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Based on the area between the curve of the membership function and the horizontal real axes, a new index, called the expansion center for fuzzy numbers is proposed. An intuitive and reasonable ranking method for fuzzy numbers based on their expansion center is also established. This new ranking method is useful in fuzzy decision making and fuzzy data mining.
The concept of fuzzy numbers is a generalization of the concept of real numbers. Intuitively, there are more fuzzy numbers than real numbers, that is, the cardinality of the set consisting of all fuzzy numbers should not be smaller than the cardinality of the set of all real numbers. In this work, based on a newly established Decomposition Theorem IV for fuzzy sets, a one-to-one mapping from the set...
Based on the area between the curve of the membership function and the horizontal real axis, concepts of left and right wingspans are introduced. By them, a new index, called the w-center for fuzzy numbers is proposed. It is continuous with respect to the convergence of fuzzy number sequence. An intuitive and reasonable ranking method for fuzzy numbers based on their w-center is also established....
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