Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 7677

Search results for: Takagi-Sugano (TS) fuzzy model

7677 A Fuzzy Mathematical Model for Order Acceptance and Scheduling Problem

Authors: E. Koyuncu

Abstract:

The problem of Order Acceptance and Scheduling (OAS) is defined as a joint decision of which orders to accept for processing and how to schedule them. Any linear programming model representing real-world situation involves the parameters defined by the decision maker in an uncertain way or by means of language statement. Fuzzy data can be used to incorporate vagueness in the real-life situation. In this study, a fuzzy mathematical model is proposed for a single machine OAS problem, where the orders are defined by their fuzzy due dates, fuzzy processing times, and fuzzy sequence dependent setup times. The signed distance method, one of the fuzzy ranking methods, is used to handle the fuzzy constraints in the model.

Keywords: Fuzzy mathematical programming, fuzzy ranking, order acceptance, single machine scheduling.

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7676 Reliability Evaluation using Triangular Intuitionistic Fuzzy Numbers Arithmetic Operations

Authors: G. S. Mahapatra, T. K. Roy

Abstract:

In general fuzzy sets are used to analyze the fuzzy system reliability. Here intuitionistic fuzzy set theory for analyzing the fuzzy system reliability has been used. To analyze the fuzzy system reliability, the reliability of each component of the system as a triangular intuitionistic fuzzy number is considered. Triangular intuitionistic fuzzy number and their arithmetic operations are introduced. Expressions for computing the fuzzy reliability of a series system and a parallel system following triangular intuitionistic fuzzy numbers have been described. Here an imprecise reliability model of an electric network model of dark room is taken. To compute the imprecise reliability of the above said system, reliability of each component of the systems is represented by triangular intuitionistic fuzzy numbers. Respective numerical example is presented.

Keywords: Fuzzy set, Intuitionistic fuzzy number, Systemreliability, Triangular intuitionistic fuzzy number.

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7675 Implementation of Intuitionistic Fuzzy Approach in Maximizing Net Present Value

Authors: Gaurav Kumar, Rakesh Kumar Bajaj

Abstract:

The applicability of Net Present Value (NPV) in an investment project is becoming more and more popular in the field of engineering economics. The classical NPV methodology involves only the precise and accurate data of the investment project. In the present communication, we give a new mathematical model for NPV which uses the concept of intuitionistic fuzzy set theory. The proposed model is based on triangular intuitionistic fuzzy number, which may be known as Intuitionistic Fuzzy Net Present Value (IFNPV). The model has been applied to an example and the results are presented.

Keywords: Net Present Value, Intuitionistic Fuzzy Set, Investment Projects.

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7674 Evolution of Fuzzy Neural Networks Using an Evolution Strategy with Fuzzy Genotype Values

Authors: Hidehiko Okada

Abstract:

Evolution strategy (ES) is a well-known instance of evolutionary algorithms, and there have been many studies on ES. In this paper, the author proposes an extended ES for solving fuzzy-valued optimization problems. In the proposed ES, genotype values are not real numbers but fuzzy numbers. Evolutionary processes in the ES are extended so that it can handle genotype instances with fuzzy numbers. In this study, the proposed method is experimentally applied to the evolution of neural networks with fuzzy weights and biases. Results reveal that fuzzy neural networks evolved using the proposed ES with fuzzy genotype values can model hidden target fuzzy functions even though no training data are explicitly provided. Next, the proposed method is evaluated in terms of variations in specifying fuzzy numbers as genotype values. One of the mostly adopted fuzzy numbers is a symmetric triangular one that can be specified by its lower and upper bounds (LU) or its center and width (CW). Experimental results revealed that the LU model contributed better to the fuzzy ES than the CW model, which indicates that the LU model should be adopted in future applications of the proposed method.

Keywords: Evolutionary algorithm, evolution strategy, fuzzy number, feedforward neural network, neuroevolution.

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7673 Auto Regressive Tree Modeling for Parametric Optimization in Fuzzy Logic Control System

Authors: Arshia Azam, J. Amarnath, Ch. D. V. Paradesi Rao

Abstract:

The advantage of solving the complex nonlinear problems by utilizing fuzzy logic methodologies is that the experience or expert-s knowledge described as a fuzzy rule base can be directly embedded into the systems for dealing with the problems. The current limitation of appropriate and automated designing of fuzzy controllers are focused in this paper. The structure discovery and parameter adjustment of the Branched T-S fuzzy model is addressed by a hybrid technique of type constrained sparse tree algorithms. The simulation result for different system model is evaluated and the identification error is observed to be minimum.

