A Granular Unified Min-Max Fuzzy-Neuro Framework for Learning Fuzzy Systems

2009 ◽  
Vol 13 (5) ◽  
pp. 520-528 ◽  
Author(s):  
Mokhtar Beldjehem ◽  
Keyword(s):  
Cognitive Processes ◽  
Fuzzy Systems ◽  
Main Idea ◽  
Fuzzy Rules ◽  
Approximation Procedure ◽  
Unified Framework ◽  
Fine Grained ◽  
Neuro Fuzzy ◽  
Fuzzy Partitions ◽  
Hypotheses Generation

We propose a novel computational granular unified framework that is cognitively motivated for learning if-then fuzzy weighted rules by using a hybrid neuro-fuzzy or fuzzy-neuro possibilistic model appropriately crafted as a means to automatically extract or learn fuzzy rules from only input-output examples by integrating some useful concepts from the human cognitive processes and adding some interesting granular functionalities. This learning scheme uses an exhaustive search over the fuzzy partitions of involved variables, automatic fuzzy hypotheses generation, formulation and testing, and approximation procedure of Min-Max relational equations. The main idea is to start learning from coarse fuzzy partitions of the involved variables (both input and output) and proceed progressively toward fine-grained partitions until finding the appropriate partitions that fit the data. According to the complexity of the problem at hand, it learns the whole structure of the fuzzy system, i.e. conjointly appropriate fuzzy partitions, appropriate fuzzy rules, their number and their associated membership functions.

RSPOP: Rough Set–Based Pseudo Outer-Product Fuzzy Rule Identification Algorithm

2005 ◽  
Vol 17 (1) ◽  
pp. 205-243 ◽  
Author(s):  
Kai Keng Ang ◽  
Chai Quek
Keyword(s):  
Computational Complexity ◽  
Rough Set ◽  
Fuzzy Systems ◽  
Fuzzy Neural Networks ◽  
Fuzzy Rules ◽  
Published Data ◽  
Identification Algorithm ◽  
Highway Traffic ◽  
Outer Product ◽  
Neuro Fuzzy

System modeling with neuro-fuzzy systems involves two contradictory requirements: interpretability verses accuracy. The pseudo outer-product (POP) rule identification algorithm used in the family of pseudo outer-product-based fuzzy neural networks (POPFNN) suffered from an exponential increase in the number of identified fuzzy rules and computational complexity arising from high-dimensional data. This decreases the interpretability of the POPFNN in linguistic fuzzy modeling. This article proposes a novel rough set–based pseudo outer-product (RSPOP) algorithm that integrates the sound concept of knowledge reduction from rough set theory with the POP algorithm. The proposed algorithm not only performs feature selection through the reduction of attributes but also extends the reduction to rules without redundant attributes. As many possible reducts exist in a given rule set, an objective measure is developed for POPFNN to correctly identify the reducts that improve the inferred consequence. Experimental results are presented using published data sets and real-world application involving highway traffic flow prediction to evaluate the effectiveness of using the proposed algorithm to identify fuzzy rules in the POPFNN using compositional rule of inference and singleton fuzzifier (POPFNN-CRI(S)) architecture. Results showed that the proposed rough set–based pseudo outer-product algorithm reduces computational complexity, improves the interpretability of neuro-fuzzy systems by identifying significantly fewer fuzzy rules, and improves the accuracy of the POPFNN.

Rule Base Simplification and Constrained Learning for Interpretability in TSK Neuro-Fuzzy Modelling

2020 ◽  
Vol 9 (2) ◽  
pp. 31-58
Author(s):  
Sharifa Rajab
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Systems ◽  
Fuzzy Model ◽  
Fuzzy Rules ◽  
Data Driven ◽  
Similarity Analysis ◽  
Rule Base ◽  
Generalization Capability ◽  
Fuzzy Modelling ◽  
Neuro Fuzzy

Neuro-fuzzy systems based on a fuzzy model proposed by Takagi, Sugeno and Kang known as the TSK fuzzy model provide a powerful method for modelling uncertain and highly complex non-linear systems. The initial fuzzy rule base in TSK neuro-fuzzy systems is usually obtained using data driven approaches. This process induces redundancy into the system by adding redundant fuzzy rules and fuzzy sets. This increases complexity which adversely affects generalization capability and transparency of the fuzzy model being designed. In this article, the authors explore the potential of TSK fuzzy modelling in developing comparatively interpretable neuro-fuzzy systems with better generalization capability in terms of higher approximation accuracy. The approach is based on three phases, the first phase deals with automatic data driven rule base induction followed by rule base simplification phase. Rule base simplification uses similarity analysis to remove similar fuzzy sets and resulting redundant fuzzy rules from the rule base, thereby simplifying the neuro-fuzzy model. During the third phase, the parameters of membership functions are fine-tuned using a constrained hybrid learning technique. The learning process is constrained which prevents unchecked updates to the parameters so that a highly complex rule base does not emerge at the end of model optimization phase. An empirical investigation of this methodology is done by application of this approach to two well-known non-linear benchmark forecasting problems and a real-world stock price forecasting problem. The results indicate that rule base simplification using a similarity analysis effectively removes redundancy from the system which improves interpretability. The removal of redundancy also increased the generalization capability of the system measured in terms of increased forecasting accuracy. For all the three forecasting problems the proposed neuro-fuzzy system demonstrated better accuracy-interpretability tradeoff as compared to two well-known TSK neuro-fuzzy models for function approximation.

