Search results for: Hybrid Fuzzy Selecting
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1871

Search results for: Hybrid Fuzzy Selecting

1721 On λ− Summable of Orlicz Space of Entire Sequences of Fuzzy Numbers

Authors: N. Subramanian, U. K. Misra, M. S. Panda

Abstract:

In this paper the concept of strongly (λM)p - Ces'aro summability of a sequence of fuzzy numbers and strongly λM- statistically convergent sequences of fuzzy numbers is introduced.

Keywords: Fuzzy numbers, statistical convergence, Orlicz space, entire sequence.

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1720 The Analysis of Different Classes of Weighted Fuzzy Petri Nets and Their Features

Authors: Yurii Bloshko, Oksana Olar

Abstract:

This paper presents the analysis of six different classes of Petri nets: fuzzy Petri nets (FPN), generalized fuzzy Petri nets (GFPN), parameterized fuzzy Petri nets (PFPN), T2GFPN, flexible generalized fuzzy Petri nets (FGFPN), binary Petri nets (BPN). These classes were simulated in the special software PNeS® for the analysis of its pros and cons on the example of models which are dedicated to the decision-making process of passenger transport logistics. The paper includes the analysis of two approaches: when input values are filled with the experts’ knowledge; when fuzzy expectations represented by output values are added to the point. These approaches fulfill the possibilities of triples of functions which are replaced with different combinations of t-/s-norms.

Keywords: Fuzzy petri net, intelligent computational techniques, knowledge representation, triangular norms.

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1719 Characteristics of Aluminum Hybrid Composites

Authors: S. O. Adeosun, L. O. Osoba, O. O. Taiwo

Abstract:

Aluminum hybrid reinforcement technology is a response to the dynamic ever increasing service requirements of such industries as transportation, aerospace, automobile, marine, etc. It is unique in that it offers a platform of almost unending combinations of materials to produce various hybrid composites. This article reviews the studies carried out on various combinations of aluminum hybrid composite and the effects on mechanical, physical and chemical properties. It is observed that the extent of enhancement of these properties of hybrid composites is strongly dependent on the nature of the reinforcement, its hardness, particle size, volume fraction, uniformity of dispersion within the matrix and the method of hybrid production.

Keywords: Aluminum alloy, hybrid composites, properties, reinforcements.

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1718 A Diagnostic Fuzzy Rule-Based System for Congenital Heart Disease

Authors: Ersin Kaya, Bulent Oran, Ahmet Arslan

Abstract:

In this study, fuzzy rule-based classifier is used for the diagnosis of congenital heart disease. Congenital heart diseases are defined as structural or functional heart disease. Medical data sets were obtained from Pediatric Cardiology Department at Selcuk University, from years 2000 to 2003. Firstly, fuzzy rules were generated by using medical data. Then the weights of fuzzy rules were calculated. Two different reasoning methods as “weighted vote method" and “singles winner method" were used in this study. The results of fuzzy classifiers were compared.

Keywords: Congenital heart disease, Fuzzy rule-basedclassifiers, Classification

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1717 A Type-2 Fuzzy Adaptive Controller of a Class of Nonlinear System

Authors: A. El Ougli, I. Lagrat, I. Boumhidi

Abstract:

In this paper we propose a robust adaptive fuzzy controller for a class of nonlinear system with unknown dynamic. The method is based on type-2 fuzzy logic system to approximate unknown non-linear function. The design of the on-line adaptive scheme of the proposed controller is based on Lyapunov technique. Simulation results are given to illustrate the effectiveness of the proposed approach.

Keywords: Fuzzy set type-2, Adaptive fuzzy control, Nonlinear system.

