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

Moments and Semi-Moments for fuzzy portfolios selection

The aim of this paper is to consider the moments and the semi-moments (i.e semi-kurtosis) for portfolio selection with fuzzy risk factors (i.e. trapezoidal risk factors). In order to measure the leptokurtocity of fuzzy portfolio return, notions of moments (i.e. Kurtosis) kurtosis and semi-moments(i.e. Semi-kurtosis) for fuzzy port- folios are originally introduced in this paper, and their mathematical properties are studied. As an extension of the mean-semivariance-skewness model for fuzzy portfolio, the mean-semivariance-skewness- semikurtosis is presented and its four corresponding variants are also considered. We briefly designed the genetic algorithm integrating fuzzy simulation for our optimization models.Fuzzy moments, Credibility theory, Portfolios, Asset allocation, multi-objective optimization

The Application of Imperialist Competitive Algorithm for Fuzzy Random Portfolio Selection Problem

This paper presents an implementation of the Imperialist Competitive Algorithm (ICA) for solving the fuzzy random portfolio selection problem where the asset returns are represented by fuzzy random variables. Portfolio Optimization is an important research field in modern finance. By using the necessity-based model, fuzzy random variables reformulate to the linear programming and ICA will be designed to find the optimum solution. To show the efficiency of the proposed method, a numerical example illustrates the whole idea on implementation of ICA for fuzzy random portfolio selection problem.Comment: 5 pages, 2 tables, Published with International Journal of Computer Applications (IJCA

A fuzzy approach to building thermal systems optimization.

Optimization of building thermal systems is treated in the paper in the framework of fuzzy mathematical programming. This new approach allows to formulate more precisely the problem which compromises energy saving and thermal comfort satisfaction under given constraints. Fuzzy optimization problem is solved analytically under some assumptions. An example illustrates the viability of the approach proposed. A solution which significantly (with 38%) improves comfort is found which is more energetically expensive with only 0.6%. (c) IFS

A review of training methods of ANFIS for applications in business and economic

Fuzzy Neural Networks (FNNs) techniques have been effectively used in applications that range from medical to mechanical engineering, to business and economics. Despite of attracting researchers in recent years and outperforming other fuzzy systems, Adaptive Neuro-Fuzzy Inference System (ANFIS) still needs effective parameter training and rule-base optimization methods to perform efficiently when the number of inputs increase. Moreover, the standard gradient based learning via two pass learning algorithm is prone slow and prone to get stuck in local minima. Therefore many researchers have trained ANFIS parameters using metaheuristic algorithms however very few have considered optimizing the ANFIS rule-base. Mostly Particle Swarm Optimization (PSO) and its variants have been applied for training approaches used. Other than that, Genetic Algorithm (GA), Firefly Algorithm (FA), Ant Bee Colony (ABC) optimization methods have been employed for effective training of ANFIS networks when solving various problems in the field of business and finance