Rule base normalization in Takagi-Sugeno ensemble

2011 ◽  
Author(s):  
Marcin Korytkowski ◽  
Leszek Rutkowski ◽  
Rafal Scherer
Keyword(s):  
Rule Base ◽  
Takagi Sugeno

A New Clustering Method with Fuzzy Approach Based on Takagi-Sugeno Model in Queuing Systems

2013 ◽  
Vol 3 (2) ◽  
pp. 32-54
Author(s):  
Farzaneh Gholami Zanjanbar ◽  
Inci Sentarli
Keyword(s):  
Fuzzy Model ◽  
Extraction Process ◽  
Queuing System ◽  
Rule Base ◽  
Queuing Systems ◽  
Clustering Method ◽  
Hard Clustering ◽  
Sugeno Model ◽  
Takagi Sugeno ◽  
Linear Controllers

In this paper, the authors propose a new hard clustering method to provide objective knowledge on field of fuzzy queuing system. In this method, locally linear controllers are extracted and translated into the first-order Takagi-Sugeno rule base fuzzy model. In this extraction process, the region of fuzzy subspaces of available inputs corresponding to different implications is used to obtain the clusters of outputs of the queuing system. Then, the multiple regression functions associated with these separate clusters are used to interpret the performance of queuing systems. An application of the method also is presented and the performance of the queuing system is discussed.

Fuzzy Rule Interpolation

2011 ◽  
pp. 728-733 ◽  
Author(s):  
Szilveszter Kovács
Keyword(s):  
Fuzzy Inference ◽  
Fuzzy Rule ◽  
Fuzzy Reasoning ◽  
Fuzzy Relation ◽  
Rule Base ◽  
Rule Based ◽  
Fuzzy Rule Base ◽  
Current Observation ◽  
Rule Bases ◽  
Takagi Sugeno

The “fuzzy dot” (or fuzzy relation) representation of fuzzy rules in fuzzy rule based systems, in case of classical fuzzy reasoning methods (e.g. the Zadeh-Mamdani- Larsen Compositional Rule of Inference (CRI) (Zadeh, 1973) (Mamdani, 1975) (Larsen, 1980) or the Takagi - Sugeno fuzzy inference (Sugeno, 1985) (Takagi & Sugeno, 1985)), are assuming the completeness of the fuzzy rule base. If there are some rules missing i.e. the rule base is “sparse”, observations may exist which hit no rule in the rule base and therefore no conclusion can be obtained. One way of handling the “fuzzy dot” knowledge representation in case of sparse fuzzy rule bases is the application of the Fuzzy Rule Interpolation (FRI) methods, where the derivable rules are deliberately missing. Since FRI methods can provide reasonable (interpolated) conclusions even if none of the existing rules fires under the current observation. From the beginning of 1990s numerous FRI methods have been proposed. The main goal of this article is to give a brief but comprehensive introduction to the existing FRI methods.

scholarly journals The applicability of Generic Self-Evolving Takagi-Sugeno-Kang neuro-fuzzy model in modeling rainfall–runoff and river routing

2019 ◽  
Vol 50 (4) ◽  
pp. 991-1001 ◽  
Author(s):  
Mohammad Ashrafi ◽  
Lloyd H. C. Chua ◽  
Chai Quek
Keyword(s):  
Fuzzy Inference System ◽  
Hydrological Modeling ◽  
Fuzzy Inference ◽  
Training Dataset ◽  
Rule Base ◽  
Rainfall Runoff ◽  
Inference System ◽  
Neuro Fuzzy ◽  
Takagi Sugeno ◽  
River Routing