Keywords: Fuzzy logic, branch T-S fuzzy model, tree modeling, complex nonlinear system.

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7672 Fuzzy Modeling Tool for Creating a Component Model of Information System

Authors: Bogdan Walek, Jiri Bartos, Cyril Klimes, Jaroslav Prochazka, Pavel Smolka, Juraj Masar, Martin Pesl

Abstract:

This paper focuses on creating a component model of information system under uncertainty. The paper identifies problem in current approach of component modeling and proposes fuzzy tool, which will work with vague customer requirements and propose components of the resulting component model. The proposed tool is verified on specific information system and results are shown in paper. After finding suitable sub-components of the resulting component model, the component model is visualised by tool.

Keywords: Component, component model, fuzzy, fuzzy rules, fuzzy sets, information system, modelling, tool.

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7671 Fuzzy Multi-Component DEA with Shared and Undesirable Fuzzy Resources

Authors: Jolly Puri, Shiv Prasad Yadav

Abstract:

Multi-component data envelopment analysis (MC-DEA) is a popular technique for measuring aggregate performance of the decision making units (DMUs) along with their components. However, the conventional MC-DEA is limited to crisp input and output data which may not always be available in exact form. In real life problems, data may be imprecise or fuzzy. Therefore, in this paper, we propose (i) a fuzzy MC-DEA (FMC-DEA) model in which shared and undesirable fuzzy resources are incorporated, (ii) the proposed FMC-DEA model is transformed into a pair of crisp models using α cut approach, (iii) fuzzy aggregate performance of a DMU and fuzzy efficiencies of components are defined to be fuzzy numbers, and (iv) a numerical example is illustrated to validate the proposed approach.

Keywords: Multi-component DEA, fuzzy multi-component DEA, fuzzy resources.

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7670 Variable Rough Set Model and Its Knowledge Reduction for Incomplete and Fuzzy Decision Information Systems

Authors: Da-kuan Wei, Xian-zhong Zhou, Dong-jun Xin, Zhi-wei Chen

Abstract:

The information systems with incomplete attribute values and fuzzy decisions commonly exist in practical problems. On the base of the notion of variable precision rough set model for incomplete information system and the rough set model for incomplete and fuzzy decision information system, the variable rough set model for incomplete and fuzzy decision information system is constructed, which is the generalization of the variable precision rough set model for incomplete information system and that of rough set model for incomplete and fuzzy decision information system. The knowledge reduction and heuristic algorithm, built on the method and theory of precision reduction, are proposed.

Keywords: Rough set, Incomplete and fuzzy decision information system, Limited valued tolerance relation, Knowledge reduction, Variable rough set model

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7669 A Fuzzy Nonlinear Regression Model for Interval Type-2 Fuzzy Sets

Authors: O. Poleshchuk, E.Komarov

Abstract:

This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.

Keywords: Interval type-2 fuzzy sets, fuzzy regression, weighted interval.

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7668 Application of 0-1 Fuzzy Programming in Optimum Project Selection

Authors: S. Sadi-Nezhad, K. Khalili Damghani, N. Pilevari

Abstract:

In this article, a mathematical programming model for choosing an optimum portfolio of investments is developed. The investments are considered as investment projects. The uncertainties of the real world are associated through fuzzy concepts for coefficients of the proposed model (i. e. initial investment costs, profits, resource requirement, and total available budget). Model has been coded by using LINGO 11.0 solver. The results of a full analysis of optimistic and pessimistic derivative models are promising for selecting an optimum portfolio of projects in presence of uncertainty.

Keywords: Fuzzy Programming, Fuzzy Knapsack, FuzzyCapital Budgeting, Fuzzy Project Selection

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7667 Order Penetration Point Location using Fuzzy Quadratic Programming

Authors: Hamed Rafiei, Masoud Rabbani

Abstract:

This paper addresses one of the most important issues have been considered in hybrid MTS/MTO production environments. To cope with the problem, a mathematical programming model is applied from a tactical point of view. The model is converted to a fuzzy goal programming model, because a degree of uncertainty is involved in hybrid MTS/MTO context. Finally, application of the proposed model in an industrial center is reported and the results prove the validity of the model.