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1716 Energy Management System with Temperature Rise Prevention on Hybrid Ships

Authors: Asser S. Abdelwahab, Nabil H. Abbasy, Ragi A. Hamdy

Abstract:

Marine shipping has now become one of the major worldwide contributors to pollution and greenhouse gas emissions. Hybrid ships technology based on multiple energy sources has taken a great scope of research to get rid of ship emissions and cut down fuel expenses. Insufficiency between power generated and the demand load to withstand the transient behavior on ships during severe climate conditions will lead to a blackout. Thus, an efficient energy management system (EMS) is a mandatory scope for achieving higher system efficiency while enhancing the lifetime of the onboard storage systems is another salient EMS scope. Considering energy storage system conditions, both the battery state of charge (SOC) and temperature represent important parameters to prevent any malfunction of the storage system that eventually degrades the whole system. In this paper, a two battery packs ratio fuzzy logic control model is proposed. The overall aim is to control the charging/discharging current while including both the battery SOC and temperature in the energy management system. The full designs of the proposed controllers are described and simulated using Matlab. The results prove the successfulness of the proposed controller in stabilizing the system voltage during both loading and unloading while keeping the energy storage system in a healthy condition.

Keywords: energy storage system, fuzzy logic control, hybrid ship, thermal runaway

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1715 The Approximate Solution of Linear Fuzzy Fredholm Integral Equations of the Second Kind by Using Iterative Interpolation

Authors: N. Parandin, M. A. Fariborzi Araghi

Abstract:

in this paper, we propose a numerical method for the approximate solution of fuzzy Fredholm functional integral equations of the second kind by using an iterative interpolation. For this purpose, we convert the linear fuzzy Fredholm integral equations to a crisp linear system of integral equations. The proposed method is illustrated by some fuzzy integral equations in numerical examples.

Keywords: Fuzzy function integral equations, Iterative method, Linear systems, Parametric form of fuzzy number.

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1714 On Some Subspaces of Entire Sequence Space of Fuzzy Numbers

Authors: T. Balasubramanian, A. Pandiarani

Abstract:

In this paper we introduce some subspaces of fuzzy entire sequence space. Some general properties of these sequence spaces are discussed. Also some inclusion relation involving the spaces are obtained. Mathematics Subject Classification: 40A05, 40D25.

Keywords: Fuzzy Numbers, Entire sequences, completeness, Fuzzy entire sequences

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1713 Hybridized Technique to Analyze Workstress Related Data via the StressCafé

Authors: Anusua Ghosh, Andrew Nafalski, Jeffery Tweedale, Maureen Dollard

Abstract:

This paper presents anapproach of hybridizing two or more artificial intelligence (AI) techniques which arebeing used to fuzzify the workstress level ranking and categorize the rating accordingly. The use of two or more techniques (hybrid approach) has been considered in this case, as combining different techniques may lead to neutralizing each other-s weaknesses generating a superior hybrid solution. Recent researches have shown that there is a need for a more valid and reliable tools, for assessing work stress. Thus artificial intelligence techniques have been applied in this instance to provide a solution to a psychological application. An overview about the novel and autonomous interactive model for analysing work-stress that has been developedusing multi-agent systems is also presented in this paper. The establishment of the intelligent multi-agent decision analyser (IMADA) using hybridized technique of neural networks and fuzzy logic within the multi-agent based framework is also described.

Keywords: Fuzzy logic, intelligent agent, multi-agent systems, neural network, workplace stress.

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1712 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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1711 Nonlinear Fuzzy Tracking Real-time-based Control of Drying Parameters

Authors: Marco Soares dos Santos, Camila Nicola Boeri, Jorge Augusto Ferreira, Fernando Neto da Silva

Abstract:

The highly nonlinear characteristics of drying processes have prompted researchers to seek new nonlinear control solutions. However, the relation between the implementation complexity, on-line processing complexity, reliability control structure and controller-s performance is not well established. The present paper proposes high performance nonlinear fuzzy controllers for a real-time operation of a drying machine, being developed under a consistent match between those issues. A PCI-6025E data acquisition device from National Instruments® was used, and the control system was fully designed with MATLAB® / SIMULINK language. Drying parameters, namely relative humidity and temperature, were controlled through MIMOs Hybrid Bang-bang+PI (BPI) and Four-dimensional Fuzzy Logic (FLC) real-time-based controllers to perform drying tests on biological materials. The performance of the drying strategies was compared through several criteria, which are reported without controllers- retuning. Controllers- performance analysis has showed much better performance of FLC than BPI controller. The absolute errors were lower than 8,85 % for Fuzzy Logic Controller, about three times lower than the experimental results with BPI control.