Abstract Recent advancements in neuro-fuzzy models (NFMs) have made possible the implementation of dynamic rule base systems. This is in comparison with static applications commonly seen in global NFMs such as the Adaptive-Network-Based Fuzzy Inference System (ANFIS) model widely used in hydrological modeling. This study underlines key differences between local and global NFMs with an emphasis on rule base dynamics, in the context of two common flow forecast applications. A global NFM, ANFIS, and two local NFMs, Dynamic Evolving Neural-Fuzzy Inference System (DENFIS) and Generic Self-Evolving Takagi-Sugeno-Kang (GSETSK), were tested. Results from all NFMs compared favorably when benchmarked against physically based models. Rainfall–runoff modeling is a complex process which benefits from the advanced rule generation and pruning mechanisms in GSETSK, resulting in a more compact rule base. Although ANFIS resulted in the same number of rules, this came about at the expense of having the need for a large training dataset. All NFMs generated a similar number of rules for the river routing application, although local NFMs yielded better results for forecasts at longer lead times. This is attributed to the fact that the routing procedure is less complex and can be adequately modeled by static NFMs.

scholarly journals The Fuzzy Inference System with Least Square Optimization for Time Series Forecasting

2018 ◽  
Vol 11 (3) ◽  
pp. 1015 ◽  
Author(s):  
Samingun Handoyo ◽  
Marji Marji
Keyword(s):  
Fuzzy Inference System ◽  
Fuzzy Inference ◽  
Least Square ◽  
Training Data ◽  
Lookup Table ◽  
Rule Base ◽  
Inference System ◽  
Rule Bases ◽  
Takagi Sugeno ◽  
Development And Validation

The rule base on the fuzzy inference system (FIS) has a major role since the output generated by the system is highly dependent on it. The rule base is usually obtained from an expert but in this study proposed the rule base generated based on input-output data pairs with generating rule bases using lookup table scheme, then consequent part of each rule optimized with ordinary least square(OLS), so finally formed rule base from model FIS Takagi-Sugeno orde zero. The exchange rate dataset of EURO to USD is used for the development and validation of the system. In this study, 12 FISs were developed from a combination of linguistic values of n = 3,5,7, 9 with the number of lag (k) assumed to have an effect on output for k = 2,3,5. In training data, values R<sup>2</sup> ranged between 0.989 and 0.993, MAPE values ranged between 0.381% and 0.473% where the FIS with the combination of n = 9 and k = 5 has the best performance. In the testing data, values R<sup>2</sup> ranged between 0.203 and 0.7858, MAPE values ranged between 0.5136% and 0.9457% where FIS n = 3 and k = 2 perform best.

RULE CORRELATION AND CHOQUET INTEGRATION IN FUZZY INFERENCE SYSTEMS

2008 ◽  
Vol 16 (05) ◽  
pp. 601-626 ◽  
Author(s):  
R. A. MARQUES PEREIRA ◽  
R. A. RIBEIRO ◽  
P. SERRA
Keyword(s):  
Fuzzy Inference System ◽  
Correlation Matrix ◽  
Fuzzy Inference ◽  
Integration Scheme ◽  
Rule Base ◽  
Inference System ◽  
Aggregation Scheme ◽  
Inference Systems ◽  
Rule Bases ◽  
Takagi Sugeno

We propose an extension of the Takagi-Sugeno-Kang (TSK) fuzzy inference system, using Choquet integration for aggregating the single rule outputs. In the new Choquet-TSK fuzzy inference system, the pairwise synergies between rules are encoded in a rule correlation matrix computed from the activation pattern of the rule base. The rule correlation matrix is then used to modulate the parameters of the Choquet integration scheme in order to compensate for the effect of rule synergies, which are present in most rule bases to a higher or lesser extent.The standard TSK fuzzy inference system remains a particular instance of the proposed Choquet-TSK extension and corresponds to the ideal case of rule independence. However, when rule correlation is present, the Choquet-TSK fuzzy inference system takes it into account when computing the final output of the system. On the basis of the rule correlation matrix, the new aggregation scheme of the Choquet-TSK fuzzy inference system attenuates the effective weight of positively correlated rules and emphasizes that of negatively correlated rules. Some case studies are discussed in order to illustrate the proposed methodology.