DESIGNING BOOSTING ENSEMBLE OF RELATIONAL FUZZY SYSTEMS

2010 ◽  
Vol 20 (05) ◽  
pp. 381-388 ◽  
Author(s):  
RAFAŁ SCHERER
Keyword(s):  
Fuzzy Systems ◽  
Fuzzy Relation ◽  
Classification Systems ◽  
Fuzzy Rules ◽  
Neuro Fuzzy ◽  
Fuzzy Classifiers ◽  
Rule Bases ◽  
Fuzzy Relation Matrix ◽  
Fuzzy Linguistic ◽  
Novel Design

A method frequently used in classification systems for improving classification accuracy is to combine outputs of several classifiers. Among various types of classifiers, fuzzy ones are tempting because of using intelligible fuzzy if-then rules. In the paper we build an AdaBoost ensemble of relational neuro-fuzzy classifiers. Relational fuzzy systems bond input and output fuzzy linguistic values by a binary relation; thus, fuzzy rules have additional, comparing to traditional fuzzy systems, weights — elements of a fuzzy relation matrix. Thanks to this the system is better adjustable to data during learning. In the paper an ensemble of relational fuzzy systems is proposed. The problem is that such an ensemble contains separate rule bases which cannot be directly merged. As systems are separate, we cannot treat fuzzy rules coming from different systems as rules from the same (single) system. In the paper, the problem is addressed by a novel design of fuzzy systems constituting the ensemble, resulting in normalization of individual rule bases during learning. The method described in the paper is tested on several known benchmarks and compared with other machine learning solutions from the literature.

A Neuro-Fuzzy Approach to Detect Rumors in Online Social Networks

2020 ◽  
Vol 17 (1) ◽  
pp. 64-82 ◽  
Author(s):  
Santhoshkumar Srinivasan ◽  
Dhinesh Babu L.D.
Keyword(s):  
Social Networks ◽  
Online Social Networks ◽  
Fuzzy Systems ◽  
Input Data ◽  
State Of The Art ◽  
Fuzzy Rules ◽  
Fuzzy Classification ◽  
Fuzzy Approach ◽  
Neuro Fuzzy ◽  
Common Problems

Along with true information, rumors spread in online social networks (OSN) on an unprecedented scale. In recent days, rumor identification gains more interest among the researchers. Finding rumors also poses other critical challenges like noisy and imprecise input data, data sparsity, and unclear interpretations of the output. To address these issues, we propose a neuro-fuzzy classification approach called the neuro-fuzzy rumor detector (NFRD) to automatically identify the rumors in OSNs. NFRD quickly transforms the input to fuzzy rules which classify the rumor. Neural networks handle larger input data. Fuzzy systems are better in handling uncertainty and imprecision in input data by producing fuzzy rules that effectively eliminate the unclear inputs. NFRD also considers the semantic aspects of information to ensure better classification. The neuro-fuzzy approach addresses the most common problems such as uncertainty elimination, noise reduction, and quicker generalization. Experimental results show the proposed approach performs well against state-of-the-art rumor detecting techniques.

NEURO-FUZZY SYSTEMS APPLIED ON A FIXED-WING AIRCRAFT CONTROL

2019 ◽  
Author(s):  
Renata Bernardes ◽  
Bruno Luiz Pereira ◽  
Felipe Machini Malachias Marques ◽  
Roberto Mendes Finzi Neto
Keyword(s):  
Fuzzy Systems ◽  
Aircraft Control ◽  
Neuro Fuzzy

Essentially non-oscillatory and weighted essentially non-oscillatory schemes

Acta Numerica ◽  
2020 ◽  
Vol 29 ◽  
pp. 701-762
Author(s):  
Chi-Wang Shu
Keyword(s):  
Main Idea ◽  
High Order Accuracy ◽  
Finite Difference Schemes ◽  
Approximation Procedure ◽  
Discontinuous Solutions ◽  
Weno Schemes ◽  
Convection Diffusion ◽  
Different Types ◽  
Basic Ideas ◽  
Weighted Eno

Essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes were designed for solving hyperbolic and convection–diffusion equations with possibly discontinuous solutions or solutions with sharp gradient regions. The main idea of ENO and WENO schemes is actually an approximation procedure, aimed at achieving arbitrarily high-order accuracy in smooth regions and resolving shocks or other discontinuities sharply and in an essentially non-oscillatory fashion. Both finite volume and finite difference schemes have been designed using the ENO or WENO procedure, and these schemes are very popular in applications, most noticeably in computational fluid dynamics but also in other areas of computational physics and engineering. Since the main idea of the ENO and WENO schemes is an approximation procedure not directly related to partial differential equations (PDEs), ENO and WENO schemes also have non-PDE applications. In this paper we will survey the basic ideas behind ENO and WENO schemes, discuss their properties, and present examples of their applications to different types of PDEs as well as to non-PDE problems.

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