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Investigating a relevance of fuzzy mappings
1Dept. of Electr. & Comput. Eng., Alberta Univ., Edmonton, Alta.
Summary
This study quantifies the relevance of fuzzy mappings using shadowed sets, offering a quality assessment before detailed construction. Shadowed sets provide a three-valued measure for fuzzy mapping relevance in granular computing and rule-based systems.
Area of Science:
- Fuzzy computing
- Granular computing
- Rule-based systems
Background:
- Fuzzy mappings are fundamental in granular computing and rule-based systems.
- Quantifying the quality of fuzzy mappings is crucial before their construction.
- Existing methods lack a robust approach for pre-construction quality assessment.
Purpose of the Study:
- Introduce and define the concept of relevance for fuzzy mappings.
- Develop a method for quantifying fuzzy mapping relevance.
- Apply the proposed method to triangular and Gaussian fuzzy sets.
Main Methods:
- Introduction of shadowed sets as a framework for relevance quantification.
- Development of an algorithmic approach using shadowed sets.
- Detailed calculations for triangular and Gaussian fuzzy sets.
Main Results:
- Shadowed sets provide a three-valued quantification of fuzzy mapping relevance: acceptable, marginal, or lack of mapping.
- The proposed method allows for quality assessment prior to detailed fuzzy mapping construction.
- Numerical studies demonstrate the effectiveness of shadowed sets for relevance quantification.
Conclusions:
- Shadowed sets offer a valuable tool for assessing fuzzy mapping relevance in granular computing.
- The three-valued quantification provides nuanced insights into mapping quality.
- This approach enhances the development and application of rule-based systems.
