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 Approximate reasoning with fuzzy rule interpolation: background and recent advances

2021 ◽  
Author(s):  
Fangyi Li ◽  
Changjing Shang ◽  
Ying Li ◽  
Jing Yang ◽  
Qiang Shen
Keyword(s):  
Fuzzy Inference ◽  
Fuzzy Rule ◽  
Approximate Reasoning ◽  
Rule Based ◽  
Reasoning Systems ◽  
Significant Interest ◽  
Recent Developments ◽  
Rule Bases ◽  
The Given ◽  
Computing Approach

AbstractApproximate reasoning systems facilitate fuzzy inference through activating fuzzy if–then rules in which attribute values are imprecisely described. Fuzzy rule interpolation (FRI) supports such reasoning with sparse rule bases where certain observations may not match any existing fuzzy rules, through manipulation of rules that bear similarity with an unmatched observation. This differs from classical rule-based inference that requires direct pattern matching between observations and the given rules. FRI techniques have been continuously investigated for decades, resulting in various types of approach. Traditionally, it is typically assumed that all antecedent attributes in the rules are of equal significance in deriving the consequents. Recent studies have shown significant interest in developing enhanced FRI mechanisms where the rule antecedent attributes are associated with relative weights, signifying their different importance levels in influencing the generation of the conclusion, thereby improving the interpolation performance. This survey presents a systematic review of both traditional and recently developed FRI methodologies, categorised accordingly into two major groups: FRI with non-weighted rules and FRI with weighted rules. It introduces, and analyses, a range of commonly used representatives chosen from each of the two categories, offering a comprehensive tutorial for this important soft computing approach to rule-based inference. A comparative analysis of different FRI techniques is provided both within each category and between the two, highlighting the main strengths and limitations while applying such FRI mechanisms to different problems. Furthermore, commonly adopted criteria for FRI algorithm evaluation are outlined, and recent developments on weighted FRI methods are presented in a unified pseudo-code form, easing their understanding and facilitating their comparisons.

Enhancing Quality of Learning Experience Through Intelligent Agent in E-Learning

2017 ◽  
Vol 25 (01) ◽  
pp. 31-52
Author(s):  
S. Bhattacharya ◽  
S. Chowdhury ◽  
S. Roy
Keyword(s):  
Fuzzy Inference ◽  
Learning Experience ◽  
Fuzzy Rule ◽  
School Level ◽  
Rule Base ◽  
Learning Tools ◽  
Inference System ◽  
Fuzzy Rule Base ◽  
Quality Of Learning

In this paper an interactive recommending agent is proposed which helps an e-learner to enhance the quality of learning experience resulting in efficient achievement of learning objectives. The agent achieves this with the help of a fuzzy rule base working on a variety of learning materials and recommending the appropriate learning path through them. In a learner-centric environment the learning behaviour of a learner may vary to a great extent due to the characteristics of the learner and his environment. Students are often misled while choosing the appropriate path of web learning tools owing to non-availability of a human teacher/guide. By the response of a learner to different positive and negative motivation factors the proposed system employs a fuzzy machine that is fed with realization parameters e.g. Satisfied, Depressed etc. The fuzzy machine working on the paradigm of fuzzy inference system processes these realization parameters with the help of a fuzzy rule base to produce the crisp measures of the learner’s cognitive states in terms of Belief, Behaviour and Attitude. On the basis of these defuzzified crisp diagnostic parameters the proposed system will enhanced the quality of learning experience of an e-learner. To ensure this the system will provide more detailed discussion on the subject matter along with some additional learning tools. Learners often get confused to select the proper tools among various. Therefore the proposed system will also suggest most popular path among those learners with the same understanding. This recommendation comes from the analysis of data mining result. The system was tested with a wide variety of school-level students. The response obtained indicates that it is able to enhance the quality of learning experience through its recommendation.

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.