Keywords: Drying control, Fuzzy logic control, Intelligent temperature-humidity control.

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1710 Predicting the Impact of the Defect on the Overall Environment in Function Based Systems

Authors: Parvinder S. Sandhu, Urvashi Malhotra, E. Ardil

Abstract:

There is lot of work done in prediction of the fault proneness of the software systems. But, it is the severity of the faults that is more important than number of faults existing in the developed system as the major faults matters most for a developer and those major faults needs immediate attention. In this paper, we tried to predict the level of impact of the existing faults in software systems. Neuro-Fuzzy based predictor models is applied NASA-s public domain defect dataset coded in C programming language. As Correlation-based Feature Selection (CFS) evaluates the worth of a subset of attributes by considering the individual predictive ability of each feature along with the degree of redundancy between them. So, CFS is used for the selecting the best metrics that have highly correlated with level of severity of faults. The results are compared with the prediction results of Logistic Models (LMT) that was earlier quoted as the best technique in [17]. The results are recorded in terms of Accuracy, Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE). The results show that Neuro-fuzzy based model provide a relatively better prediction accuracy as compared to other models and hence, can be used for the modeling of the level of impact of faults in function based systems.

Keywords: Software Metrics, Fuzzy, Neuro-Fuzzy, Software Faults, Accuracy, MAE, RMSE.

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1709 A New Reliability Allocation Method Based On Fuzzy Numbers

Authors: Peng Li, Chuanri Li, Tao Li

Abstract:

Reliability allocation is quite important during early design and development stages for a system to apportion its specified reliability goal to subsystems. This paper improves the reliability fuzzy allocation method, and gives concrete processes on determining the factor and sub-factor sets, weight sets, judgment set, and multi-stage fuzzy evaluation. To determine the weight of factor and sub-factor sets, the modified trapezoidal numbers are proposed to reduce errors caused by subjective factors. To decrease the fuzziness in fuzzy division, an approximation method based on linear programming is employed. To compute the explicit values of fuzzy numbers, centroid method of defuzzification is considered. An example is provided to illustrate the application of the proposed reliability allocation method based on fuzzy arithmetic.

Keywords: Reliability allocation, fuzzy arithmetic, allocation weight.

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1708 Recurrent Neural Network Based Fuzzy Inference System for Identification and Control of Dynamic Plants

Authors: Rahib Hidayat Abiyev

Abstract:

This paper presents the development of recurrent neural network based fuzzy inference system for identification and control of dynamic nonlinear plant. The structure and algorithms of fuzzy system based on recurrent neural network are described. To train unknown parameters of the system the supervised learning algorithm is used. As a result of learning, the rules of neuro-fuzzy system are formed. The neuro-fuzzy system is used for the identification and control of nonlinear dynamic plant. The simulation results of identification and control systems based on recurrent neuro-fuzzy network are compared with the simulation results of other neural systems. It is found that the recurrent neuro-fuzzy based system has better performance than the others.

Keywords: Fuzzy logic, neural network, neuro-fuzzy system, control system.

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1707 Fuzzy-Genetic Optimal Control for Four Degreeof Freedom Robotic Arm Movement

Authors: V. K. Banga, R. Kumar, Y. Singh

Abstract:

In this paper, we present optimal control for movement and trajectory planning for four degrees-of-freedom robot using Fuzzy Logic (FL) and Genetic Algorithms (GAs). We have evaluated using Fuzzy Logic (FL) and Genetic Algorithms (GAs) for four degree-of-freedom (4 DOF) robotics arm, Uncertainties like; Movement, Friction and Settling Time in robotic arm movement have been compensated using Fuzzy logic and Genetic Algorithms. The development of a fuzzy genetic optimization algorithm is presented and discussed. The result are compared only GA and Fuzzy GA. This paper describes genetic algorithms, which is designed to optimize robot movement and trajectory. Though the model represents is a general model for redundant structures and could represent any n-link structures. The result is a complete trajectory planning with Fuzzy logic and Genetic algorithms demonstrating the flexibility of this technique of artificial intelligence.

