Fuzzy Modeling by Active Learning Method

Abstract

The constructions of different modeling methods are similar. The models are consisted of the following major stages: 1Recognizing the true or most effective inputs. 2Finding the numerical relationship between inputs and output. 3Explaining the numerical relationship mathematically. 4Utilizing the mathematical expressions to calculate the output using different inputs. 5Comparing the calculated and actual outputs and calculating the error. 6Modifying the mathematical expressions based on the calculated error. These stages seem to be complicated. This complexity seems to be due to the quantitative and exact definitions of the mentioned stages (Bagheri Shouraki and Honda, 1998). There are some demonstrations that the mentioned stages are performed qualitative with nonexact concepts in the human brain (Schmidt, 1985), therefore any effort toward of expressing them using exact expressions (such as mathematics) are expected to have some differences with human thinking or modeling method. In the other words, the utilizing of exact mathematics in modeling has contradiction with human abilities (Bagheri Shouraki and Honda, 1999). Fuzzy concepts (e.g. Zadeh 1965) and related inferences (e.g. Mamdani 1974) proposed a new approach to human modeling and calculation methods. Although, different powerful fuzzy modeling methods have been developed up to now, but some of these methods are different with real human modeling method, because of utilized mathematics and exact calculations in their constructions (Bagheri Shouraki and Honda, 1999). The construction of human modeling is similar to the above stages, but avoids of mathematical complexities. Active Learning Method (ALM) is one of the fuzzy modeling methods Which uses basic level of mathematics. ALM was innovated by Bagheri Shouraki and Honda (1997). ALM has very simple algorithm that avoids of mathematical complexity and its accuracy and exactness increase unlimitedly by increasing the number of iterations of its algorithm. It is very difficult for human to memorize the numerical data points but tries to memorize the general behavior function of data points. In addition, for modeling, the human converts a MIMO (Multi Inputs Multi Outputs) system to some SISO (Single Input – Single Output) systems and then human tries to find the general behavior function in each SISO system and the effects of other inputs are considered as the deviation of data points around of the general behavior function. In addition, human can save the data points on a continuous path 12