It is well known that a conventional feedforward neural network always has bias terms, which is necessary for it to solve classification or approximation problems. But for fuzzy neural networks (FNNs), it seems not quite clear yet whether the bias is dispensable or not. Some authors introduce the bias, while the others do not. This note tries to partly answer this question for two simple buildi...

This paper discusses robust function approximation when the Takagi-Sugeno type model is used for the consequent part of fuzzy rules. With this model, the parameters of the liner equation that defines the output value of the fuzzy rule are determined by the least-squares method. Therefore, if the training data include outliers, the method fails to determine the parameter values correctly. To ove...

We will focus here on approximating functions that map from the vector-valued real domain to the vector-valued real range. A Fuzzy ARTMAP (FAM) architecture, called Fuzzy Artmap with Relevance factor (FAMR, defined in [1]) is considered here as an alternative to function approximation. FAMR uses a relevance factor assigned to each sample pair, proportional to the importance of the respective pa...

Traditional approaches for modeling TSK fuzzy rules are trying to adjust the parameters in models, and not considering the training data distribution. Hence it will result in an improper clustering structure, especially, when outliers exist. In this paper, a clustering algorithm termed as Robust Proper Structure Fuzzy Regression Algorithm (RPSFR) is proposed to define fuzzy subspaces in a fuzzy...

Reinforcement learning (RL) is a machine learning technique for sequential decision making. This approach is well proven in many small-scale domains. The true potential of this technique cannot be fully realised until it can adequately deal with the large domain sizes that typically describe real world problems. RL with function approximation is one method of dealing with the domain size proble...

Fuzzy techniques have been originally invented as a methodology that transforms the knowledge of experts formulated in terms of natural language into a precise computer-implementable form. There are many successful applications of this methodology to situations in which expert knowledge exist, the most well known is an application to fuzzy control. In some cases, fuzzy methodology is applied ev...

The main goal of the structural optimization is to minimize the weight of structure or the vertical deflection of loaded joint while satisfying all design requirements imposed by design codes. In general fuzzy sets are used to analyze the fuzzy structural optimization. In this paper, a planer truss structural model in intuitionistic fuzzy environment has been developed. This paper proposes an i...

Since many real-world engineering systems are too complex to be defined in precise terms, imprecision is often involved in any engineering design process. Fuzzy linear programming problems have an essential role in fuzzy modeling, which can formulate uncertainty in actual environment. One of the most practicable subjects in recent studies is based on LR fuzzy number, which was defined and used ...