Keywords: Fuzzy sets theory, Hybrid MTS/MTO, Order penetration point, Quadratic programming.

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7666 Speed Control of a Permanent Magnet Synchronous Machine (PMSM) Fed by an Inverter Voltage Fuzzy Control Approach

Authors: Jamel Khedri, Mohamed Chaabane, Mansour Souissi, Driss Mehdi

Abstract:

This paper deals with the synthesis of fuzzy controller applied to a permanent magnet synchronous machine (PMSM) with a guaranteed H∞ performance. To design this fuzzy controller, nonlinear model of the PMSM is approximated by Takagi-Sugeno fuzzy model (T-S fuzzy model), then the so-called parallel distributed compensation (PDC) is employed. Next, we derive the property of the H∞ norm. The latter is cast in terms of linear matrix inequalities (LMI-s) while minimizing the H∞ norm of the transfer function between the disturbance and the error ( ) ev T . The experimental and simulations results were conducted on a permanent magnet synchronous machine to illustrate the effects of the fuzzy modelling and the controller design via the PDC.

Keywords: Feedback controller, Takagi-Sugeno fuzzy model, Linear Matrix Inequality (LMI), PMSM, H∞ performance.

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7665 Nonlinear Controller for Fuzzy Model of Double Inverted Pendulums

Authors: I. Zamani, M. H. Zarif

Abstract:

In this paper a method for designing of nonlinear controller for a fuzzy model of Double Inverted Pendulum is proposed. This system can be considered as a fuzzy large-scale system that includes offset terms and disturbance in each subsystem. Offset terms are deterministic and disturbances are satisfied a matching condition that is mentioned in the paper. Based on Lyapunov theorem, a nonlinear controller is designed for this fuzzy system (as a model reference base) which is simple in computation and guarantees stability. This idea can be used for other fuzzy large- scale systems that include more subsystems Finally, the results are shown.

Keywords: Controller, Fuzzy Double Inverted Pendulums, Fuzzy Large-Scale Systems, Lyapunov Stability.

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7664 Constructing a Fuzzy Net Present Value Method to Evaluating the BOT Sport Facilities

Authors: Huei-Fu Lu

Abstract:

This paper is to develop a fuzzy net present value (FNPV) method by taking vague cash flow and imprecise required rate of return into account for evaluating the value of the Build-Operate-Transfer (BOT) sport facilities. In order to clearly manifest a more realistic capital budgeting model based on the classical net present value (NPV) method, some uncertain financial elements in NPV formula will be fuzzified as triangular fuzzy numbers. Through the conscientious manipulation of fuzzy set theory, we will find that the proposed FNPV model is a more explicit extension of classical (crisp) model and could be more practicable for the financial managers to capture the essence of capital budgeting of sport facilities than non-fuzzy model.

Keywords: Fuzzy sets; Capital budgeting, Sport facility, Net present value (NPV), Build-Operate-Transfer (BOT) scheme

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7663 A Fuzzy Linear Regression Model Based on Dissemblance Index

Authors: Shih-Pin Chen, Shih-Syuan You

Abstract:

Fuzzy regression models are useful for investigating the relationship between explanatory variables and responses in fuzzy environments. To overcome the deficiencies of previous models and increase the explanatory power of fuzzy data, the graded mean integration (GMI) representation is applied to determine representative crisp regression coefficients. A fuzzy regression model is constructed based on the modified dissemblance index (MDI), which can precisely measure the actual total error. Compared with previous studies based on the proposed MDI and distance criterion, the results from commonly used test examples show that the proposed fuzzy linear regression model has higher explanatory power and forecasting accuracy.

Keywords: Dissemblance index, fuzzy linear regression, graded mean integration, mathematical programming.

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7662 Improving Ride Comfort of a Bus Using Fuzzy Logic Controlled Suspension

Authors: Mujde Turkkan, Nurkan Yagiz

Abstract:

In this study an active controller is presented for vibration suppression of a full-bus model. The bus is modeled having seven degrees of freedom. Using the achieved model via Lagrange Equations the system equations of motion are derived. The suspensions of the bus model include air springs with two auxiliary chambers are used. Fuzzy logic controller is used to improve the ride comfort. The numerical results, verifies that the presented fuzzy logic controller improves the ride comfort.

