Economic modelling of financial markets means to model highly complex systems in which expectations can be the dominant driving forces. Therefore it is necessary to focus on how agents form their expectations. We believe that they look for patterns, hypothesize, try, make mistakes, learn and adapt. Agents’ bounded rationality leads us to a rule-based approach which we model using Fuzzy Rule-Bas...

The motive of this paper is, to develop accurate and parameter uniform numerical method for solving singularly perturbed delay parabolic differential equation with non-local boundary condition exhibiting layers. Also, the term that occurs in space variable gives rise interior layer. Fitted operator finite difference on mesh uses procedures line spatial discretization backward Euler resulting sy...

In this paper, we study fuzzy calculus in two main branches differential and integral.  Some rules for finding limit and $gH$-derivative of $gH$-difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating  $gH$-derivative of a composite function.  Two techniques namely,  Leibniz's rule and integration by parts are introduced for ...

Fuzzy technology became a very important controlling method in complex systems where traditional methods are unsuccessful. It was proved in [19] that fuzzy rule systems can be used as general approximators of any complex continuous systems. The key element of the approximation process is the construction of the corresponding fuzzy rule system that encapsulates the knowledge on the problem domai...

In fuzzy rule-based classification systems, rule weight has often been used to improve the classification accuracy. In past research, a number of heuristic methods for rule weight specification have been proposed. In this paper, a method of fuzzy rule weight specification using Receiver Operating Characteristic (ROC) analysis is proposed. In order to specify the weight of a fuzzy rule, using 2-...

The Mamdani and TSK fuzzy models are fuzzy inference engines which have been most widely applied in real-world problems. Compared to the Mamdani approach, the TSK approach is more convenient when the crisp outputs are required. Common to both approaches, when a given observation does not overlap with any rule antecedent in the rule base (which usually termed as a sparse rule base), no rule can ...

A fuzzy rule-based classification system (FRBCS) is one of the most popular approaches used in pattern classification problems. One advantage of a fuzzy rule-based system is its interpretability. However, we're faced with some challenges when generating the rule-base. In high dimensional problems, we can not generate every possible rule with respect to all antecedent combinations. In this paper...

Abstract. This paper presents the synthesis and analysis of the enhanced predictive fuzzy Hammerstein model of the water tank system. Fuzzy Hammerstein model was compared with three other fuzzy models: the first was synthesized using Mamdani type rule base, the second – Takagi-Sugeno type rule base and the third – composed of Mamdani and Takagi-Sugeno rule bases. The synthesized model is invert...

In this contribution we carry out an analysis of the Fuzzy Reasoning Methods for Fuzzy Rule Based Classification Systems in the framework of balanced and imbalanced data-sets with different degrees of imbalance. We analyze the behaviour of the Fuzzy Rule Based Classification Systems searching for the best type of Fuzzy Reasoning Method in each case, also studying the cooperation of some pre-pro...

The Kóczy-Hirota Fuzzy Interpolation (“KH” method, Kóczy and Hirota, 1991) is the first method adapting the declarative way of fuzzy function definition and the related “fuzzy dot” rule representation by introducing the concept of Fuzzy Rule Interpolation (FRI). The original KH method had many followers. Most of the FRI methods have difficulties in freely defining the relation of the observatio...