scholarly journals Inference Algorithm Independent SVD Fuzzy Rule Base Complexity Reduction

2001 ◽  
Vol 5 (1) ◽  
pp. 22-30 ◽  
Author(s):  
Péter Baranyi ◽  
◽  
Yeung Yamb ◽  
Chi Tin Yang ◽  
Péter Várlakic ◽  
...  
Keyword(s):  
Reduction Method ◽  
Fuzzy Rule ◽  
Reduction Process ◽  
Complexity Reduction ◽  
Rule Base ◽  
Inference Algorithm ◽  
Reduction Techniques ◽  
Fuzzy Algorithms ◽  
Rule Bases ◽  
Exponential Complexity

This paper is motivated by the fact that fuzzy technique is popular engineering tool, however, its use is restricted by its exponential complexity. One of the complexity reduction techniques is the SVD based reduction method which deals with arbitrary shaped fuzzy sets. Despite its advantages it is applicable to rule bases only which are based on product-sum-gravity (PSG) inference algorithm. This paper introduces the extension of the PSG based SVD-reduction method to arbitrary inference based fuzzy algorithms. An example with the control of an automatic guided system is presented to demonstrate the reduction process.

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 Fuzzy Rule Interpolation and Extrapolation Techniques: Criteria and Evaluation Guidelines

2011 ◽  
Vol 15 (3) ◽  
pp. 254-263 ◽  
Author(s):  
Domonkos Tikk ◽  
◽  
Zsolt Csaba Johanyák ◽  
Szilveszter Kovács ◽  
Kok Wai Wong ◽  
...  
Keyword(s):  
Fuzzy Rule ◽  
Complexity Reduction ◽  
Control Problems ◽  
Approximation Techniques ◽  
Initial Investigation ◽  
Classical Inference ◽  
Rule Bases

This paper comprehensively analyzes Fuzzy Rule Interpolation and extrapolation Techniques (FRITs). Because extrapolation techniques are usually extensions of fuzzy rule interpolation, we treat them both as approximation techniques designed to be applied where sparse or incomplete fuzzy rule bases are used, i.e., when classical inference fails. FRITs have been investigated in the literature from aspects such as applicability to control problems, usefulness regarding complexity reduction and logic. Our objectives are to create an overall FRIT standard with a general set of criteria and to set a framework for guiding their classification and comparison. This paper is our initial investigation of FRITs. We plan to analyze details in later papers on how individual techniques satisfy the groups of criteria we propose. For analysis,MATLAB FRI Toolbox provides an easy-to-use testbed, as shown in experiments.

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.

HIERARCHICAL-INTERPOLATIVE FUZZY SYSTEM CONSTRUCTION BY GENETIC AND BACTERIAL MEMETIC PROGRAMMING APPROACHES

2012 ◽  
Vol 20 (supp02) ◽  
pp. 105-131 ◽  
Author(s):  
KRISZTIÁN BALÁZS ◽  
LÁSZLÓ T. KÓCZY
Keyword(s):  
Machine Learning ◽  
System Modeling ◽  
Fuzzy Rule ◽  
Knowledge Bases ◽  
Learning System ◽  
Supervised Machine Learning ◽  
Rule Base ◽  
System Construction ◽  
Rule Bases ◽  
Programming Algorithms

In this paper a family of new methods are proposed for constructing hierarchical-interpolative fuzzy rule bases in the frame of a fuzzy rule based supervised machine learning system modeling black box systems defined by input-output pairs. The resulting hierarchical rule base is constructed by using structure building pure evolutionary and memetic techniques, namely, Genetic and Bacterial Programming Algorithms and their memetic variants containing local search steps. Applying hierarchical-interpolative fuzzy rule bases is a rather efficient way of reducing the complexity of knowledge bases, whereas evolutionary methods (including memetic techniques) ensure a relatively fast convergence in the learning process. As it is presented in the paper, by applying a newly proposed representation schema these approaches can be combined to form hierarchical-interpolative machine learning systems.

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

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.

Fuzzy rule based cluster analysis to segment consumers’ preferences to eco and non-eco friendly products

2021 ◽  
Vol 24 (4) ◽  
pp. 343-351
Author(s):  
Sanjukta Ghosh ◽  
Doan Van Thang ◽  
Suresh Chandra Satapathy ◽  
Sachi Nandan Mohanty
Keyword(s):  
Fuzzy Rule ◽  
Environmental Knowledge ◽  
Purchase Behavior ◽  
Health Improvement ◽  
Rule Base ◽  
Environmental Attitude ◽  
Rule Based ◽  
Product Categories ◽  
Central Pollution Control Board ◽  
Develop Strategy

Environment protection and basic health improvement of all social communities is now considered as one of the key parameters for the development. It has become a responsibility for both industry and academia to optimize the usage of finite natural resources and preserve them. Efficient promotion and strategic marketing of Eco Friendly products can contribute to this development. It is important to consider any market as a heterogeneous mix, which requires well-organized and intelligent split or segmentation. A survey was conducted in Kolkata, metropolitan city in India, through a structured questionnaire to measure Perceived Environmental Knowledge, Perceived Environmental Attitude and Green Purchase Behavior associated to 18 product categories identified by Central Pollution Control Board for Eco Mark Scheme, 2002. Two hundred and twenty three data inputs from the respondents were analysed for this study. Here in this study a fuzzy rule based clustering technique was performed to segregate customers into two sections considering three parameters like Perceived Environmental Knowledge, Perceived Environmental Attitude and Green Purchase Behavior associated to Eco friendly product, which acts as an input variable. The rule base has linguistic variables like Significantly High, Little High, Medium, Little Low and Significantly Low and output as “Eco friendly” or “Non-ecofriendly” consumers. A set of 5×5×5= 125 rules were developed for output determination. They were designed manually and the method is applied for detection of a set of good rules. Thirteen such good rules were identified through Fuzzy Reasoning Tool, which can lead to better Decision Making and facilitate the marketers to develop strategy and take up effective marketing decisions.

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