Keywords: Ride comfort, air spring, bus, fuzzy logic controller.

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7661 Fuzzy Control of Macroeconomic Models

Authors: Andre A. Keller

Abstract:

The optimal control is one of the possible controllers for a dynamic system, having a linear quadratic regulator and using the Pontryagin-s principle or the dynamic programming method . Stochastic disturbances may affect the coefficients (multiplicative disturbances) or the equations (additive disturbances), provided that the shocks are not too great . Nevertheless, this approach encounters difficulties when uncertainties are very important or when the probability calculus is of no help with very imprecise data. The fuzzy logic contributes to a pragmatic solution of such a problem since it operates on fuzzy numbers. A fuzzy controller acts as an artificial decision maker that operates in a closed-loop system in real time. This contribution seeks to explore the tracking problem and control of dynamic macroeconomic models using a fuzzy learning algorithm. A two inputs - single output (TISO) fuzzy model is applied to the linear fluctuation model of Phillips and to the nonlinear growth model of Goodwin.

Keywords: fuzzy control, macroeconomic model, multiplier - accelerator, nonlinear accelerator, stabilization policy.

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7660 Fuzzy PID Controller with Coupled Rules for a Nonlinear Quarter Car Model

Authors: Şaban Çetin, Özgür Demir

Abstract:

In this study, Fuzzy PID Control scheme is designed for an active suspension system. The main goal of an active suspension system for using in a vehicle model is reducing body deflections and handling high comfort for a passenger car. The present system was modelled as a two-degree-of-freedom (2-DOF) nonlinear vehicle model.

Keywords: Active suspension system, Fuzzy PID controller, a nonlinear quarter car model.

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7659 Identification of a PWA Model of a Batch Reactor for Model Predictive Control

Authors: Gorazd Karer, Igor Skrjanc, Borut Zupancic

Abstract:

The complex hybrid and nonlinear nature of many processes that are met in practice causes problems with both structure modelling and parameter identification; therefore, obtaining a model that is suitable for MPC is often a difficult task. The basic idea of this paper is to present an identification method for a piecewise affine (PWA) model based on a fuzzy clustering algorithm. First we introduce the PWA model. Next, we tackle the identification method. We treat the fuzzy clustering algorithm, deal with the projections of the fuzzy clusters into the input space of the PWA model and explain the estimation of the parameters of the PWA model by means of a modified least-squares method. Furthermore, we verify the usability of the proposed identification approach on a hybrid nonlinear batch reactor example. The result suggest that the batch reactor can be efficiently identified and thus formulated as a PWA model, which can eventually be used for model predictive control purposes.

Keywords: Batch reactor, fuzzy clustering, hybrid systems, identification, nonlinear systems, PWA systems.

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7658 Estimating Development Time of Software Projects Using a Neuro Fuzzy Approach

Authors: Venus Marza, Amin Seyyedi, Luiz Fernando Capretz

Abstract:

Software estimation accuracy is among the greatest challenges for software developers. This study aimed at building and evaluating a neuro-fuzzy model to estimate software projects development time. The forty-one modules developed from ten programs were used as dataset. Our proposed approach is compared with fuzzy logic and neural network model and Results show that the value of MMRE (Mean of Magnitude of Relative Error) applying neuro-fuzzy was substantially lower than MMRE applying fuzzy logic and neural network.

Keywords: Artificial Neural Network, Fuzzy Logic, Neuro-Fuzzy, Software Estimation

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7657 Genetic Algorithm with Fuzzy Genotype Values and Its Application to Neuroevolution

Authors: Hidehiko Okada

Abstract:

The author proposes an extension of genetic algorithm (GA) for solving fuzzy-valued optimization problems. In the proposed GA, values in the genotypes are not real numbers but fuzzy numbers. Evolutionary processes in GA are extended so that GA can handle genotype instances with fuzzy numbers. The proposed method is applied to evolving neural networks with fuzzy weights and biases. Experimental results showed that fuzzy neural networks evolved by the fuzzy GA could model hidden target fuzzy functions well despite the fact that no training data was explicitly provided.

Keywords: Evolutionary algorithm, genetic algorithm, fuzzy number, neural network, neuroevolution.

