Extracting Interpretable Fuzzy Models for Nonlinear Systems Using Gradient-based Continuous Ant Colony OptimizationEftekhari, M.; Zeinalkhani, M.
2013 Fuzzy Information and Engineering
doi: 10.1007/s12543-013-0144-2
AbstractThis paper exploits the ability of a novel ant colony optimization algorithm called gradient-based continuous ant colony optimization, an evolutionary methodology, to extract interpretable first-order fuzzy Sugeno models for nonlinear system identification. The proposed method considers all objectives of system identification task, namely accuracy, interpretability, compactness and validity conditions. First, an initial structure of model is obtained by means of subtractive clustering. Then, an iterative two-step algorithm is employed to produce a simplified fuzzy model in terms of number of fuzzy sets and rules. In the first step, the parameters of the model are adjusted by utilizing the gradient-based continuous ant colony optimization. In the second step, the similar membership functions of an obtained model merge. The results obtained on three case studies illustrate the applicability of the proposed method to extract accurate and interpretable fuzzy models for nonlinear system identification.
Note on New Solutions of LR Fuzzy Linear Systems Using Ranking Functions and ABS AlgorithmsGhanbari, Mojtaba; Nuraei, Rahele
2013 Fuzzy Information and Engineering
doi: 10.1007/s12543-013-0145-1
AbstractRecently, Ghanbari and Mahdavi-Amiri focused on solving LR fuzzy linear systems by use of ranking functions. They applied a ranking function introduced by Cheng, which is based on the centroid point, to illustrate their method. Also, they presented an important lemma using the centroid formulae provided by Cheng, to determine the centroid point for a class of fuzzy numbers. Unfortunately, they didn't consider that the formulae are incorrect and have led to some misapplications as pointed out by Wang and his colleagues. Therefore, in this paper, we first show that Lemma 19 of Ghanbari and Mahdavi-Amiri's paper is not true and then correct it using the centroid formulae suggested by Wang. Finally, we correct the results obtained in Ghanbari and Mahdavi-Amiri's paper for a special example.
Fuzzy Quasi C*-algebraFattahi, Fatemeh
2013 Fuzzy Information and Engineering
doi: 10.1007/s12543-013-0152-2
AbstractAt the present paper, the new concepts of fuzzy quasi norm, fuzzy Banach space, fuzzy quasi continuity and fuzzy quasi boundedness is introduced. Furthermore, we define the fuzzy quasi operator norm and also it is shown that the set all of fuzzy quasi bounded operator from X to Y is fuzzy quasi Banach space. Finally, we have introduced and investigated some notions and some results on *-algebra theory.
Environmental Risk Modelling under Probability-normal Interval-valued Fuzzy NumberChutia, Rituparna
2013 Fuzzy Information and Engineering
doi: 10.1007/s12543-013-0150-4
AbstractIn almost all the realistic circumstances, such as health risk assessment and uncertainty analysis of atmospheric dispersion, it is very essential to include all the information into modelling. The parameters associated to a particular model may include different kind of variability, imprecision and uncertainty. More often, it is seen that available informations are interpreted in probabilistic sense. Probability theory is a well-established theory to measure such kind of variability. However, not all of available information, data or model parameters affected by variability, imprecision and uncertainty can be handled by traditional probability theory. Uncertainty or imprecision may occur due to incomplete information or data, measurement errors or data obtained from expert judgement or subjective interpretation of available data or information. Thus, model parameters, data may be affected by subjective uncertainty. Traditional probability theory is inappropriate to represent them. Possibility theory and fuzzy set theory is another branch of mathematics which is used as a tool to describe the parameters with insufficient or vague knowledge. In this paper, an attempt has been made to combine probability knowledge and possibility knowledge and draw the uncertainty. The paper describes an algorithm for combining probability distribution and interval-valued fuzzy number and applied to environmental risk modelling with a case study. The primary aim of this paper is to propagate the proposed method. Computer codes are prepared for the proposed method using MATLAB.