A fuzzy control system with application to production planning problems

A considerable part of the literature on fuzzy sets is devoted to the field of fuzzy control system. In this paper, an alternative control system is introduced to describe a dynamic system with fuzzy white noise. In order to find optimal ways to control such a system, fuzzy optimal control theory is further developed. Specifically, a linear quadratic model is formulated and solved as a fuzzy optimal control problem. The formulation and solution of this model provide an economic interpretation of a production planning model both in the finite horizon and in the infinite horizon.     

A production-recycling model with variable demand,demand-dependent fuzzy return rate: A fuzzy differential equation approach

A two warehouse production-recycling system for a single item with stock-dependent demand is considered. Item is produced at a production plant situated at a market place having sufficiently large warehouse with a small decorated showroom. Units are continuously transformed from production center to a showroom at the market for sale and excess units are stored at the production center warehouse. Production is stopped at regular intervals and after some production cycles, recycling process is commissioned. Used units are collected from the customers (up to beginning of last recycling cycle) at a demand-dependent fuzzy rate and then repaired to new condition before being sold again. Model is formulated using fuzzy differential equation and α-cut of fuzzy average profit is obtained. In the first approach, Modified Graded Mean Integration Value (MGMIV) of the average profit is optimized to derive decisions for the decision maker (DM). A genetic algorithm with binary mode representation, Roulette wheel selection and random mutation process is used to solve the model. In the second approach, using fuzzy preference ordering of intervals (FPOIs), α-cut of fuzzy average profit is optimized using the above GA to derive optimum decisions for DM. The proposed models are illustrated with numerical examples.     

A fuzzy DEA model with undesirable fuzzy outputs and its application to the banking sector in India

Data envelopment analysis (DEA) is a widely used technique for measuring the relative efficiencies of decision making units (DMUs) with multiple inputs and multiple outputs. However, in real life applications, undesirable outputs may be present in the production process which needs to be minimized. The present study endeavors to propose a DEA model with undesirable outputs and further to extend it in fuzzy environment in view of the fact that input/output data are not always available in exact form in real life problems. We propose a fuzzy DEA model with undesirable fuzzy outputs which can be solved as crisp linear program for each α in (0, 1] using α-cut approach. Further, cross-efficiency technique is applied to increase the discrimination power of the proposed models and to rank the efficient DMUs at every α in (0, 1]. Moreover, for better understanding of the proposed methodology, we present a numerical illustration followed by an application to the banking sector in India. This is the first study which attempts to measure the performance of public sector banks (PuSBs) in India using fuzzy input/output data for the period 2009–2011. The results obtained from the proposed methodology not only depict the impact of undesirable output on the performance of PuSBs but also analyze efficiently the influence of the presence of uncertainty in the data over the efficiency results. The findings show that the efficiency results of many PuSBs vary with the variation in α during the selected period.     

A geometric data structure for parallel finite elements and the application to multigrid methods with block smoothing

We present a data structure for parallel computing which is directly linked to geometric quantities of an underlying mesh and which is well adapted to the requirements of a general finite element realization. In addition, we define an abstract linear algebra model which supports multigrid methods (extending our previous work in Comp. Vis. Sci. 1 (1997), 27–40). Finally, we apply the parallel multigrid preconditioner to several configurations in linear elasticity and we compute the condition number numerically for different smoothers, resulting in a quantitative evaluation of parallel multigrid performance.     

A fuzzy MCDM method and an application to solid transportation problem with mode preference

In this paper we propose a computationally efficient fuzzy multi-criteria decision making (FMCDM) method. For this purpose we define a ranking function based on credibility measure to rank a fuzzy number over another fuzzy number. A comparative result of our proposed ranking method with the other well known methods is provided. The proposed FMCDM method is successfully applied to find most preferred transportation mode among available modes with respect to some evaluation criteria for a solid transportation problem (STP). Here the evaluation ratings of the alternatives and criteria weights are presented in terms of linguistic variables. The importance weights of the available transportation modes as obtained by this method are then assigned to the STP. Numerical example is provided to illustrate the proposed method and problem.     

