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Rukhin et al. (2010) proposed the non-overlapping template matching test as one of methods for statistical testing of randomness in cryptographic applications. This test is the very interesting, but statistical properties of this test and any methods on setting the template have not been shown. Our new contribution in this paper is to propose a modified version of this test including the setting of the template and to show how this modified test works effectively by some simulation studies.

approach given by Miyamoto and Mukaidono [3]. The regularization approach can also provide the fuzzy c l w tering with crisp regions by introducing the quadratic regularizing function, for example (151). Our approach differs from the regularization approach, and then results are different. In the regularization approach, the meaning of the regularking function is not necwarily Instead of the regularizing function we introduce an explicit classification function which can be interpreted ezcr ilV A n e w h z z Y k-means clustering m&hod is Proposed by introducing crisp regions of clusters. &~u n d a r~~~ Of the redom are determined hYPerbolas admembenhiP are given b y one o r zero in each region. The area between crisp regiom is a fuzzy region, where membership MIues are P r o P o r t i o n d to distances t o crisp regions-A new method is a direct extension of the traditional hard k-means.

Abstrac-A time series model based on fnzzy if-then rules is intmdnced and its estimation problem is considered. The proposed model is an application of the Takagi-Sugeno's f u z y system and is a generalization of the threshold antoregressive model for time series. The applicability of the proposed model is considered by applying to real time series.