Keywords: Inverse kinematics, Genetic algorithms (GAs), Fuzzy logic (FL), Trajectory planning.

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1706 Application of Adaptive Neuro-Fuzzy Inference System in Smoothing Transition Autoregressive Models

Authors: Ε. Giovanis

Abstract:

In this paper we propose and examine an Adaptive Neuro-Fuzzy Inference System (ANFIS) in Smoothing Transition Autoregressive (STAR) modeling. Because STAR models follow fuzzy logic approach, in the non-linear part fuzzy rules can be incorporated or other training or computational methods can be applied as the error backpropagation algorithm instead to nonlinear squares. Furthermore, additional fuzzy membership functions can be examined, beside the logistic and exponential, like the triangle, Gaussian and Generalized Bell functions among others. We examine two macroeconomic variables of US economy, the inflation rate and the 6-monthly treasury bills interest rates.

Keywords: Forecasting, Neuro-Fuzzy, Smoothing transition, Time-series

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1705 A New Approach For Ranking Of Generalized Trapezoidal Fuzzy Numbers

Authors: Amit Kumar, Pushpinder Singh, Parampreet Kaur, Amarpreet Kaur

Abstract:

Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples it is proved that ranking method proposed by Chen and Chen (Expert Systems with Applications 36 (2009) 6833-6842) is incorrect. The main aim of this paper is to propose a new approach for the ranking of generalized trapezoidal fuzzy numbers. The main advantage of the proposed approach is that the proposed approach provide the correct ordering of generalized and normal trapezoidal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets and Systems 118 (2001) 375-385).

Keywords: Ranking function, Generalized trapezoidal fuzzy numbers

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1704 Fuzzy Gauge Capability (Cg and Cgk) through Buckley Approach

Authors: Seyed Habib A. Rahmati, Mohsen Sadegh Amalnick

Abstract:

Different terms of the Statistical Process Control (SPC) has sketch in the fuzzy environment. However, Measurement System Analysis (MSA), as a main branch of the SPC, is rarely investigated in fuzzy area. This procedure assesses the suitability of the data to be used in later stages or decisions of the SPC. Therefore, this research focuses on some important measures of MSA and through a new method introduces the measures in fuzzy environment. In this method, which works based on Buckley approach, imprecision and vagueness nature of the real world measurement are considered simultaneously. To do so, fuzzy version of the gauge capability (Cg and Cgk) are introduced. The method is also explained through example clearly.

Keywords: SPC, MSA, gauge capability, Cg, Cgk.

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1703 Numerical Solving of General Fuzzy Linear Systems by Huang's Method

Authors: S. J. Hosseini Ghoncheh, M. Paripour

Abstract:

In this paper the Huang-s method for solving a m×n fuzzy linear system when, m≤ n, is considered. The method in detail is discussed and illustrated by solving some numerical examples.

Keywords: Fuzzy number, fuzzy linear systems, Huang's method.

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1702 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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1701 On Q-Fuzzy Ideals in Γ-Semigroups

Authors: Samit Kumar Majumder

Abstract:

In this paper the concept of Q-fuzzification of ideals of Γ-semigroups has been introduced and some important properties have been investigated. A characterization of regular Γ-semigroup in terms of Q-fuzzy ideals has been obtained. Operator semigroups of a Γ-semigroup has been made to work by obtaining various relationships between Q-fuzzy ideals of a Γ-semigroup and that of its operator semigroups.

Keywords: Q-Fuzzy set, Γ-semigroup, Regular Γ-semigroup, Q-Fuzzy left(right) ideal, Operator semigroups.

