The World of Combinatorial Fuzzy Problems and the Efficiency of Fuzzy Approximation Algorithms

We re-examine a practical aspect of combinatorial fuzzy problems of various types, including search, counting, optimization, and decision problems. We are focused only on those fuzzy problems that take series of fuzzy input objects and produce fuzzy values. To solve such problems efficiently, we design fast fuzzy algorithms, which are modeled by polynomial-time deterministic fuzzy Turing machines equipped with read-only auxiliary tapes and write-only output tapes and also modeled by polynomial-size fuzzy circuits composed of fuzzy gates. We also introduce fuzzy proof verification systems to model the fuzzification of nondeterminism. Those models help us identify four complexity classes: Fuzzy-FPA of fuzzy functions, Fuzzy-PA and Fuzzy-NPA of fuzzy decision problems, and Fuzzy-NPAO of fuzzy optimization problems. Based on a relative approximation scheme targeting fuzzy membership degree, we formulate two notions of "reducibility" in order to compare the computational complexity of two fuzzy problems. These reducibility notions make it possible to locate the most difficult fuzzy problems in Fuzzy-NPA and in Fuzzy-NPAO.Comment: A4, 10pt, 10 pages. This extended abstract already appeared in the Proceedings of the Joint 7th International Conference on Soft Computing and Intelligent Systems (SCIS 2014) and 15th International Symposium on Advanced Intelligent Systems (ISIS 2014), December 3-6, 2014, Institute of Electrical and Electronics Engineers (IEEE), pp. 29-35, 201

An immune algorithm based fuzzy predictive modeling mechanism using variable length coding and multi-objective optimization allied to engineering materials processing

In this paper, a systematic multi-objective fuzzy modeling approach is proposed, which can be regarded as a three-stage modeling procedure. In the first stage, an evolutionary based clustering algorithm is developed to extract an initial fuzzy rule base from the data. Based on this model, a back-propagation algorithm with momentum terms is used to refine the initial fuzzy model. The refined model is then used to seed the initial population of an immune inspired multi-objective optimization algorithm in the third stage to obtain a set of fuzzy models with improved transparency. To tackle the problem of simultaneously optimizing the structure and parameters, a variable length coding scheme is adopted to improve the efficiency of the search. The proposed modeling approach is applied to a real data set from the steel industry. Results show that the proposed approach is capable of eliciting not only accurate but also transparent fuzzy models

A Hybrid Intelligent Early Warning System for Predicting Economic Crises: The Case of China

This paper combines artificial neural networks (ANN), fuzzy optimization and time-series econometric models in one unified framework to form a hybrid intelligent early warning system (EWS) for predicting economic crises. Using quarterly data on 12 macroeconomic and financial variables for the Chinese economy during 1999 and 2008, the paper finds that the hybrid model possesses strong predictive power and the likelihood of economic crises in China during 2009 and 2010 remains high.Computational intelligence; artificial neural networks; fuzzy optimization; early warning system; economic crises

Fuzzy Rules Optimization in Fuzzy Expert System for Machinability Data Selection: Genetic Algorithms Approach

Machinability data selection is complex and cannot be easily formulated by any mathematical model to meet design specification. Fuzzy logic is a good approach to solve such problems. Fuzzy rules optimization is always a problems for a complex fuzzy rules from more than 10 thousand combinations. (Wong et aL 1997) developed fuzzy models for machinability data selection. There are more than 2 x 1029 possible sets of rules for each model. Situation would be more complicated if further increase the number of inputs and/or outputs. The fuzzy rules were selected by trial and error and intuition in reference (Wong et aL 1997). Genetic optimization is suggested in this paper to further optimizing the fuzzy rules optimization with genetic algorithms has been developed. Weighted centroid method is used for output defuzzi fication to save processing time. Comparisons between the results of the new models and the previously published literatures are made

Presenting a fuzzy model for fuzzy portfolio optimization with the mean absolute deviation risk function