A multi-objective decision-making model with fuzzy rough coefficients and its application to the inventory problem

In this paper, we concentrate on developing a fuzzy rough multi-objective decision-making model according to uncertainty theory. We present some equivalent models and a traditional algorithm based on an interactive fuzzy satisfying method, which is similar to the interactive fuzzy rough satisfying method, in order to obtain a satisfying solution for the decision maker. In addition, the technique of fuzzy rough simulation is applied to deal with general fuzzy rough objective functions and fuzzy rough constraints which are usually difficult to convert into their equivalents. Furthermore, combined with the techniques of fuzzy rough simulation, a genetic algorithm using the compromise approach is designed for solving a fuzzy rough multi-objective programming problem. Finally, a model is applied to an inventory problem to illustrate the usefulness of the proposed model and algorithm, and then a sensitivity analysis is made.     

A stable adaptive fuzzy sliding-mode control for affine nonlinearsystems with application to four-bar linkage systems

In this paper, a stable adaptive fuzzy sliding-mode control for affine highly nonlinear systems is developed. First, the external part of a transformed system via a feedback linearizing control evolves a linear dynamic system with uncertainties. A reference model with the desired amplitude and phase properties is given to obtain an error model. Since the uncertainties are assumed to be large, a fuzzy model is employed to model these uncertainties. A learning law with e-modification for the weight of a fuzzy model is considered to ensure the boundedness of learning weight without the requirement of persistent excitation condition. Then, an equivalent control using the known part of system dynamics and the learning fuzzy model is designed to achieve the desired control behavior. Furthermore, the uncertainties caused by the approximation of fuzzy model and the error of learning weight are tackled by a switching control. Finally, the stability of the overall system is verified by the Lyapunov theory. Simulations and experiments of the velocity control of a four-bar-linkage system are presented to verify the usefulness of the proposed control     

A thresholding method based on interval-valued intuitionistic fuzzy sets: an application to image segmentation

This paper proposes a new fuzzy approach for the segmentation of images. L-interval-valued intuitionistic fuzzy sets (IVIFSs) are constructed from two L-fuzzy sets that corresponds to the foreground (object) and the background of an image. Here, L denotes the number of gray levels in the image. The length of the membership interval of IVIFS quantifies the influence of the ignorance in the construction of the membership function. Threshold for an image is chosen by finding an IVIFS with least entropy. Contributions also include a comparative study with ten other image segmentation techniques. The results obtained by each method have been systematically evaluated using well-known measures for judging the segmentation quality. The proposed method has globally shown better results in all these segmentation quality measures. Experiments also show that the results acquired from the proposed method are highly correlated to the ground truth images.     

A fuzzy approach for performance modeling in a batch plant:application to semiconductor manufacturing

In the current literature dealing with job shop scheduling, most of the approaches have developed models based on the assumption that the problem domain does not contain any imprecision. However, this hypothesis is strongly challenged in the implementation phase of such models-imprecision is inherent to production systems involving human intervention. The aim of this paper is to demonstrate the advantages of possibilistic production data modeling in a real-world application, i.e., semiconductor manufacturing. In this work, a discrete-event simulation model (MELISSA) for performance evaluation of a batch-manufacturing facility previously developed in our laboratory has been extended to treat uncertainties modeled by fuzzy numbers. Due to the confidential nature of industrial data, an illustrative example, presenting the same typical features as a real problem, is treated and analyzed using fuzzy concepts. Inclusion of fuzzy techniques provides the decision-maker with a range of possible values for completion times, average storage times, and operator workload instead of a unique value (which has little significance due to the variety of human operators). In addition, the negative portion of average waiting times yields useful information for the manager to detect deficient resources in the production system     

A multi-objective problem based on fuzzy inference with application to parametric design of an electrophotographic system

This paper proposes a systematic approach to conduct system-level optimal parametric design for a class of electrophotographic systems. A conventional monochrome laser printer serves as the platform for verification of the proposed optimal design approach. Besides performance, we incorporate two other practical indices, i.e., cost and energy consumption, into design objectives and formulate a multi-objective optimization problem. A fuzzy inference system is established to provide the nonlinear or linguistic mapping between the decision variables and the design objectives. For comparative purpose, the problem is solved using both single-objective and multi-objective optimization algorithms. Note that the proposed approach is also applicable to other complex systems.     

