Iranian journal of fuzzy systems
Volume:11 Issue: 3, Jun 2014

Annihilation or reduction of each kind of noise blended in correct data signals is a field that has attracted many researchers. It is a fact that fuzzy theory presents full capability in this field. Fuzzy filters are often strong in smoothing corrupted signals, whereas they have simple structures. In this paper, a new powerful yet simple fuzzy procedure is introduced for sharpness reduction in two-dimensional signals. It is indeed an extension of our previously published one-dimensional fuzzy smoothing filter. This procedure has been designed for annihilation of all unknown noises in two-dimensional corrupted signals, although works the best for impulse noise. The proposed method looks for emph{sharp points} in the corrupted signal and then smoothes them out by emph{sharing} their values with eight (or more) neighboring point values. Preservation of correct data in the corrupted signal is an important advantage of this method. To obtain experimental results of the proposed procedure, both color and black & white images are used as the most common two-dimensional signals, and the results are compared with several other filters recently cited in the literature. Experimental results exhibit a high capability of our method in both numerical measures and visual inspection, preserving its simplicity. Finally, application of the proposed filter to socio-economic fields is presented using a demographic mixed data set to better illustrate original motivation for this idea.

The option-pricing problem is always an important part in modern finance. Assuming that the stock diffusion is a constant, some literature has introduced many stock models and given corresponding option pricing formulas within the framework of the uncertainty theory. In this paper, we propose a new stock model with uncertain stock diffusion for uncertain markets. Some option pricing formulas on the proposed uncertain stock model are derived and a numerical calculation is illustrated.

In this paper, we propose a new residual analysis method using Fourier series transform into fuzzy time series model for improving the forecasting performance. This hybrid model takes advantage of the high predictable power of fuzzy time series model and Fourier series transform to fit the estimated residuals into frequency spectra, select the low-frequency terms, filter out high-frequency terms, and then have well forecasting performance.Two numerical examples are given to show that our proposed model can be applied with the best forecasting performance than the other models.

Fuzzy Rule-Based Classification Systems (FRBCS) are highly investigated by researchers due to their noise-stability and interpretability. Unfortunately, generating a rule-base which is sufficiently both accurate and interpretable, is a hard process. Rule weighting is one of the approaches to improve the accuracy of a pre-generated rule-base without modifying the original rules. Most of the proposed methods by now, may over-fit on training data due to generating complex decision boundaries. In this paper, a margin-based optimization model is proposed to improve the performance on unseen data. By this model, fixed-size margins are defined along the decision boundaries and the rule weights are adjusted such that the marginal space would be empty of training instances as much as possible. This model is proposed to support the single-winner reasoning method with a special cost-function to remove undesired effects of noisy instances. The model is proposed to be solved by a fast well-known local search method. With this solving method, a huge amount of irrelevant and redundant rules are removed as a side effect.Two artificial and 16 real world datasets from UCI repository are used to show that the proposed method significantly outperforms other methods with proper choice of the margin size, which is the single parameter of this method.

Predicting different behaviors in computer networks is the subject of many data mining researches. Providing a balanced Intrusion Detection System (IDS) that directly addresses the trade-off between the ability to detect new attack types and providing low false detection rate is a fundamental challenge. Many of the proposed methods perform well in one of the two aspects, and concentrate on a subset of system requirements. There are many non-functional requirements for an applicable and practical IDS. The process should be online, incremental and adaptive to ever changing behaviors of normal users and attackers. Moreover providing comprehensive and interactive IDS could both, enhance the performance of the system and extend the knowledge of domain experts.In this paper, we propose a fuzzy rule-based classification system using a hierarchical rule learning method. In each stage of the hierarchy, a set of rules with certain length of antecedent are investigated. A novel rule weighting method, based on the entropy measure, determines the appropriateness of each rule. The experimental results on KDD99 intrusion detection dataset show the effectiveness of the proposed method in tackling the tradeoff between accuracy and comprehensibility of fuzzy rule-based systems. Although the dimension of antecedents is not limited, the resultant rule-base contains a small number of complex rules, which are essential to reach the desired accuracy.

Motivated by Samet et al. [Nonlinear Anal., 75(4) (2012), 2154-2165], we introduce the notions of $alpha$-$phi$-fuzzy contractive mapping and $beta$-$psi$-fuzzy contractive mapping and prove two theorems which ensure the existence and uniqueness of a fixed point for these two types of mappings. The presented theorems extend, generalize and improve the corresponding results given in the literature.

Following the idea of $L$-fuzzy neighborhood system as introduced by Fu-Gui Shi, and its generalization to $(L,M)$-fuzzy neighborhood system, the relationship between $(L,M)$-fuzzy topology and $(L,M)$-fuzzy neighborhood system will be further studied. As an application of the obtained results, we will describe the initial structures of $(L,M)$-fuzzy neighborhood subspaces and $(L,M)$-fuzzy topological product spaces.

We introduce and study fuzzy (co-)inner product and fuzzy (co-)norm of hyperspaces. In this regard by considering the notion of hyperspaces, as a generalization of vector spaces, first we will introduce the notion of fuzzy (co-)inner product in hyperspaces and will apply it to formulate the notions of fuzzy (co-)norm and fuzzy (co-)orthogonality in hyperspaces. In particular, we will prove that to every fuzzy hyperspace there is an associated unique fuzzy inner product in a natural way.