzzy sets have widely been acknowledged as more proficient in modeling suspicions and practical in assigning an interval of values where allotting an accurate and precise number to an expert’s outlook is too restrictive. They endow with a more appropriate background to characterize higher order of uncertainties and fuzziness of real world. To solve linear programming network problems with constraints concerning interval-valued neutrosophic numbers, a technique has been established by using score function and upper and lower membership functions of interval-valued neutrosophic numbers. An application of energy scheduling problem with constraints represented as interval-valued trapezoidal neutrosophic numbers has been discussed and solved via this technique. Also an additional example to exemplify the proposed method by implementing it on minimum spanning tree and shortest path problem is employed. Furthermore, a comparative examination was performed to validate the effectiveness and usefulness of the projected methodology.

Fuzzy-rough set models and fuzzy-rough data reduction

Rough set theory is a powerful tool to analysis the information systems. Fuzzy rough set is introduced as a fuzzy generalization of rough sets. This paper reviewed the most important contributions to the rough set theory, fuzzy rough set theory and their applications. In many real world situations, some of the attribute values for an object may be in the set-valued form. In this paper, to handle this problem, we present a more general approach to the fuzzification of rough sets. Specially, we define a broad family of fuzzy rough sets. This paper presents a new development for the rough set theory by incorporating the classical rough set theory and the interval-valued fuzzy sets. The proposed methods are illustrated by an numerical example on the real case.

New results of fuzzy implications satisfying I(x,I(y,z))=I(I(x,y),I(x,z))

Cruz et al. (2018) [10] investigated the fuzzy generalization of Frege's Law: x→(y→z)≡(x→y)→(x→z), i.e., I(x,I(y,z))=I(I(x,y),I(x,z)), which is called generalized Frege's Law. They showed conditions such that the generalized Frege's Law holds for (S,N)-implications (R-, QL-, D-, (T,N)-, H-, respectively).In this paper, firstly, a new necessary condition such that the generalized Frege's Law holds is given: NI, the natural negation of I, is not continuous or has no fixed point. Based on this result, some propositions in [10] with contradictory assumptions are pointed out, and a correction is given. Secondly, new solutions of the equation I(x,I(y,z))=I(I(x,y),I(x,z)) in (S,N)-implications are given. Finally, the necessary and sufficient conditions under which the generalized Frege's Law holds for the (U,N)-implications (f-, g-, T-Power based implications, respectively) are studied.

T-Equivalences: The Metric Behavior Revisited

Since the notion of T-equivalence, where T is a t-norm, was introduced as a fuzzy generalization of the notion of crisp equivalence relation, many researchers have worked in the study of the metric behavior of such fuzzy relations. Concretely, a few techniques to induce metrics from T-equivalences, and vice versa, have been developed. In several fields of computer science and artificial intelligence, a generalization of pseudo-metric, known as partial pseudo-metrics, have shown to be useful. Recently, Bukatin, Kopperman and Matthews have stated that the notion of partial pseudo-metric and a type of generalized T-equivalence are linked. Inspired by the preceding fact, in this paper, we state a concrete relationship between partial pseudo-metrics and the aforesaid generalized T-equivalences. Specifically, a method for constructing partial pseudo-metrics from the new type of T-equivalences and, reciprocally, for constructing the generalized T-equivalences from partial pseudo-metrics are provided. However, important differences between the new approach and the classical one are established. Special interest is paid to the case in which the minimum, drastic, and Łukasiewicz t-norms are under consideration.

Multi-criteria decision making method based on Bonferroni mean aggregation operators of complex intuitionistic fuzzy numbers

Complex intuitionistic fuzzy sets (CIFSs), characterized by complex-valued grades of membership and non-membership, are a generalization of standard intuitionistic fuzzy (IF) sets that better speak to time-periodic issues and handle two-dimensional data in a solitary set. Under this environment, in this article, various mean-type operators, namely complex IF Bonferroni means (CIFBM) and complex IF weighted Bonferroni mean (CIFWBM) are presented along with their properties and numerous particular cases of CIFBM are discussed. Further, using the presented operators a decision-making approach is developed and is illustrated with the help of a practical example. Also, the reliability of the developed methodology is investigated with the aid of validity test criteria and the example results are compared with prevailing methods based on operators.

Fuzzy Generalized Conformable Fractional Derivative

We give a new definition of fuzzy fractional derivative called fuzzy conformable fractional derivative. Using this definition, we prove some results and we introduce new definition of generalized fuzzy conformable fractional derivative.

Fuzzy Generalized Hebbian Algorithm for Large-Scale Intrusion Detection System

The huge number of irrelevant and redundant data used in building intrusion detection systems (IDS) is one of the common issues in network intrusion detection systems. This paper proposed the use of Fuzzy Generalized Hebbian Algorithm as a novel data reduction method to overcome this problem of data redundancy in IDS. Two methods for dimensionality reduction (GHA and Fuzzy GHA) were used and compared in this study. This allowed retaining the most relevant traffic data information from the network. Furthermore, the K Nearest Neighbor algorithm was applied for the classification of the test connections into 2 categories (attack or normal). The investigations were carried out on the KDDCUP ‘99 dataset and the results showed the Fuzzy GHA method to perform better than GHA in the detection of both U2R and DoS attacks.

