Possibility measure based fuzzy support function machine for set-based fuzzy classifications.

In real-world applications, there are many set-based fuzzy classifications. However, the current researches have some limitations in solving such classifications. Therefore, a method called possibility measure based fuzzy support function machine (PMFSFM) is discussed in this work. Firstly, two notes are provided as improvement of SFM in theoretical and experimental perspective. Secondly, a set-based fuzzy classification in Euclidean space Rd is converted into a function-based task in Banach space C(S) based on support function and membership degree. Thirdly, a fuzzy optimization problem based on possibility measure is derived and some properties are discussed. Subsequently, a PMFSFM for set-based fuzzy classification is constructed, and it can give both the fuzzy class and the membership degree of a given input to the fuzzy class. Experiment results concerning water quality evaluation in fuzzy environment show the effectiveness of PMFSFM.