(R1958) On Deferred Statistical Convergence of Fuzzy Variables

In this paper, within framework credibility theory, we examine several notions of convergence and statistical convergence of fuzzy variable sequences. The convergence of fuzzy variable sequences such as the notion of convergence in credibility, convergence in distribution, convergence in mean, and convergence uniformly virtually certainly via postponed Cesàro mean and a regular matrix are researched using fuzzy variables. We investigate the connections between these concepts. Significant results on deferred statistical convergence for fuzzy variable sequences are thoroughly investigated

A fuzzy decision variables framework based on directed sampling for large-scale multiobjective optimization

The enormous search space in large-scale multiobjective optimization presents a significant challenge to the convergence of existing evolutionary algorithms (EAs). It is necessary to further improve the convergence efficiency of the fuzzy decision variables framework (FDV) for large-scale multiobjective optimization. Therefore, this paper proposes a fuzzy decision variables framework based on directed sampling (FDVDS) for large-scale multiobjective optimization. After initializing the population, guided solutions are generated by directed sampling to improve the diversity of the population and speed up the convergence of the population. Finally, some representative EAs are embedded into FDVDS, and the framework’s effectiveness is verified by performing comparative experiments on large-scale multiobjective optimization test problems with up to 5000 decision variables

Fuzzy Adaptive Tuning of a Particle Swarm Optimization Algorithm for Variable-Strength Combinatorial Test Suite Generation

Combinatorial interaction testing is an important software testing technique that has seen lots of recent interest. It can reduce the number of test cases needed by considering interactions between combinations of input parameters. Empirical evidence shows that it effectively detects faults, in particular, for highly configurable software systems. In real-world software testing, the input variables may vary in how strongly they interact, variable strength combinatorial interaction testing (VS-CIT) can exploit this for higher effectiveness. The generation of variable strength test suites is a non-deterministic polynomial-time (NP) hard computational problem \cite{BestounKamalFuzzy2017}. Research has shown that stochastic population-based algorithms such as particle swarm optimization (PSO) can be efficient compared to alternatives for VS-CIT problems. Nevertheless, they require detailed control for the exploitation and exploration trade-off to avoid premature convergence (i.e. being trapped in local optima) as well as to enhance the solution diversity. Here, we present a new variant of PSO based on Mamdani fuzzy inference system \cite{Camastra2015,TSAKIRIDIS2017257,KHOSRAVANIAN2016280}, to permit adaptive selection of its global and local search operations. We detail the design of this combined algorithm and evaluate it through experiments on multiple synthetic and benchmark problems. We conclude that fuzzy adaptive selection of global and local search operations is, at least, feasible as it performs only second-best to a discrete variant of PSO, called DPSO. Concerning obtaining the best mean test suite size, the fuzzy adaptation even outperforms DPSO occasionally. We discuss the reasons behind this performance and outline relevant areas of future work.Comment: 21 page

Unknown input observer for Takagi-Sugeno implicit models with unmeasurable premise variables

Recent years have seen a great deal of interest in implicit nonlinear systems, which are used in many different engineering applications. This study is dedicated to presenting a new method of fuzzy unknown inputs observer design to estimate simultaneously both non-measurable states and unknown inputs of continuous-time nonlinear implicit systems defined by Takagi-Sugeno (T-S) models with unmeasurable premise variables. The suggested observer is based on the singular value decomposition approach and rewritten the continuous-time T-S implicit models into an augmented fuzzy system, which gathers the unknown inputs and the state vector. The exponential convergence condition of the observer is established by using the Lyapunov theory and linear matrix inequalities are solved to determine the gains of the observer. Finally, the effectiveness of the suggested method is then assessed using a numerical application. It demonstrates that the estimated variables and the unknown input converge to the real variables accurately and quickly (less than 0.5 s)

Fuzzy Logic Modeling and Observers Applied to Estimate Compositions in Batch Distillation Columns

In this chapter, the analysis and design of a fuzzy observer based on a Takagi-Sugeno model of a batch distillation column are presented. The observer estimates the molar compositions and temperatures of the light component in the distillation column considering a binary mixture. This estimation aims to allow monitoring the physical variables in the process to improve the quality of the distillated product as well as to detect failures that could affect the system performance. The Takagi-Sugeno fuzzy model is based on eight linear subsystems determined by three premise variables: the opening percentage of the reflux valve and the liquid molar composition of the light element of the binary mixture in the boiler and in the condenser. The stability analysis and the observer gains are obtained by linear matrix inequalities (LMIs). The observer is validated by MATLAB® simulations using real data obtained from a distillation column to verify the observer’s convergence and analyze its response under system disturbances

Approximating Pareto frontier using a hybrid line search approach

This is the post-print version of the final paper published in Information Sciences. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2010 Elsevier B.V.The aggregation of objectives in multiple criteria programming is one of the simplest and widely used approach. But it is well known that this technique sometimes fail in different aspects for determining the Pareto frontier. This paper proposes a new approach for multicriteria optimization, which aggregates the objective functions and uses a line search method in order to locate an approximate efficient point. Once the first Pareto solution is obtained, a simplified version of the former one is used in the context of Pareto dominance to obtain a set of efficient points, which will assure a thorough distribution of solutions on the Pareto frontier. In the current form, the proposed technique is well suitable for problems having multiple objectives (it is not limited to bi-objective problems) and require the functions to be continuous twice differentiable. In order to assess the effectiveness of this approach, some experiments were performed and compared with two recent well known population-based metaheuristics namely ParEGO and NSGA II. When compared to ParEGO and NSGA II, the proposed approach not only assures a better convergence to the Pareto frontier but also illustrates a good distribution of solutions. From a computational point of view, both stages of the line search converge within a short time (average about 150 ms for the first stage and about 20 ms for the second stage). Apart from this, the proposed technique is very simple, easy to implement and use to solve multiobjective problems.CNCSIS IDEI 2412, Romani

"Can Banks Learn to Be Rational?"

Can banks learn to be rational in their lending activities? The answer depends on the institutionally bounded constraints to learning. From an evolutionary perspective the functionality (for survival) of "learning to be rational" creates strong incentives for such learning without, however, guaranteeing that each member of the particular economic species actually achieves increased fitness. I investigate this issue for a particular economic species, namely, commrercial banks. The purpose of this paper is to illustrate the key issues related to learning in an economic model by proposing a new screening model for bank commercial loans that uses the neuro fuzzy technique. The technical modeling aspect is integrally connected in a rigorous way to the key conceptual and theoretical aspects of the capabilities for learning to be rational in a broad but precise sense. This paper also compares the relative predictability of loan default among three methods of prediction--- discriminant analysis, logit type regression, and neuro fuzzy--- based on the real data obtained from one of the banks in Taiwan.The neuro fuzzy model, in contrast with the other two, incorporates recursive learning in a real world, imprecise linguistic environment. The empirical results show that in addition to its better screening ability, the neuro fuzzy model is superior in explaining the relationship among the variables as well. With further modifications,this model could be used by bank regulatory agencies for loan examination and by bank loan officers for loan review. The main theoretical conclusion to draw from this demonstration is that non-linear learning in a vague semantic world is both possible and useful. Therefore the search for alternatives to the full neoclassical rationality and its equivalent under uncertainty---rational expectations--- is a plausible and desirable search, especially when the probability for convergence to a rational expectations equilibrium is low.