Special Issue on Fuzzy Rule Interpolation

2011 ◽  
Vol 15 (3) ◽  
pp. 253-253 ◽  
Author(s):  
Szilveszter Kov?cs
Keyword(s):  
Knowledge Representation ◽  
Fuzzy Sets ◽  
Fuzzy Rule ◽  
Rule Base ◽  
Special Issue ◽  
Control Applications ◽  
Euclidean Metric ◽  
Fuzzy Rule Base ◽  
Fuzzy Function ◽  
Rule Bases

Fuzzy Rule Interpolation (FRI) methods are well known tools for reasoning in case of insufficient knowledge expressed as sparse fuzzy rule-bases. It also provides a simple way to define fuzzy functions. Despite these advantages, FRI techniques are relatively rarely applied in practice. Enabling sparse fuzzy rule-bases, FRI dramatically simplifies rule-base creation. Regardless of whether the rule-base is generated by a human expert, or automatically from input-output data, the ability to provide reasonable interpolated conclusions even if no rule fires for a given observation, help to concentrate on cardinal actions alone. This reduces the number of rules needed, speeds up parameter optimization and validation steps, and hence simplifies rule-base creation itself. This special issuefs six papers take six different directions in current FRI research. The first introduces the FRI concept and sets up a unified criteria and evaluation system. This work collects the main properties an FRI method generally has to fulfill. The next two papers are related to the constantly important mainstream research on the more and more sophisticated FRI methods, the endeavor of finding the best way for defining a fuzzy valued fuzzy function based on data given in the form of the relation of fuzzy sets, i.e., in fuzzy rules. The second paper introduces a novel FRI method that is able to handle fuzzy observations activating multiple rule antecedents applying the concept of nonlinear fuzzy-valued function. The third paper presents a novel ganalogical-basedh FRI method that rather fits into the traditional FRI research line, improving the n-rule-based gscale and move transformationh FRI to ensure continuous approximate functions. The fourth paper addresses the issue of defining a distance function between fuzzy sets on a domain that is not necessarily Euclidean metric space. In FRI, this takes on the importance if antecedent or consequent domains are non-Euclidean metric spaces. The last two papers discuss direct FRI control applications. One is an example proving that the sparse fuzzy rule-base is an efficient knowledge representation in intelligent control solutions. The last deals with the computational efficiency of implemented FRI methods applied to direct control area, clearly showing that the sparse fuzzy rule-base is not only a convenient way for knowledge representation, but also makes FRI methods possible devices for direct embedded control applications.

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.

On Obtaining Fuzzy Rule Base from Ensemble of Takagi-Sugeno Systems

2007 ◽  
Author(s):  
Marcin Korytkowski ◽  
Leszek Rutkowski ◽  
Rafal Scherer ◽  
Grzegorz Drozda
Keyword(s):  
Fuzzy Rule ◽  
Rule Base ◽  
Fuzzy Rule Base ◽  
Takagi Sugeno

Query-focused multi-document text summarization using fuzzy inference

2021 ◽  
pp. 1-12
Author(s):  
Raksha Agarwal ◽  
Niladri Chatterjee
Keyword(s):  
Fuzzy Inference ◽  
Fuzzy Rule ◽  
Text Summarization ◽  
Rule Base ◽  
Decision Variable ◽  
Inference System ◽  
Fuzzy Rule Base ◽  
Integer Linear Programming Problem ◽  
Processing Step ◽  
Small Set

The present paper proposes a fuzzy inference system for query-focused multi-document text summarization (MTS). The overall scheme is based on Mamdani Inferencing scheme which helps in designing Fuzzy Rule base for inferencing about the decision variable from a set of antecedent variables. The antecedent variables chosen for the task are from linguistic and positional heuristics, and similarity of the documents with the user-defined query. The decision variable is the rank of the sentences as decided by the rules. The final summary is generated by solving an Integer Linear Programming problem. For abstraction coreference resolution is applied on the input sentences in the pre-processing step. Although designed on the basis of a small set of antecedent variables the results are very promising.

Fuzzy Rule Base Design With Probabilistic Weights

2016 ◽  
Author(s):  
Leonardo G. Melo ◽  
Luís A. Lucas ◽  
Myriam R. Delgado
Keyword(s):  
Fuzzy Rule ◽  
Rule Base ◽  
Fuzzy Rule Base ◽  
Base Design
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