Nonlinear location and scale estimators of fuzzy numbers

In this correspondence, the extension principle is used in order to fuzzify location and scale estimators when used on fuzzy numbers. First, fuzzy nonlinear means are defined as extensions of the corresponding crisp means. Fuzzy L location and scale estimators, which are based on fuzzy-order statistics, are defined as extensions of the crisp L location and scale estimators. The most widely used scale estimator, which is known as 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.