Search

The development of a conventional cumulative entropy was reported in this research within a fuzzy domain. For this purpose, the cumulative entropy and its estimators were developed based on fuzzy random variables to explore the predictability of the failure time of a system. Some common properties of the proposed fuzzy cumulative entropy and fuzzy empirical cumulative entropy were also discussed. The developed fuzzy entropies were illustrated via several numerical evaluations. [ABSTRACT FROM AUTHOR]

There are several studies on fuzzy univariate hypothesis tests corresponding to a normal distribution. A fuzzy statistical test was proposed in this study for mean and variance–covariance matrix of a multivariate normal with fuzzy random variables. For this purpose, a notion of fuzzy multivariate normal random variable with fuzzy mean and non-fuzzy variance–covariance matrix was first developed. Then, the concepts of the fuzzy type-I error, fuzzy type-II error, fuzzy power, non-fuzzy significance level and fuzzy p-value were extended. A degree-based criterion was also suggested to compare the fuzzy p-values as well as a specific significance level to decide whether accepting or rejecting the underlying hypotheses. The effectiveness of the proposed fuzzy hypothesis test was also examined through some numerical examples. [ABSTRACT FROM AUTHOR]

This paper extends the ordinary kriging prediction method and proposes a trend removal method for observed spatial data represented as LR-fuzzy numbers. To this end, a covariance concept was developed and discussed in the fuzzy domain. Then, a notion of semi-variogram and its empirical estimator were proposed. The proposed semi-variogram exhibited all of the characteristics of a typical semi-variogram in the fuzzy domain. A non-parametric kernel-based method was proposed to remove the trend across the fuzzy data. Some common goodness-of-fit criteria were employed to examine the performance of the proposed kriging prediction method. The proposed method was then put to test using a simulated set of fuzzy data. In order to demonstrate the applicability of this approach, it was applied to a set of pH data in the fuzzy domain to investigate the quality of groundwater. The results proved the potentials of the proposed method for the fuzzy spatial data encountered in real applications. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to introduce a notion of fuzzy absolute error distance measure between two fuzzy numbers. For this purpose, a notion of generalised difference operation between two fuzzy numbers and absolute value of a fuzzy number was first introduced. The proposed methods were conducted on the basis of α-values of fuzzy numbers. Main properties of the proposed fuzzy distance measure was also verified in the space of fuzzy numbers. The proposed fuzzy distance measure evaluates the fuzzy distance between the two fuzzy numbers as a fuzzy number. Notably, the main advantage of such generalised difference operation is that it always exists. Therefore, it improves the shortcoming of a well-known generalised difference operation called Hakuhara difference. Some of the main properties of the proposed fuzzy absolute error distance measure including robustness were also studied in the space of fuzzy numbers. Several fuzzy distance measures, especially fuzzy absolute error distance, have been proposed so far. However, none of them save all reasonable properties required for an absolute error distance measure in fuzzy environment. Shortcomings relevant to other methods and advantages of the proposed method were also discussed. [ABSTRACT FROM AUTHOR]