Rough-set-driven approach for attribute reduction in fuzzy formal concept analysis

The reduction of the set of attributes is an important preliminary challenge in order to obtain information from knowledge systems. Two remarkable formal tools for extracting such information are Rough Set Theory (RST) and Formal Concept Analysis (FCA), as well as their fuzzy generalizations. This work introduces a new method to reduce attributes in Fuzzy FCA considering the reduction philosophy given in RST and studies its main properties. This method allows us to carry out a deeper study of the relation between these two theories. Moreover, the proposed methodology has been compared with other existing reduction mechanisms.

Core for Game with Fuzzy Generalized Triangular Payoff Value

In this paper, we investigate cooperative game with fuzzy payoff value in the generalized triangular fuzzy number directly. Based on the fuzzy max order, we define three kinds of fuzzy cores, i.e., fuzzy strong core, fuzzy non-dominated core and fuzzy weak core. All three kinds of fuzzy cores can be regarded as the generalization of crisp core. Convexity is one of the sufficient conditions for the existence of fuzzy core. By the balanced cooperative game, a necessary and sufficient existence condition of fuzzy strong core is also given. Further, the fuzzy strong core is represented by crisp core, and the relationship between fuzzy strong core and crisp one is shown. For the fuzzy non-dominated core and fuzzy weak core, we show their necessary and sufficient existence condition, and their properties to construct the fuzzy imputations. Hence, the verification of fuzzy non-dominated core and fuzzy weak core become easier. The above three fuzzy cores are all the extensions of crisp core, but their stable conditions are not different. The weak core is least restricted, but is least stable. Hence, we could choose the fuzzy core according the stable neediness of fuzzy cooperative game.

Fuzzy Noise-Induced Codimension-Two Bifurcations Captured by Fuzzy Generalized Cell Mapping with Adaptive Interpolation

In this paper, the Fuzzy Generalized Cell Mapping (FGCM) method is developed with the help of the Adaptive Interpolation (AI) in the space of fuzzy parameters. The adaptive interpolation on the set-valued fuzzy parameter is introduced in computing the one-step transition membership matrix to enhance the efficiency of the FGCM. For each of initial points in the state space, a coarse database is constructed at first, and then interpolation nodes are inserted into the database iteratively each time errors are examined with the explicit formula of interpolation error until the maximal errors are just under the error bound. With such an adaptively expanded database on hand, interpolating calculations assure the required accuracy with maximum efficiency gains. The new method is termed as Fuzzy Generalized Cell Mapping with Adaptive Interpolation (FGCM with AI), and is used to investigate codimension-two bifurcations in two-dimensional and three-dimensional nonlinear dynamical systems with fuzzy noise. It is found that global changes in fuzzy dynamics are dominated by the underlying deterministic counterparts, and the fuzzy attractor expands along the unstable manifold leading to a collision with a saddle when a bifurcation occurs. The examples show that the FGCM with AI has a thirtyfold to fiftyfold efficiency over the traditional FGCM to achieve the same analyzing accuracy.

Interval-valued fuzzy multi-criteria decision-making based on simple additive weighting and relative preference relation

To encompass imprecise messages, traditional multi-criteria decision-making (MCDM) was generalized into fuzzy multi-criteria decision-making(FMCDM) in solving decision-making problems. In numerous MCDM methods, simple additive weighting(SAW) is the simplest one, but fuzzy multiplication for generalizing SAW under fuzzy environment is still complicated, especially interval-valued fuzzy numbers. In the past, Wang proposed a model based on SAW and relative preference relation to resolve fuzzy multiplication tie. Practically, Wang's model is useful to fuzzy generalization of SAW. However, the model is only used in triangular fuzzy numbers. Recently, more and varied messages are obtained and processed for decision-making problems. Triangular fuzzy numbers are insufficient to express the variance, whereas interval-valued fuzzy numbers are suitable. Therefore, SAW had to be generalized under interval-valued fuzzy environment. In this paper, we combine SAW with a relative preference relation into interval-valued FMCDM to avoid fuzzy multiplication and grasp more messages. Our proposed relative preference relation improved from Lee's fuzzy preference relation is similar to Wang's relative preference relation. The main difference is that the proposed relation is utilized in interval-valued fuzzy numbers, whereas Wang's is used in triangular fuzzy numbers. To sum up, we provide the FMCDM to solve decision-making problems with interval-valued fuzzy numbers easily and quickly.