Analytical Structures of Takagi-Sugeno Fuzzy Two-Input Two-Output Proportional-Integral/Proportional-Derivative Controllers With Multiple Fuzzy Sets

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Ritu Raj ◽  
B. M. Mohan
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Controller ◽  
Control Strategies ◽  
Rule Base ◽  
Complete Control ◽  
Proportional Integral ◽  
Control Rules ◽  
Gain Variation ◽  
Multiple Input ◽  
Takagi Sugeno

In this paper, an attempt is made to generalize the analytical structures of Takagi-Sugeno (TS) fuzzy two-input two-output (TITO) proportional-integral (PI)/proportional-derivative (PD) controllers using multiple input fuzzy sets. Two models of fuzzy TITO PI/PD controllers are proposed based on two distinct control strategies. The inputs are fuzzified by multiple fuzzy sets with trapezoidal/triangular membership functions. The generalized rule base consists of nine control rules imbibing the complete control strategy and is closer in spirit to the original TS rule base. Algebraic product (AP) triangular norm, bounded sum (BS) triangular conorm, and center of gravity (CoG) defuzzifier are applied to derive the models. The models of the fuzzy TITO PI/PD controllers with multiple input fuzzy sets are (nonlinear) variable gain/structure controllers. Also, each output of the fuzzy controller is the sum of two nonlinear PI/PD controllers with variable gains. The gain variation and properties of the proposed controllers are studied. Two examples of nonlinear dynamic processes are considered to demonstrate the applicability of the proposed controllers.

Multi-gene genetic programming to building up fuzzy rule-base in Neo-Fuzzy-Neuron networks

2021 ◽  
pp. 1-18
Author(s):  
Glender Brás ◽  
Alisson Marques Silva ◽  
Elizabeth Fialho Wanner
Keyword(s):  
Genetic Programming ◽  
Fuzzy Rule ◽  
Rule Base ◽  
Genetic Operators ◽  
Neuro Fuzzy ◽  
Proposed Model ◽  
Gradient Based ◽  
Non Linear System ◽  
Takagi Sugeno ◽  
Fuzzy Network

This paper introduces a new approach to build the rule-base on Neo-Fuzzy-Neuron (NFN) Networks. The NFN is a Neuro-Fuzzy network composed by a set of n decoupled zero-order Takagi-Sugeno models, one for each input variable, each one containing m rules. Employing Multi-Gene Genetic Programming (MG-GP) to create and adjust Gaussian membership functions and a Gradient-based method to update the network parameters, the proposed model is dubbed NFN-MG-GP. In the proposed model, each individual of MG-GP represents a complete rule-base of NFN. The rule-base is adjusted by genetic operators (Crossover, Reproduction, Mutation), and the consequent parameters are updated by a predetermined number of Gradient method epochs, every generation. The algorithm uses Elitism to ensure that the best rule-base is not lost between generations. The performance of the NFN-MG-GP is evaluated using instances of time series forecasting and non-linear system identification problems. Computational experiments and comparisons against state-of-the-art alternative models show that the proposed algorithms are efficient and competitive. Furthermore, experimental results show that it is possible to obtain models with good accuracy applying Multi-Gene Genetic Programming to construct the rule-base on NFN Networks.

scholarly journals A New Clustering Method with Fuzzy Approach Based on Takagi-Sugeno Model in Queuing Systems

2014 ◽  
pp. 411-430
Author(s):  
Farzaneh Gholami Zanjanbar ◽  
İnci Şentarlı
Keyword(s):  
Fuzzy Model ◽  
Extraction Process ◽  
Queuing System ◽  
Rule Base ◽  
Queuing Systems ◽  
Clustering Method ◽  
Hard Clustering ◽  
Sugeno Model ◽  
Takagi Sugeno ◽  
Linear Controllers

In this paper, the authors propose a new hard clustering method to provide objective knowledge on field of fuzzy queuing system. In this method, locally linear controllers are extracted and translated into the first-order Takagi-Sugeno rule base fuzzy model. In this extraction process, the region of fuzzy subspaces of available inputs corresponding to different implications is used to obtain the clusters of outputs of the queuing system. Then, the multiple regression functions associated with these separate clusters are used to interpret the performance of queuing systems. An application of the method also is presented and the performance of the queuing system is discussed.

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