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7656 Black Box Model and Evolutionary Fuzzy Control Methods of Coupled-Tank System

Authors: S. Yaman, S. Rostami

Abstract:

In this study, a black box modeling of the coupled-tank system is obtained by using fuzzy sets. The derived model is tested via adaptive neuro fuzzy inference system (ANFIS). In order to achieve a better control performance, the parameters of three different controller types, classical proportional integral controller (PID), fuzzy PID and function tuner method, are tuned by one of the evolutionary computation method, genetic algorithm. All tuned controllers are applied to the fuzzy model of the coupled-tank experimental setup and analyzed under the different reference input values. According to the results, it is seen that function tuner method demonstrates better robust control performance and guarantees the closed loop stability.

Keywords: Function tuner method, fuzzy modeling, fuzzy PID controller, genetic algorithm.

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7655 Simulating and Forecasting Qualitative Marcoeconomic Models Using Rule-Based Fuzzy Cognitive Maps

Authors: Spiros Mazarakis, George Matzavinos, Peter P. Groumpos

Abstract:

Economic models are complex dynamic systems with a lot of uncertainties and fuzzy data. Conventional modeling approaches using well known methods and techniques cannot provide realistic and satisfactory answers to today-s challenging economic problems. Qualitative modeling using fuzzy logic and intelligent system theories can be used to model macroeconomic models. Fuzzy Cognitive maps (FCM) is a new method been used to model the dynamic behavior of complex systems. For the first time FCMs and the Mamdani Model of Intelligent control is used to model macroeconomic models. This new model is referred as the Mamdani Rule-Based Fuzzy Cognitive Map (MBFCM) and provides the academic and research community with a new promising integrated advanced computational model. A new economic model is developed for a qualitative approach to Macroeconomic modeling. Fuzzy Controllers for such models are designed. Simulation results for an economic scenario are provided and extensively discussed

Keywords: Macroeconomic Models, Mamdani Rule Based- FCMs(MBFCMs), Qualitative and Dynamics System, Simulation.

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7654 Improved Fuzzy Neural Modeling for Underwater Vehicles

Authors: O. Hassanein, Sreenatha G. Anavatti, Tapabrata Ray

Abstract:

The dynamics of the Autonomous Underwater Vehicles (AUVs) are highly nonlinear and time varying and the hydrodynamic coefficients of vehicles are difficult to estimate accurately because of the variations of these coefficients with different navigation conditions and external disturbances. This study presents the on-line system identification of AUV dynamics to obtain the coupled nonlinear dynamic model of AUV as a black box. This black box has an input-output relationship based upon on-line adaptive fuzzy model and adaptive neural fuzzy network (ANFN) model techniques to overcome the uncertain external disturbance and the difficulties of modelling the hydrodynamic forces of the AUVs instead of using the mathematical model with hydrodynamic parameters estimation. The models- parameters are adapted according to the back propagation algorithm based upon the error between the identified model and the actual output of the plant. The proposed ANFN model adopts a functional link neural network (FLNN) as the consequent part of the fuzzy rules. Thus, the consequent part of the ANFN model is a nonlinear combination of input variables. Fuzzy control system is applied to guide and control the AUV using both adaptive models and mathematical model. Simulation results show the superiority of the proposed adaptive neural fuzzy network (ANFN) model in tracking of the behavior of the AUV accurately even in the presence of noise and disturbance.

Keywords: AUV, AUV dynamic model, fuzzy control, fuzzy modelling, adaptive fuzzy control, back propagation, system identification, neural fuzzy model, FLNN.

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7653 A Centroid Ranking Approach Based Fuzzy MCDM Model

Authors: T. C. Chu, S.H. Wu

Abstract:

This paper suggests ranking alternatives under fuzzy MCDM (multiple criteria decision making) via an centroid based ranking approach, where criteria are classified to benefit qualitative, benefit quantitative and cost quantitative ones. The ratings of alternatives versus qualitative criteria and the importance weights of all criteria are assessed in linguistic values represented by fuzzy numbers. The membership function for the final fuzzy evaluation value of each alternative can be developed through α-cuts and interval arithmetic of fuzzy numbers. The distance between the original point and the relative centroid is applied to defuzzify the final fuzzy evaluation values in order to rank alternatives. Finally a numerical example demonstrates the computation procedure of the proposed model.

Keywords: Fuzzy MCDM, Criteria, Fuzzy number, Ranking, Relative centroid.