The main purpose of this paper is portfolio optimization with the use of fuzzy method based on the mean absolute deviation risk function in firms listed in Tehran Stock Market. In the present research, for the purpose of fuzzy portfolio optimization the stock portfolio Value at Risk criterion and for calculation of this value the parametric method and for fuzzy optimization also the Hybrid intelligent algorithms (genetic algorithms and neural networks) have been used. For selecting the portfolio with 15 during the research time span (2005-2011) fuzzy optimization based on the following six criteria were used including Asymmetric Value at Risk, Symmetric Value at Risk , Interval Value at Risk (interval of 5%-95%), Interval Value at Risk (interval of 10%-90%), and Normal Value at Risk. Since the calculated probability ratio statistic Kupiec based on fuzzy optimization for the 6 above mentioned models is larger than the obtained critical value from chi-square distribution at the confidence level of 95%, the research hypothesis stating that the application of fuzzy optimization method improves the efficiency of portfolio in the actual world problems with lack of certainty was confirmed. Also, the results of the Kupiec probability ratio statistic indicate that the model of value at risk based on the mean absolute deviation risk function (MVAR) is more successful and have less failure comparing to other models, hence; the research hypothesis stating that fuzzy variables have a higher ability in modeling asymmetric uncertainties in financial domains is also confirmed

Presenting a fuzzy model for fuzzy portfolio optimization with the mean absolute deviation risk function

The main purpose of this paper is portfolio optimization with the use of fuzzy method based on the mean absolute deviation risk function in firms listed in Tehran Stock Market. In the present research, for the purpose of fuzzy portfolio optimization the stock portfolio Value at Risk criterion and for calculation of this value the parametric method and for fuzzy optimization also the Hybrid intelligent algorithms (genetic algorithms and neural networks) have been used. For selecting the portfolio with 15 during the research time span (2005-2011) fuzzy optimization based on the following six criteria were used including Asymmetric Value at Risk, Symmetric Value at Risk , Interval Value at Risk (interval of 5%-95%), Interval Value at Risk (interval of 10%-90%), and Normal Value at Risk. Since the calculated probability ratio statistic Kupiec based on fuzzy optimization for the 6 above mentioned models is larger than the obtained critical value from chi-square distribution at the confidence level of 95%, the research hypothesis stating that the application of fuzzy optimization method improves the efficiency of portfolio in the actual world problems with lack of certainty was confirmed. Also, the results of the Kupiec probability ratio statistic indicate that the model of value at risk based on the mean absolute deviation risk function (MVAR) is more successful and have less failure comparing to other models, hence; the research hypothesis stating that fuzzy variables have a higher ability in modeling asymmetric uncertainties in financial domains is also confirmed

Presenting a fuzzy model for fuzzy portfolio optimization with the mean absolute deviation risk function

The main purpose of this paper is portfolio optimization with the use of fuzzy method based on the mean absolute deviation risk function in firms listed in Tehran Stock Market. In the present research, for the purpose of fuzzy portfolio optimization the stock portfolio Value at Risk criterion and for calculation of this value the parametric method and for fuzzy optimization also the Hybrid intelligent algorithms (genetic algorithms and neural networks) have been used. For selecting the portfolio with 15 during the research time span (2005-2011) fuzzy optimization based on the following six criteria were used including Asymmetric Value at Risk, Symmetric Value at Risk , Interval Value at Risk (interval of 5%-95%), Interval Value at Risk (interval of 10%-90%), and Normal Value at Risk. Since the calculated probability ratio statistic Kupiec based on fuzzy optimization for the 6 above mentioned models is larger than the obtained critical value from chi-square distribution at the confidence level of 95%, the research hypothesis stating that the application of fuzzy optimization method improves the efficiency of portfolio in the actual world problems with lack of certainty was confirmed. Also, the results of the Kupiec probability ratio statistic indicate that the model of value at risk based on the mean absolute deviation risk function (MVAR) is more successful and have less failure comparing to other models, hence; the research hypothesis stating that fuzzy variables have a higher ability in modeling asymmetric uncertainties in financial domains is also confirmed