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1700 A New Condition for Conflicting Bifuzzy Sets Based On Intuitionistic Evaluation

Authors: Imran C.T., Syibrah M.N., Mohd Lazim A.

Abstract:

Fuzzy sets theory affirmed that the linguistic value for every contraries relation is complementary. It was stressed in the intuitionistic fuzzy sets (IFS) that the conditions for contraries relations, which are the fuzzy values, cannot be greater than one. However, complementary in two contradict phenomena are not always true. This paper proposes a new idea condition for conflicting bifuzzy sets by relaxing the condition of intuitionistic fuzzy sets. Here, we will critically forward examples using triangular fuzzy number in formulating a new condition for conflicting bifuzzy sets (CBFS). Evaluation of positive and negative in conflicting phenomena were calculated concurrently by relaxing the condition in IFS. The hypothetical illustration showed the applicability of the new condition in CBFS for solving non-complement contraries intuitionistic evaluation. This approach can be applied to any decision making where conflicting is very much exist.

Keywords: Conflicting bifuzzy set, conflicting degree, fuzzy sets, fuzzy numbers.

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1699 Evaluation of Fuzzy ARTMAP with DBSCAN in VLSI Application

Authors: K. A. Sumithradevi, Vijayalakshmi. M. N., Annamma Abraham., Dr. Vasanta

Abstract:

The various applications of VLSI circuits in highperformance computing, telecommunications, and consumer electronics has been expanding progressively, and at a very hasty pace. This paper describes a new model for partitioning a circuit using DBSCAN and fuzzy ARTMAP neural network. The first step is concerned with feature extraction, where we had make use DBSCAN algorithm. The second step is the classification and is composed of a fuzzy ARTMAP neural network. The performance of both approaches is compared using benchmark data provided by MCNC standard cell placement benchmark netlists. Analysis of the investigational results proved that the fuzzy ARTMAP with DBSCAN model achieves greater performance then only fuzzy ARTMAP in recognizing sub-circuits with lowest amount of interconnections between them The recognition rate using fuzzy ARTMAP with DBSCAN is 97.7% compared to only fuzzy ARTMAP.

Keywords: VLSI, Circuit partitioning, DBSCAN, fuzzyARTMAP.

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1698 Navigation of Multiple Mobile Robots using Rule-based-Neuro-Fuzzy Technique

Authors: Saroj Kumar Pradhan, Dayal Ramakrushna Parhi, Anup Kumar Panda

Abstract:

This paper deals with motion planning of multiple mobile robots. Mobile robots working together to achieve several objectives have many advantages over single robot system. However, the planning and coordination between the mobile robots is extremely difficult. In the present investigation rule-based and rulebased- neuro-fuzzy techniques are analyzed for multiple mobile robots navigation in an unknown or partially known environment. The final aims of the robots are to reach some pre-defined goals. Based upon a reference motion, direction; distances between the robots and obstacles; and distances between the robots and targets; different types of rules are taken heuristically and refined later to find the steering angle. The control system combines a repelling influence related to the distance between robots and nearby obstacles and with an attracting influence between the robots and targets. Then a hybrid rule-based-neuro-fuzzy technique is analysed to find the steering angle of the robots. Simulation results show that the proposed rulebased- neuro-fuzzy technique can improve navigation performance in complex and unknown environments compared to this simple rulebased technique.

Keywords: Mobile robots, Navigation, Neuro-fuzzy, Obstacle avoidance, Rule-based, Target seeking

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1697 Standard Fuzzy Sets for Aircraft Selection using Multiple Criteria Decision Making Analysis

Authors: C. Ardil

Abstract:

This study uses two-dimensional standard fuzzy sets to enhance multiple criteria decision-making analysis for passenger aircraft selection, allowing decision-makers to express judgments with uncertain and vague information. Using two-dimensional fuzzy numbers, three decision makers evaluated three aircraft alternatives according to seven decision criteria. A validity analysis based on two-dimensional standard fuzzy weighted geometric (SFWG) and two-dimensional standard fuzzy weighted average (SFGA) operators is conducted to test the proposed approach's robustness and effectiveness in the fuzzy multiple criteria decision making (MCDM) evaluation process. 