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7652 A New Quantile Based Fuzzy Time Series Forecasting Model

Authors: Tahseen A. Jilani, Aqil S. Burney, C. Ardil

Abstract:

Time series models have been used to make predictions of academic enrollments, weather, road accident, casualties and stock prices, etc. Based on the concepts of quartile regression models, we have developed a simple time variant quantile based fuzzy time series forecasting method. The proposed method bases the forecast using prediction of future trend of the data. In place of actual quantiles of the data at each point, we have converted the statistical concept into fuzzy concept by using fuzzy quantiles using fuzzy membership function ensemble. We have given a fuzzy metric to use the trend forecast and calculate the future value. The proposed model is applied for TAIFEX forecasting. It is shown that proposed method work best as compared to other models when compared with respect to model complexity and forecasting accuracy.

Keywords: Quantile Regression, Fuzzy time series, fuzzy logicalrelationship groups, heuristic trend prediction.

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7651 Determination of Adequate Fuzzy Inequalities for their Usage in Fuzzy Query Languages

Authors: Marcel Shirvanian, Wolfram Lippe

Abstract:

Although the usefulness of fuzzy databases has been pointed out in several works, they are not fully developed in numerous domains. A task that is mostly disregarded and which is the topic of this paper is the determination of suitable inequalities for fuzzy sets in fuzzy query languages. This paper examines which kinds of fuzzy inequalities exist at all. Afterwards, different procedures are presented that appear theoretically appropriate. By being applied to various examples, their strengths and weaknesses are revealed. Furthermore, an algorithm for an efficient computation of the selected fuzzy inequality is shown.

Keywords: Fuzzy Databases, Fuzzy Inequalities, Fuzzy QueryLanguages, Fuzzy Ranking.

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7650 A Comparison of Grey Model and Fuzzy Predictive Model for Time Series

Authors: A. I. Dounis, P. Tiropanis, D. Tseles, G. Nikolaou, G. P. Syrcos

Abstract:

The prediction of meteorological parameters at a meteorological station is an interesting and open problem. A firstorder linear dynamic model GM(1,1) is the main component of the grey system theory. The grey model requires only a few previous data points in order to make a real-time forecast. In this paper, we consider the daily average ambient temperature as a time series and the grey model GM(1,1) applied to local prediction (short-term prediction) of the temperature. In the same case study we use a fuzzy predictive model for global prediction. We conclude the paper with a comparison between local and global prediction schemes.

Keywords: Fuzzy predictive model, grey model, local andglobal prediction, meteorological forecasting, time series.

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7649 Portfolio Management: A Fuzzy Set Based Approach to Monitoring Size to Maximize Return and Minimize Risk

Authors: Margaret F. Shipley

Abstract:

Fuzzy logic can be used when knowledge is incomplete or when ambiguity of data exists. The purpose of this paper is to propose a proactive fuzzy set- based model for reacting to the risk inherent in investment activities relative to a complete view of portfolio management. Fuzzy rules are given where, depending on the antecedents, the portfolio size may be slightly or significantly decreased or increased. The decision maker considers acceptable bounds on the proportion of acceptable risk and return. The Fuzzy Controller model allows learning to be achieved as 1) the firing strength of each rule is measured, 2) fuzzy output allows rules to be updated, and 3) new actions are recommended as the system continues to loop. An extension is given to the fuzzy controller that evaluates potential financial loss before adjusting the portfolio. An application is presented that illustrates the algorithm and extension developed in the paper.

Keywords: Portfolio Management, Financial Market Monitoring, Fuzzy Controller, Fuzzy Logic,

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7648 Applying Half-Circle Fuzzy Numbers to Control System: A Preliminary Study on Development of Intelligent System on Marine Environment and Engineering

Authors: Chen-Yuan Chen, Wan-I Lee, Yi-Chaio Sui, Cheng-Wu Chen

Abstract:

This study focuses on the development of triangular fuzzy numbers, the revising of triangular fuzzy numbers, and the constructing of a HCFN (half-circle fuzzy number) model which can be utilized to perform more plural operations. They are further transformed for trigonometric functions and polar coordinates. From half-circle fuzzy numbers we can conceive cylindrical fuzzy numbers, which work better in algebraic operations. An example of fuzzy control is given in a simulation to show the applicability of the proposed half-circle fuzzy numbers.

Keywords: triangular fuzzy number, half-circle fuzzy numbers, predictions, polar coordinates, Lyapunov method

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