Fuzzy Rule Interpolation by the Conservation of Relative Fuzziness

2000 ◽  
Vol 4 (1) ◽  
pp. 95-101 ◽  
Author(s):  
Laszlo T. Koczy ◽  
◽  
Kaoru Hirota ◽  
Tamas D. Gedeon ◽  
◽  
...  
Keyword(s):  
Fuzzy Sets ◽  
Interpolation Method ◽  
Fundamental Equation ◽  
Fuzzy Rule ◽  
Membership Functions ◽  
Inference Control ◽  
Multiple Dimensions ◽  
Linear Rule ◽  
Rule Bases ◽  
Refined Version

If the number of variables is growing the size of fuzzy rule bases increase exponentially. To reduce size and inference/control time, it is often necessary to deal with sparse rule bases. In such bases, classic algorithms such as the CRI of Zadeh and the Mamdani-method do not function. In such rule bases, rule interpolation techniques are necessary. The linear rule interpolation (KHinterpolation) based on the Fundamental Equation of Interpolation introduced by Koczy and Hirota is suitable for dealing with sparse bases, but this method often results in conclusions which are not directly interpretable, and need some further transformations. One of the possible ways to avoid this problem is the interpolation method based on the conservation of fuzziness, proposed recently by Gedeon and Koczy for trapezoidal fuzzy sets. In this paper, a refined version of that method will be presented that is fully in accordance with the Fundamental Equation, with extensions to multiple dimensions, and then to arbitrarily shaped membership functions. Several possibilities for the latter will be shown.

scholarly journals Neuro-Fuzzy Assessment of Building Damage and Safety After an Earthquake

2007 ◽  
pp. 123-157 ◽  
Author(s):  
Martha Carreño ◽  
Omar Cardona ◽  
Alex Barbat
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy System ◽  
Fuzzy Rule ◽  
Neuro Fuzzy ◽  
Computational Intelligence Technique ◽  
Artificial Neural ◽  
Fuzzy Assessment ◽  
Rule Bases ◽  
Building Occupancy

This chapter describes the algorithmic basis of a computational intelligence technique, based on a neuro-fuzzy system, developed with the objective of assisting nonexpert professionals of building construction to evaluate the damage and safety of buildings after strong earthquakes, facilitating decision-making during the emergency response phase on their habitability and reparability. A hybrid neuro-fuzzy system is proposed, based on a special three-layer feedforward artificial neural network and fuzzy rule bases. The inputs to the system are fuzzy sets, taking into account that the damage levels of the structural components are linguistic variables, defined by means of qualifications such as slight, moderate or severe, which are very appropriate to handle subjective and incomplete information. The chapter is a contribution to the understanding of how soft computing applications, such as artificial neural networks and fuzzy sets, can be used to complex and urgent processes of engineering decision-making, like the building occupancy after a seismic disaster.

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.

scholarly journals A HEDGE ALGEBRAS BASED REASONING METHOD FOR FUZZY RULE BASED CLASSIFIER

2019 ◽  
Vol 57 (5) ◽  
pp. 631
Author(s):  
Phạm Đình Phong ◽  
Nguyễn Đức Dư ◽  
Hoàng Văn Thông
Keyword(s):  
Fuzzy Sets ◽  
Design Method ◽  
Fuzzy Rule ◽  
Design Methods ◽  
Rule Based ◽  
Classifier Design ◽  
Real World Datasets ◽  
Rule Based Classifier ◽  
Rule Bases ◽  
Sets Theory

The fuzzy rule based classifier (FRBC) design methods have intensively been being studied during last years. The ones designed by utilizing hedge algebras as a formalism to generate the optimal linguistic values along with their (triangular and trapezoidal) fuzzy sets based semantics for the FRBCs have been proposed. Those design methods generate the fuzzy sets based semantics because the classification reasoning method still bases on the fuzzy set theory.  One question which has been arisen is whether there is a pure hedge algebras classification reasoning method so that the fuzzy sets based semantic of the linguistic values in the fuzzy rule bases can be replaced with the hedge algebras based semantic. This paper answers that question by presenting a fuzzy rule based classifier design method based on hedge algebras with a pure hedge algebras classification reasoning method. The experimental results over 17 real world datasets are compared to the existing methods based on hedge algebras and fuzzy sets theory showing that the proposed method is effective and produces good results.

An Alternative Backward Fuzzy Rule Interpolation Method

2014 ◽  
Vol 6 (4) ◽  
pp. 47-71 ◽  
Author(s):  
Shangzhu Jin
Keyword(s):  
Analogical Reasoning ◽  
Interpolation Method ◽  
Effective Means ◽  
Fuzzy Rule ◽  
Final Conclusion ◽  
Rule Based ◽  
Fuzzy Interpolation ◽  
Fuzzy Models ◽  
Real World Applications ◽  
Rule Bases

Fuzzy set theory allows for the inclusion of vague human assessments in computing problems. Also, it provides an effective means for conflict resolution of multiple criteria and better assessment of options. Fuzzy rule interpolation offers a useful means for enhancing the robustness of fuzzy models by making inference possible in sparse rule-based systems. However, in real-world applications of inter-connected rule bases, situations may arise when certain crucial antecedents are absent from given observations. If such missing antecedents were involved in the subsequent interpolation process, the final conclusion would not be deducible using conventional means. To address this issue, an approach named backward fuzzy rule interpolation and extrapolation has been proposed recently, allowing the observations which directly relate to the conclusion to be inferred or interpolated from the known antecedents and conclusion. As such, it significantly extends the existing fuzzy rule interpolation techniques. However, the current idea has only been implemented via the use of the scale and move transformation-based fuzzy interpolation method, which utilise analogical reasoning mechanisms. In order to strengthen the versatility and feasibility of backward fuzzy interpolative reasoning, in this paper, an alternative a-cut-based interpolation method is proposed. Two numerical examples and comparative studies are provided in order to demonstrate the efficacy of the proposed work.

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.

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