A LOGICAL ANALYSIS OF RULE INCONSISTENCY

2011 ◽  
Vol 05 (03) ◽  
pp. 271-280 ◽  
Author(s):  
PHILIPPE BESNARD
Keyword(s):  
Natural Deduction ◽  
Logical Analysis ◽  
Production Rules ◽  
Rule Based ◽  
Material Implication ◽  
Classical Sense ◽  
Rule Based System ◽  
New Information ◽  
Rule Consistency ◽  
Rule Based Systems

Representing knowledge in a rule-based system takes place by means of "if…then…" statements. These are called production rules for the reason that new information is produced when the rule fires. The logic attached to rule-based systems is taken to be classical inasmuch as "if…then…" is encoded by material implication. However, it appears that the notion of triggering "if…then…" amounts to different logical definitions. The paper investigates the matter, with an emphasis upon consistency because reading "if… then…" statements as rules calls for a notion of rule consistency that does not conform with consistency in the classical sense. Natural deduction is used to explore entailment and equivalence among various formulations and properties.

A Review of Multi-Objective Evolutionary Based Fuzzy Classifiers

2020 ◽  
Vol 13 (1) ◽  
pp. 77-85
Author(s):  
Praveen Kumar Dwivedi ◽  
Surya Prakash Tripathi
Keyword(s):  
Fuzzy Systems ◽  
Evolutionary Process ◽  
Fuzzy Rule ◽  
Fuzzy Classification ◽  
Multi Objective Optimization ◽  
Fuzzy Classifier ◽  
Rule Based ◽  
Trade Off ◽  
Multi Objective ◽  
Rule Based Systems

Background: Fuzzy systems are employed in several fields like data processing, regression, pattern recognition, classification and management as a result of their characteristic of handling uncertainty and explaining the feature of the advanced system while not involving a particular mathematical model. Fuzzy rule-based systems (FRBS) or fuzzy rule-based classifiers (mainly designed for classification purpose) are primarily the fuzzy systems that consist of a group of fuzzy logical rules and these FRBS are unit annexes of ancient rule-based systems, containing the "If-then" rules. During the design of any fuzzy systems, there are two main objectives, interpretability and accuracy, which are conflicting with each another, i.e., improvement in any of those two options causes the decrement in another. This condition is termed as Interpretability –Accuracy Trade-off. To handle this condition, Multi-Objective Evolutionary Algorithms (MOEA) are often applied within the design of fuzzy systems. This paper reviews the approaches to the problem of developing fuzzy systems victimization evolutionary process Multi-Objective Optimization (EMO) algorithms considering ‘Interpretability-Accuracy Trade-off, current research trends and improvement in the design of fuzzy classifier using MOEA in the future scope of authors. Methods: The state-of-the-art review has been conducted for various fuzzy classifier designs, and their optimization is reviewed in terms of multi-objective. Results: This article reviews the different Multi-Objective Optimization (EMO) algorithms in the context of Interpretability -Accuracy tradeoff during fuzzy classification. Conclusion: The evolutionary multi-objective algorithms are being deployed in the development of fuzzy systems. Improvement in the design using these algorithms include issues like higher spatiality, exponentially inhabited solution, I-A tradeoff, interpretability quantification, and describing the ability of the system of the fuzzy domain, etc. The focus of the authors in future is to find out the best evolutionary algorithm of multi-objective nature with efficiency and robustness, which will be applicable for developing the optimized fuzzy system with more accuracy and higher interpretability. More concentration will be on the creation of new metrics or parameters for the measurement of interpretability of fuzzy systems and new processes or methods of EMO for handling I-A tradeoff.

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