Generalisation of Scale and Move Transformation-Based Fuzzy Interpolation

Fuzzy interpolative reasoning has been extensively studied due to its ability to enhance the robustness of fuzzy systems and reduce system complexity. In particular, the scale and move transformation-based approach is able to handle interpolation with multiple antecedent rules involving triangular, complex polygon, Gaussian and bell-shaped fuzzy membership functions [1]. Also, this approach has been extended to deal with interpolation and extrapolation with multiple multi-antecedent rules [2]. However, the generalised extrapolation approach based on multiple rules may not degenerate back to the basic crisp extrapolation based on two rules. Besides, the approximate function of the extended approach may not be continuous. This paper therefore proposes a new approach to generalising the basic fuzzy interpolation technique of [1] in an effort to eliminate these limitations. Examples are given throughout the paper for illustration and comparative purposes. The result shows that the proposed approach avoids the identified problems, providing more reasonable interpolation and extrapolation.

Download Full-text

Fractal Diffusion Limited Aggregation of Soot Particles Based on Fuzzy Membership Functions

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127419500731 ◽

2019 ◽

Vol 29 (05) ◽

pp. 1950073 ◽

Cited By ~ 2

Author(s):

Jie Sun ◽

Wei Qiao ◽

Shuai Liu

Keyword(s):

Fuzzy Systems ◽

Soot Particle ◽

Membership Functions ◽

Engine Emissions ◽

Diffusion Limited Aggregation ◽

Soot Particles ◽

Fuzzy Membership Functions ◽

Diffusion Limited ◽

Particle Aggregates ◽

Dla Model

In this paper, the membership function in fuzzy systems is used in the Diffusion Limited Aggregation (DLA) model to investigate the fractal diffusion of soot particles from diesel engine emissions. The transformation of the morphology of soot particle aggregates and the control of fractal diffusion of soot particles are investigated by analyzing the nonlinear relationship between the motion steps and angles of diffusing particles. The simulation results demonstrate that the morphology of the aggregates varies from loose to compact by changing the particles’ motion steps and angles in membership functions. Meanwhile, the Ballistic Aggregation (BA)-like aggregates are obtained. Furthermore, the control of the morphology of soot particle aggregates is realized, which makes the settlement of the aggregates become easier. This will provide a reference for further understanding the growth mechanism of soot particle diffusion and enhancing the purification technology of the soot particles.

Download Full-text

Finding Topics in Email Using Formal Concept Analysis and Fuzzy Membership Functions

Advances in Artificial Intelligence - Lecture Notes in Computer Science ◽

10.1007/978-3-540-68825-9_11 ◽

2008 ◽

pp. 108-113 ◽

Cited By ~ 1

Author(s):

Liqiang Geng ◽

Larry Korba ◽

Yunli Wang ◽

Xin Wang ◽

Yonghua You

Keyword(s):

Formal Concept Analysis ◽

Concept Analysis ◽

Fuzzy Membership ◽

Formal Concept ◽

Membership Functions ◽

Fuzzy Membership Functions

Download Full-text

Intuitionistic Fuzzy Laplacian Twin Support Vector Machine for Semi-supervised Classification

Journal of the Operations Research Society of China ◽

10.1007/s40305-021-00354-9 ◽

2021 ◽

Author(s):

Jia-Bin Zhou ◽

Yan-Qin Bai ◽

Yan-Ru Guo ◽

Hai-Xiang Lin

Keyword(s):

Support Vector Machine ◽

Negative Impact ◽

Twin Support Vector Machine ◽

Fuzzy Membership ◽

Support Vector ◽

Membership Functions ◽

Fuzzy Membership Functions ◽

Intuitionistic Fuzzy ◽

Benchmark Datasets ◽

The Impact

AbstractIn general, data contain noises which come from faulty instruments, flawed measurements or faulty communication. Learning with data in the context of classification or regression is inevitably affected by noises in the data. In order to remove or greatly reduce the impact of noises, we introduce the ideas of fuzzy membership functions and the Laplacian twin support vector machine (Lap-TSVM). A formulation of the linear intuitionistic fuzzy Laplacian twin support vector machine (IFLap-TSVM) is presented. Moreover, we extend the linear IFLap-TSVM to the nonlinear case by kernel function. The proposed IFLap-TSVM resolves the negative impact of noises and outliers by using fuzzy membership functions and is a more accurate reasonable classifier by using the geometric distribution information of labeled data and unlabeled data based on manifold regularization. Experiments with constructed artificial datasets, several UCI benchmark datasets and MNIST dataset show that the IFLap-TSVM has better classification accuracy than other state-of-the-art twin support vector machine (TSVM), intuitionistic fuzzy twin support vector machine (IFTSVM) and Lap-TSVM.

Download Full-text

Fuzzy Differential Subordinations Based Upon the Mittag-Leffler Type Borel Distribution

Symmetry ◽

10.3390/sym13061023 ◽

2021 ◽

Vol 13 (6) ◽

pp. 1023

Author(s):

Hari Mohan Srivastava ◽

Sheza M. El-Deeb

Keyword(s):

Fuzzy Systems ◽

Special Functions ◽

Univalent Functions ◽

Local Symmetry ◽

Open Unit ◽

Fuzzy Membership Functions ◽

Non Local ◽

Differential Subordinations ◽

Two Parameter ◽

Borel Type

In this paper, we investigate several fuzzy differential subordinations that are connected with the Borel distribution series Bλ,α,β(z) of the Mittag-Leffler type, which involves the two-parameter Mittag-Leffler function Eα,β(z). Using the above-mentioned operator Bλ,α,β, we also introduce and study a class Mλ,α,βFη of holomorphic and univalent functions in the open unit disk Δ. The Mittag-Leffler-type functions, which we have used in the present investigation, belong to the significantly wider family of the Fox-Wright function pΨq(z), whose p numerator parameters and q denominator parameters possess a kind of symmetry behavior in the sense that it remains invariant (or unchanged) when the order of the p numerator parameters or when the order of the q denominator parameters is arbitrarily changed. Here, in this article, we have used such special functions in our study of a general Borel-type probability distribution, which may be symmetric or asymmetric. As symmetry is generally present in most works involving fuzzy sets and fuzzy systems, our usages here of fuzzy subordinations and fuzzy membership functions potentially possess local or non-local symmetry features.

Download Full-text