A multiple fuzzy inference systems framework for daily stock trading with application to NASDAQ stock exchange

The aim of this study is to develop an expert system for predicting daily trading decisions in a typical financial market environment. The developed system thus employs a Multiple FISs framework consisting of three dedicated FISs for stock trading decisions, Buy, Hold and Sell respectively. As input to the Multiple FISs framework, the system takes the fundamental information of the respective companies and the historical prices of the stocks which are processed to give the technical information. The framework suggests the investor to Buy, Sell or Hold on a daily basis for a portfolio of stock taken into consideration. Experimenting the framework on selected stocks of NASDAQ stock exchange shows that including the fundamental data of the stocks as input along with the technical data significantly improves the profit return than that of the system taking only technical information as input data. Characterised as a stock market indicator, the framework performs better than some of the most popularly used technical indicators such as Moving Average Convergence/Divergence (MACD), Relative Strength Index (RSI), Stochastic Oscillator (SO) and Chaikin Oscillator (CO). The developed framework also gives better profit return compared to an existing model with similar objective.     

Missing data analysis with fuzzy C-Means: A study of its application in a psychological scenario

In scientific research, and particularly in psychological studies, data for some variables in the database to be analyzed may well be missing. If not dealt with in the correct way, the missing values may weaken or even compromise the validity of research into the database, especially if it is a small one. In this paper we introduce the most common solutions to this problem offered by the most popular statistical software and a technique based on the most famous fuzzy clustering algorithm: Fuzzy C-Means (FCM). Then we compare these methodologies in order to highlight the peculiar characteristics of each solution. The comparison was made in a psychological research environment, using a database of in-patients who have a diagnosis of mental retardation. The results demonstrate that completion techniques, and in particular the one based on FCM, lead to effective data imputation, avoiding the deletion of elements with missing data, which diminishes the power of the research.     

A multi-objective dynamic vehicle routing problem with fuzzy time windows: Model,solution and application

In this paper, a multi-objective dynamic vehicle routing problem with fuzzy time windows (DVRPFTW) is presented. In this problem, unlike most of the work where all the data are known in advance, a set of real time requests arrives randomly over time and the dispatcher does not have any deterministic or probabilistic information on the location and size of them until they arrive. Moreover, this model involves routing vehicles according to customer-specific time windows, which are highly relevant to the customers’ satisfaction level. This preference information of customers can be represented as a convex fuzzy number with respect to the satisfaction for a service time. This paper uses a direct interpretation of the DVRPFTW as a multi-objective problem where the total required fleet size, overall total traveling distance and waiting time imposed on vehicles are minimized and the overall customers’ preferences for service is maximized. A solving strategy based on the genetic algorithm (GA) and three basic modules are proposed, in which the state of the system including information of vehicles and customers is checked in a management module each time. The strategy module tries to organize the information reported by the management module and construct an efficient structure for solving in the subsequent module. The performance of the proposed approach is evaluated in different steps on various test problems generalized from a set of static instances in the literature. In the first step, the performance of the proposed approach is checked in static conditions and then the other assumptions and developments are added gradually and changes are examined. The computational experiments on data sets illustrate the efficiency and effectiveness of the proposed approach.     

A new compromise solution method for fuzzy group decision-making problems with an application to the contractor selection

This paper presents a novel compromise solution method for solving fuzzy group decision-making problems by a group of experts, which can determine the best alternative by considering both conflicting quantitative and qualitative evaluation criteria in real-life applications. The compromise solution method is developed based on the concept that the chosen alternative should be as close as possible to the positive ideal solution and as far away from the negative ideal solution as possible concurrently. The performance rating values of alternatives versus conflicting criteria as well as the weights of criteria are described by linguistic variables with multi-judges and are converted to triangular fuzzy numbers. Then, a new collective index is introduced to distinguish among potential alternatives in the assessment process with respect to subjective judgment and objective information. Finally, a real case study and an application example for a contractor selection problem are provided in construction industry to demonstrate the implementation process of the proposed method.     

