研究目的
Investigating the systematic determination of membership functions with the use of the principle of justifiable granularity, focusing on information granules in the form of fuzzy sets and extending it to deal with two generalizations of the generic problem: incorporation of weights of data and involvement of inhibitory experimental evidence.
研究成果
The approach presented underlines the fact that any information granule builds on a basis of experimental data and incorporates domain knowledge. The criteria of coverage and specificity are the essential components reflecting the nature of the build-up of information granules. Fuzzy sets formed by the principle of justifiable granularity retain their semantics, standing in contrast with the construction of fuzzy sets as part of the optimization process of fuzzy models.
研究不足
The expert-driven technique could be general and might not be necessarily reflective of the experimental data for which these fuzzy sets are constructed. The data-driven approaches may result in fuzzy sets that are not semantically meaningful.
1：Experimental Design and Method Selection:
The principle of justifiable granularity is used to form membership functions of fuzzy sets, guided by the criteria of coverage and specificity. The parametric version of the principle is introduced, focusing on information granules in the form of fuzzy sets.
2：Sample Selection and Data Sources:
Numeric data X = {x1, x2, ..., xN} are used to construct an information granule G. The data points come with their corresponding weights wk identifying their relevance.
3：List of Experimental Equipment and Materials:
Not explicitly mentioned in the paper.
4：Experimental Procedures and Operational Workflow:
The bounds a and b of the membership function are optimized separately, guided by the criteria of coverage and specificity. The optimization of the performance index Q(b) = cov*Sp is carried out to determine the optimal bounds.
5：Data Analysis Methods:
The coverage criterion is expressed by computing a sum of membership grades of the data contained in the fuzzy set. Specificity is expressed by quantifying how detailed the fuzzy set is.
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