Etemadi Fuzzy Linear Regression (EFLR)

Modeling and forecasting are among the most powerful and widely-used tools in decision support systems. The Fuzzy Linear Regression (FLR) is the most fundamental method in the fuzzy modeling area in which the uncertain relationship between the target and explanatory variables is estimated and has been frequently used in a broad range of real-world applications efficaciously. The operation logic in this method is to minimize the vagueness of the model, defined as the sum of individual spreads of the fuzzy coefficients. Although this process is coherent and can obtain the narrowest α-cut interval and exceptionally the most accurate results in the training data sets, it can not guarantee to achieve the desired level of generalization. While the quality of made managerial decisions in the modeling-based field is dependent on the generalization ability of the used method. On the other hand, the generalizability of a method is generally dependent on the precision as well as reliability of results, simultaneously. In this paper, a novel methodology is presented for the fuzzy linear regression modeling; in which in contrast to conventional methods, the constructed models' reliability is maximized instead of minimizing the vagueness. In the proposed model, fuzzy parameters are estimated in such a way that the variety of the ambiguity of the model is minimized in different data conditions. In other words, the weighted variance of different ambiguities in each validation data situation is minimized in order to estimate the unknown fuzzy parameters. To comprehensively assess the proposed method's performance, 74 benchmark datasets are regarded from the UCI. Empirical outcomes show that, in 64.86% of case studies, the proposed method has better generalizability, i.e., narrower α-cut interval as well as more accurate results in the interval and point estimation, than classic versions. It is obviously demonstrated the importance of the outcomes' reliability in addition to the precision that is not considered in the traditional FLR modeling processes. Hence, the presented EFLR method can be considered as a suitable alternative in fuzzy modeling fields, especially when more generalization is favorable.

A Study on Cooperative Continuous Static Games without Differentiability under Fuzzy Environment

In this study, a fuzzy cooperative continuous static game (PQFCCSG) with n players having fuzzy parameters in all of the cost functions and the right- hand-side of constraints is characterized. Their fuzzy parameters are represented by piecewise quadratic fuzzy numbers. The α-pareto optimal solution concept is specified. In addition, the stability sets of the first and second kind without differentiability are conceptualized and established. An illustrated numerical example is discussed for proper understanding and interpretation of the proposed concept.

Ranking the Return on Assets of Tehran Stock Exchange by New Method Based on Z-numbers Data

Since real-world data is often inaccurate and working with fuzzy data and Z-numbers are very important and necessary, in the real world we need to rank and compare data. In this paper, we introduce a new method for ranking Z-numbers. This ranking algorithm is based on centroid point.We evaluate distance between centroid point, and based on this distance, we rank the Z-numbers.We use this method in two practical examples. First in ranking the return on assets of Tehran stock exchange, and second, in ranking of factors affecting the productivity of tourism security.The advantage of this method over conventional fuzzy methods is considering uncertainty, and allocating credit in the opinion of experts to estimate fuzzy parameters.

Sampling strategy for fuzzy numbers in the context of surrogate models

The paper presents an investigation of the accuracy of surrogate models for systems with uncertainties, where the uncertain parameters are represented by fuzzy numbers. Since the underlying fuzzy arithmetic using $$\alpha$$ α -level optimisation requires a large number of system evaluations, the use of numerically expensive systems becomes prohibitive with a higher number of fuzzy parameters. However, this problem can be overcome by employing less expensive surrogate models, where the accuracy of the surrogate depends strongly on the choice of the sampling points. In order to find a sufficiently accurate surrogate model with as few as possible sampling points, the influence of various sampling strategies on the accuracy of the fuzzy evaluation is investigated. As well suited for fuzzy systems, the newly developed Fuzzy Oriented Sampling Shift method is presented and compared with established sampling strategies. For the surrogate models radial basis functions and a Kriging model are employed. As test cases, the Branin and the Camelback function with fuzzy parameters are used, which demonstrate the varying accuracy for different sampling strategies. A more application oriented example of a finite element simulation of a deep drawing process is given in the end.

Setting mode for precision systems of impact and laser engraving under conditions of uncertainty of characteristics

The Hertz impact interaction formula is extended to rigid bodies, the real physical characteristics of which a priori have a significant scatter and cannot be specified exactly. Fuzzy-functions are determined that characterize a micro-impact under conditions of indistinctly specified strength properties of the material of the processed halfspace and the geometry of the impact tool. It is shown that an effective solution of applied problems of precision engraving in conditions of this kind of uncertainty of parameters is the use of adaptive IT-technology based on the interactive pre-launch setting of the system. Keywords; impact engraving technology, micro impact, fuzzy parameters, critical parameters, fuzzy surfaces, gradation scale of shades.

On a method of solving of possibilistic-probabilistic programming problems

В статье исследуется задача возможностно-вероятностной оптимизации, основанная на принципе ожидаемой возможности, и метод решения ее стохастического аналога в случае слабейшей t-нормы, описывающей взаимодействие нечетких параметров. Получены более простые для проверки условия, обеспечивающие сходимость метода стохастических квазиградиентов решения эквивалентного стохастического аналога. The paper studies possibilistic-probabilistic optimization problems, based on the principle of expected possibility, and a method for solving its stochastic analogue in the case of the weakest t-norm describing the interaction of fuzzy parameters. The conditions that are easier to verify and ensure the convergence of the method of stochastic quasigradients of the solution of an equivalent stochastic analog are obtained.

Estimation of Fuzzy Parameters in the Linear Muskingum Model with the Aid of Particle Swarm Optimization

The Muskingum method is one of the widely used methods for lumped flood routing in natural rivers. Calibration of its parameters remains an active challenge for the researchers. The task has been mostly addressed by using crisp numbers, but fuzzy seems a reasonable alternative to account for parameter uncertainty. In this work, a fuzzy Muskingum model is proposed where the assessment of the outflow as a fuzzy quantity is based on the crisp linear Muskingum method but with fuzzy parameters as inputs. This calculation can be achieved based on the extension principle of the fuzzy sets and logic. The critical point is the calibration of the proposed fuzzy extension of the Muskingum method. Due to complexity of the model, the particle swarm optimization (PSO) method is used to enable the use of a simulation process for each possible solution that composes the swarm. A weighted sum of several performance criteria is used as the fitness function of the PSO. The function accounts for the inclusive constraints (the property that the data must be included within the produced fuzzy band) and for the magnitude of the fuzzy band, since large uncertainty may render the model non-functional. Four case studies from the references are used to benchmark the proposed method, including smooth, double, and non-smooth data and a complex, real case study that shows the advantages of the approach. The use of fuzzy parameters is closer to the uncertain nature of the problem. The new methodology increases the reliability of the prediction. Furthermore, the produced fuzzy band can include, to a significant degree, the observed data and the output of the existent crisp methodologies even if they include more complex assumptions.