Nonlinear location and scale estimators of fuzzy numbers

In this paper, the extension principle is used in order to fuzzify location and scale estimators when used on fuzzy numbers. First, fuzzy nonlinear means, such as arithmetic, harmonic, geometric and fuzzy L p mean are deened as extensions of the corresponding crisp means. Fuzzy maximum and minimum operators are used to deene order statistics of fuzzy numbers. Fuzzy L location and scale estimators, which are based on fuzzy order statistics, are deened as extensions of the crisp L location and scale estimators. The most widely used scale estimator, the sample standard deviation, is also extended to fuzzy numbers, through the extension principle. Equivalent relations that can be used to calculate the fuzzy estimators by using crisp arithmetic are also given, for each one of the proposed fuzzy estimators.