An approach to the Sandia workshop static frame challenge problem: A combination of elementary probabilistic, fuzzy set, and worst scenario tools

A model static frame problem with uncertain input data is considered. The Young modulus of the frame material is known only through a limited number of measurements of its local and effective values. In the loaded frame, the displacement w at a given point is to be predicted. To tackle the uncertainty in the displacement magnitude, a set of conservative Young modulus behavior (YMB) models is constituted and the mean and the variance of w are inferred for each YMB model belonging to . Moreover, the degree of possibility of each YMB model is assessed by a weight (membership) function ν derived from measured data. The probability of w exceeding a given tolerance is inferred in each YMB model and then weighted by ν. To address the prediction problem in accordance with the worst scenario approach, the maximum is identified in the weighted probabilities. The analysis is based on elementary probabilistic tools as well as on the exploitation of computer algebra and numerical methods. The results are presented in numerous graphs.     

A fuzzy rule based expert system for stock evaluation and portfolio construction: An application to Istanbul Stock Exchange

The aim of this study is to construct appropriate portfolios by taking investor’s preferences and risk profile into account in a realistic, flexible and practical manner. In this concern, a fuzzy rule based expert system is developed to support portfolio managers in their middle term investment decisions. The proposed expert system is validated by using the data of 61 stocks that publicly traded in Istanbul Stock Exchange National-100 Index from the years 2002 through 2010. The performance of the proposed system is analyzed in comparison with the benchmark index, Istanbul Stock Exchange National-30 Index, in terms of different risk profiles and investment period lengths. The results reveal that the performance of the proposed expert system is superior relative to the benchmark index in most cases. Additionally, in parallel to our expectations, the performance of the expert system is relatively higher in case of risk-averse investor profile and middle term investment period than the performance observed in the other cases.     

Robust sampled-data fuzzy control of nonlinear systems with parametric uncertainties: Its application to depth control of autonomous underwater vehicles

This paper presents a new direct discrete-time design methodology of a robust sampled-data fuzzy controller for a class of nonlinear system with parametric uncertainties that is exactly represented by Takagi-Sugeno (T-S) fuzzy model. Based on an exact discrete-time fuzzy model in an integral form, sufficient conditions for a robust asymptotic stabilization of the nonlinear system are investigated in the discrete-time Lyapunov sense. It is shown that the resulting sampled-data controller indeed robustly asymptotically stabilizes the nonlinear plant. To illustrate the effectiveness of the proposed methodology, an example, a sampled-data depth control of autonomous underwater vehicles (AUVs) is provided.     

A Pearson-like correlation-based TOPSIS method with interval-valued Pythagorean fuzzy uncertainty and its application to multiple criteria decision analysis of stroke rehabilitation treatments

Neural Computing and Applications - This paper extends one of the most extensively used multiple criteria decision analysis (MCDA) methods, the technique for order preference by similarity to ideal...     

A new distance measure for interval valued intuitionistic fuzzy sets and its application to group decision making problems with incomplete weights information

The aim of this study is to introduce a novel generalized distance measure for interval valued intuitionistic fuzzy sets and to illustrate the applicability of the proposed distance measure to group decision making problems. Firstly, a generalized distance measure is proposed along with proofs satisfying its axioms. Then, a comparison between the proposed distance measure and well-known distance measures is performed in terms of counter-intuitive cases. Subsequently, the extension of TOPSIS method, in which the proposed distance measure is used to calculate separation measures, to an interval valued intuitionistic fuzzy (IVIF) environment is demonstrated to solve multi-criteria group decision making (MCGDM) problems using optimal criteria weights determined with linear programming model based on the concept of maximizing relative closeness coefficient. Finally, two illustrative examples are provided for proof-of-concept purposes and to demonstrate benefits of using the proposed distance measure over the existing ones in IVIF TOPSIS method for MCGDM problems.