Keywords: Standard fuzzy sets (SFSs), aircraft selection, multiple criteria decision making, intuitionistic fuzzy sets (IFSs), SFWG, SFGA, MCDM

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1696 The Intuitionistic Fuzzy Ordered Weighted Averaging-Weighted Average Operator and its Application in Financial Decision Making

Authors: Shouzhen Zeng

Abstract:

We present a new intuitionistic fuzzy aggregation operator called the intuitionistic fuzzy ordered weighted averaging-weighted average (IFOWAWA) operator. The main advantage of the IFOWAWA operator is that it unifies the OWA operator with the WA in the same formulation considering the degree of importance that each concept has in the aggregation. Moreover, it is able to deal with an uncertain environment that can be assessed with intuitionistic fuzzy numbers. We study some of its main properties and we see that it has a lot of particular cases such as the intuitionistic fuzzy weighted average (IFWA) and the intuitionistic fuzzy OWA (IFOWA) operator. Finally, we study the applicability of the new approach on a financial decision making problem concerning the selection of financial strategies.

Keywords: Intuitionistic fuzzy numbers, Weighted average, OWA operator, Financial decision making

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1695 Novel and Different Definitions for Fuzzy Union and Intersection Operations

Authors: Aarthi Chandramohan, M. V. C. Rao

Abstract:

This paper presents three new methodologies for the basic operations, which aim at finding new ways of computing union (maximum) and intersection (minimum) membership values by taking into effect the entire membership values in a fuzzy set. The new methodologies are conceptually simple and easy from the application point of view and are illustrated with a variety of problems such as Cartesian product of two fuzzy sets, max –min composition of two fuzzy sets in different product spaces and an application of an inverted pendulum to determine the impact of the new methodologies. The results clearly indicate a difference based on the nature of the fuzzy sets under consideration and hence will be highly useful in quite a few applications where different values have significant impact on the behavior of the system.

Keywords: Centroid, fuzzy set operations, intersection, triangular norms , triangular S-norms, union.

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1694 Sliding Mode Control with Fuzzy Boundary Layer to Air-Air Interception Problem

Authors: Mustafa Resa Becan

Abstract:

The performance of a type of fuzzy sliding mode control is researched by considering the nonlinear characteristic of a missile-target interception problem to obtain a robust interception process. The variable boundary layer by using fuzzy logic is proposed to reduce the chattering around the switching surface then is applied to the interception model which was derived. The performances of the sliding mode control with constant and fuzzy boundary layer are compared at the end of the study and the results are evaluated.

Keywords: Sliding mode control, fuzzy, boundary layer, interception problem.

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1693 An MADM Framework toward Hierarchical Production Planning in Hybrid MTS/MTO Environments

Authors: H. Rafiei, M. Rabbani

Abstract:

This paper proposes a new decision making structure to determine the appropriate product delivery strategy for different products in a manufacturing system among make-to-stock, make-toorder, and hybrid strategy. Given product delivery strategies for all products in the manufacturing system, the position of the Order Penetrating Point (OPP) can be located regarding the delivery strategies among which location of OPP in hybrid strategy is a cumbersome task. In this regard, we employ analytic network process, because there are varieties of interrelated driving factors involved in choosing the right location. Moreover, the proposed structure is augmented with fuzzy sets theory in order to cope with the uncertainty of judgments. Finally, applicability of the proposed structure is proven in practice through a real industrial case company. The numerical results demonstrate the efficiency of the proposed decision making structure in order partitioning and OPP location.

Keywords: Hybrid make-to-stock/make-to-order, Multi-attribute decision making, Order partitioning, Order penetration point.

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1692 Strict Stability of Fuzzy Differential Equations by Lyapunov Functions

Authors: Mustafa Bayram Gücen, Coşkun Yakar

Abstract:

In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: Fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability.

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