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The conventional fuzzy least-squares time series models show undesirable performance when the fuzzy data set involves the outliers. By introducing a strategy to detect the outliers, this paper introduced a method for reducing the influence of outliers on the future predictions. For this purpose, according to the weighted square distance error, an estimation procedure was suggested for determining the exact coefficients in the presence of outliers. The parameters of the fuzzy time series model were then estimated using an iterative algorithm. In order to identify the potential outliers of the fuzzy data, a quality control chart was employed based on the center of gravity criterion of fuzzy data. The defuzzification method was also employed to examine the performance of the proposed method via some scatter plots. Several common goodness-of-fit criteria used in traditional time series models were also extended to compare the performance of the proposed fuzzy time series method to an existing method. The effectiveness of the proposed method was illustrated through two numerical examples including a simulation study. The results clearly indicated that the proposed model performs well in terms of the both scatter plot criteria and goodness-of-fit evaluations in cases where the potential outliers exist among the fuzzy data. [ABSTRACT FROM AUTHOR]

Parametric time series models typically consists of model identification, parameter estimation, model diagnostic checking, and forecasting. However compared with parametric methods, nonparametric time series models often provide a very flexible approach to bring out the features of the observed time series. This paper suggested a novel fuzzy nonparametric method in time series models with fuzzy observations. For this purpose, a fuzzy forward fit kernel-based smoothing method was introduced to estimate fuzzy smooth functions corresponding to each observation. A simple optimization algorithm was also suggested to evaluate optimal bandwidths and autoregressive order. Several common goodness-of-fit criteria were also extended to compare the performance of the proposed fuzzy time series method compared to other fuzzy time series model based on fuzzy data. Furthermore, the effectiveness of the proposed method was illustrated through two numerical examples including a simulation study. The results indicate that the proposed model performs better than the previous ones in terms of both scatter plot criteria and goodness-of-fit evaluations. [ABSTRACT FROM AUTHOR]

This paper proposed an extension for the classical partial univariate regression model with non-fuzzy inputs and triangular fuzzy output. For this purpose, the popular non-parametric estimator and the conventional arithmetic operations of triangular fuzzy numbers were combined to construct a fuzzy univariate regression model. Then, a hybrid algorithm was developed to estimate the bandwidth and fuzzy regression coefficient. Some common goodness-of-fit criteria were also used to examine the performance of the proposed method. The effectiveness of the proposed method was then illustrated through two numerical examples including a simulation study. The proposed method was also compared with several common fuzzy linear regression models with exact inputs and fuzzy outputs. Compared to the available fuzzy linear regressions models, the numerical results clearly indicated that the proposed fuzzy regression model is capable of exhibiting more accurate performances. [ABSTRACT FROM AUTHOR]

This paper suggests a novel approach for ranking the most applicable fuzzy numbers, i.e. LR-luzzy numbers. Applying the α-optimistic values of a fuzzy number, a preference criterion is proposed for ranking fuzzy numbers using the Credibility index. The main properties of the proposed preference criterion are also studied. Moreover, the proposed method is applied for ranking fuzzy numbers using target-rank-based methods. Some numerical examples are used to illustrate the proposed ranking procedure. The proposed preference criterion is also examined in order to compare with some common methods and the feasibility and effectiveness of the proposed ranking method is cleared via some numerical comparisons. [ABSTRACT FROM AUTHOR]

This article modifies evaluating the probability of a fuzzy event based on a classical probability space introduced by Yager ( Inform. Sci. 1979;18:113-122). The presented theoretical results will be illustrated with some propositions and remarks. It is shown that a modification in the definition of fuzzy probability of fuzzy events into a concept of such probabilities has some desirable properties from mathematical points of view. Then, the proposed fuzzy probability will be compared to that of the similar proposed methods. The proposed fuzzy probability will be illustrated with some numerical examples. [ABSTRACT FROM AUTHOR]

A lot of methods and models in classical reliability theory assume that all parameters of lifetime density function are precise. But in the real world applications imprecise information is often mixed up in the lifetimes and/or parameters of systems. However, the parameters sometimes cannot be recorded precisely due to machine errors, experiment, personal judgment, estimation or some other unexpected situations. When parameters in the lifetime distribution are interval-valued, the conventional reliability system may have difficulty for handling reliability function. Therefore, estimation methods for reliability characteristics have to be adapted to the situation of interval-valued parameters of life times in order to obtain more realistic results. In this regard, the present paper will discuss the system reliability for coherent system based on a new notion of random variable with interval-valued parameters. The concepts of probability density function and cumulative distribution function of the random variable with interval-valued parameters will be stated in this paper. Using the same techniques in classical probability theory, the probability measure of the random variable can be constructed from the probability density function and cumulative distribution function. In the proceeding discussion, several numerical examples are provided in reliability systems and queueing theory to clarify our discussions. [ABSTRACT FROM AUTHOR]