Exploring the relationship between social inclusion and special educational needs: mainstream primary perspectives

This article explores the process by which children attending mainstream UK primary schools can achieve social inclusion. It presents the findings from a systematic literature review, followed by empirical research, exploring the concept of social inclusion with particular regard to the experiences of pupils identified with SEND. The article draws upon research conducted for the author’s doctoral study, which explored management of the role of Teaching Assistants on the social inclusion of pupils identified with SEND in mainstream primary schools. Reviewing relevant literature has informed the presentation of two researcher‐ devised models, tentatively depicting the process of social inclusion for pupils identified with SEND in mainstream primary communities, as ‘fuzzy generalizations’, to inform future research. Firstly, an ‘ideal’ model of social inclusion is presented, highlighting the likely process by which pupils may achieve the end goal of social inclusion: participation. Secondly, a ‘current’ model of social inclusion is presented, which draws upon the empirical research conducted in three mainstream primary contexts for the author’s doctoral study. The two models highlight the frequent disparity between the ‘ideal’ goal of social inclusion and the current outcome of the process of social inclusion for many pupils identified with SEND in mainstream primary contexts.

Gender classification using mesh networks on multiresolution multitask fMRI data.

Brain connectivity networks have been shown to represent gender differences under a number of cognitive tasks. Recently, it has been conjectured that fMRI signals decomposed into different resolutions embed different types of cognitive information. In this paper, we combine multiresolution analysis and connectivity networks to study gender differences under a variety of cognitive tasks, and propose a machine learning framework to discriminate individuals according to their gender. For this purpose, we estimate a set of brain networks, formed at different resolutions while the subjects perform different cognitive tasks. First, we decompose fMRI signals recorded under a sequence of cognitive stimuli into its frequency subbands using Discrete Wavelet Transform (DWT). Next, we represent the fMRI signals by mesh networks formed among the anatomic regions for each task experiment at each subband. The mesh networks are constructed by ensembling a set of local meshes, each of which represents the relationship of an anatomical region as a weighted linear combination of its neighbors. Then, we estimate the edge weights of each mesh by ridge regression. The proposed approach yields 2CL functional mesh networks for each subject, where C is the number of cognitive tasks and L is the number of subband signals obtained after wavelet decomposition. This approach enables one to classify gender under different cognitive tasks and different frequency subbands. The final step of the suggested framework is to fuse the complementary information of the mesh networks for each subject to discriminate the gender. We fuse the information embedded in mesh networks formed for different tasks and resolutions under a three-level fuzzy stacked generalization (FSG) architecture. In this architecture, different layers are responsible for fusion of diverse information obtained from different cognitive tasks and resolutions. In the experimental analyses, we use Human Connectome Project task fMRI dataset. Results reflect that fusing the mesh network representations computed at multiple resolutions for multiple tasks provides the best gender classification accuracy compared to the single subband task mesh networks or fusion of representations obtained using only multitask or only multiresolution data. Besides, mesh edge weights slightly outperform pairwise correlations between regions, and significantly outperform raw fMRI signals. In addition, we analyze the gender discriminative power of mesh edge weights for different tasks and resolutions.

An Improved Generalized Fuzzy Model Based on Epanechnikov Quadratic Kernel and Its Application to Nonlinear System Identification

Fuzzy models have excellent capability of describing nonlinear system, so that a wide variety of models is proposed. However, these models are difficult to train and interpret with a hypothesis of data independence. Base on the above problems, an improved generalized fuzzy model is proposed by rules centralization, a new mixture model is built by substituting Epanechnikov quadratic kernel for Gaussian kernel of Gaussian mixture model, and the mutual transformation between the two models is proved. The proposed fuzzy model can not only provide good interpretability, but also easily estimate the parameters of the fuzzy model using the proposed mixture model. In addition, this proposed fuzzy model has higher segmentation efficiency for the input space with consideration of data correlation. The experimental results of a well-known nonlinear system identification show that the proposed fuzzy model has the best performance with fewer fuzzy rules and better generalization ability than some popular models.

L-fuzzifying approximation operators in fuzzy rough sets

In rough set theory, lower and upper approximation operators are two primitive notions. Various fuzzy generalizations of lower and upper approximation operators have been introduced over the years. Considering L being a completely distributive De Morgan algebra, this paper mainly proposes a general framework of L-fuzzifying approximation operators in which constructive and axiomatic approaches are used. In the constructive approach, a pair of lower and upper L-fuzzifying approximation operators is defined. The connections between L-fuzzy relations and L-fuzzifying approximation operators are examined. In the axiomatic approach, various types of L-fuzzifying rough sets are proposed and L-fuzzifying approximation operators corresponding to each type of L-fuzzy relations as well as their compositions are characterized by single axioms. Moreover, the relationships between L-fuzzifying rough sets and L-fuzzifying topological spaces are investigated. It is shown that there is a one-to-one correspondence between reflexive and transitive L-fuzzifying approximation spaces and saturated L-fuzzifying topological spaces.