# Fuzzy Logic Research Paper 2012 Nissan

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## fuzzy logic research papers 2012

**Fuzzy Logic Based Adaptive Noise Filter for Real Time Image Processing Applications**

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ABSTRACT This paper represents Fuzzy logic based Adaptive Noise filter for real time image processing applications. Initially, the detection is performed using scan and then taking a mean of four pixels further scanning is performed. Then histogram approach is applied

**A Voltage Control Application in Distribution Network by Fuzzy Logic Controller Based AVC Relay**

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ABSTRACT Voltage control is a basic requirement for electrical power system at any level whether it is generation, transmission or distribution. To achieve the voltage control OLTC transformer is best option which controls the voltage by AVC relay, which is mostly used in

**Performance Comparison Of PID And Fuzzy Logic Controller Using Different Defuzzification Techniques For Positioning Control Of DC Motors**

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ABSTRACT In this paper fuzzy logic and proportional-integral-derivative (PID) controllers are compared for controlling the position of direct current (DC) motors. The PID controllers mostly used in industries due to their robust performance in a wide range of operating

**On the fundamental differences between interval type-2 and type-1 fuzzy logic controllers**

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ABSTRACT Interval type-2 fuzzy logic controllers (IT2 FLCs) have been attracting great research interests recently. Many reported results have shown that IT2 FLCs are better able to handle uncertainties than their type-1 (T1) counterparts. A challenging question is: What

**Framework of Semantic Web Service Discovery Based on Fuzzy Logic and Multi-phase Matching?**

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ABSTRACT Web service discovery has become increasingly more important as the prevailing use of web service. According to the inadequateness of current discovery methods to deal with the vague information of web service, a framework of semantic web service discovery

**Development of an Optimal and Delay Based Routing Algorithm for MANETs using Intelligent Agent Fuzzy Logic**

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ABSTRACT In this paper, we present a delay based routing algorithm for ad hoc wireless networks. In an ad hoc environment there is no wired infrastructure and the mobile hosts work as a router to maintain the status about the connectivity. A mobile ad hoc network is

**An Efficient Path loss Prediction mechanism in Wireless Communication Network Using Fuzzy Logic**

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ABSTRACT Fuzzy logic have been applied in many process and engineering applications to solve problems. In the case of control systems, where physical mechanisms are not well known due to high complexity and non-linearity, a fuzzy relational model may be useful.

**Landslide Suceptibility Zonation using Fuzzy Logic for Kundahpallam Watershed, Nilgris**

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ABSTRACT Landslide hazard zonation map has been prepared for the Kundahpallam watershed using fuzzy logic. This watershed is located within Nilgiris district of Tamil Nadu state and occupies an area of 4,839 hectares. Several landslides were reported earlier in

**What is graded fuzzy logic?**

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ABSTRACT The note presents a new definition of graded fuzzy logic, different from that of Behounek et al. Some few properties of graded fuzzy logic (in our new sense) are proven. Keywords: graded theories, mathematical fuzzy logic

**Adaptive Fuzzy Logic Based Sliding Mode Control of Electronic Throttle**

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ABSTRACT An electronic throttle control system regulates the throttle plate angle using a DC servo motor to adjust the inlet airflow rate of an internal combustion engine. In this paper, an adaptive fuzzy logic based sliding mode controller which is aimed to enhance the control

**Fuzzy Logic Based Channel Estimation and Performance Analysis of WiMAX Systems**

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ABSTRACT Worldwide Interoperability for Microwave Access (WiMAX) provides wireless broadband to fixed and mobile terminals. In this paper, firstly performance evaluation of WiMAX system without channel estimation is carried out. Then a fuzzy logic based

**Analysis of tea withering process through fuzzy logic approach**

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Determination of the completion of withering process at the right instant bears great significance in black tea manufacturing in so far as the quality of the finished product and cost of production are concerned. Daily harvest of plucked tea leaf whether under or over

**Elements of model theory in higher order fuzzy logic**

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ABSTRACT In this paper, we turn our attention to model theory of higher-order fuzzy logic (fuzzy type theory). This theory generalizes model theory of predicate logic but has some interesting specificities. We will introduce few basic concepts related to homomorphism,

**Belousov-Zhabotinsky Chemical Neuron as a Binary and Fuzzy Logic Processor**

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We demonstrate experimentally that the well-known oscillatory Belousov-Zhabotinsky (BZ) reaction can be exploited to process both Boolean and fuzzy logic if the input variables are either the volumes or the phase of addition of pulse-injected solutions of inhibitor (bromide

**Intelligent modeling of scheduling robotic flexible assembly cells using fuzzy logic**

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ABSTRACT This paper is concerned with scheduling robotic flexible assembly cells (RFACs) using fuzzy logic (FL) technique. A new scheduling rule is developed and evaluated called fuzzy sequencing rule (FSR). A simulation program is used to examine the performance of

**Digital Control of Magnetic Levitation System using Fuzzy Logic Controller**

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ABSTRACT This paper deals with the control aspects of magnetic levitation system using fuzzy logic controller (FLC). The magnetic levitation system is a mechatronic system already acknowledged and accepted by the field experts. For such a system it is desired to

**New Environmental Prediction Model Using Fuzzy logic and Neural Networks**

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ABSTRACT This work introduces a new prediction model. This prediction model is designed to accomplish its task by only one type of measurements while other prediction models need at least three types of measurements. This feature makes this model less expensive than

**Chaotic Time series prediction and Mackey-Glass simulation with fuzzy logic**

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The present study was performed with fuzzy logic (FL) time series prediction modeling on a fuzzy logic design was followed and hourly wind data for spring prediction were obtained (

**Aircraft Yaw Control System using LQR and Fuzzy Logic Controller**

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ABSTRACT This paper presents a comparative assessment of modern and intelligent controllers based on time response specification performance for a yaw control of an aircraft system. The dynamic modeling of yaw control system is performed and an autopilot that

**Diagnosis, Modeling and Prognosis of Learning System using Fuzzy Logic and Intelligent Decision Vectors**

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ABSTRACT In this paper fuzzy Expert Systems are used that are based on fuzzy logic and intelligent decision vectors to handle the quantitative as well as qualitative aspects in measuring the performance of an Educational Institution. The Academic performance of

**Efficiency Optimization Control of Induction Motor Using Fuzzy Logic**

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ABSTRACT Because of the low maintenance and robustness induction motors have many applications in the industries. Most of these applications need fast and smart speed control system. This paper introduces a smart speed control system for induction motor using

**Training Signalling Pathway Maps to Biochemical Data with Constrained Fuzzy Logic using CNORfuzzy**

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This is aa Mathematical models are used to understand protein signalling networks so as to provide an integrative view of pharmacological and toxicological processes at molecular level. CellNOptR is an existing package (available on Bioconductor website) that

**Antenna Array Synthesis by Implementing Non–Uniform Spacing Using Tsukamoto Fuzzy Logic Controller**

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ABSTRACT The paper is based on the work of the Antenna Array Synthesis by Space Perturbation Using Tsukamoto Fuzzy Logic Controller. Using Tsukamoto fuzzy logic controller it has been tried to get the new antenna array radiation pattern. Here in

**Pulmonary Lung Segmentation in Computed Tomography using Fuzzy Logic**

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ABSTRACT In this paper, we propose a new segmentation algorithm in which computed tomography (CT) lung image has been considered. Existing segmentation algorithms have contributed new ideas in any one of the stages like elimination of blood vessels, tissues

**A Framework for Selecting the Most Reliable Path in a Computer Network using Particle Swarm Optimization (PSO) based on Fuzzy Logic**

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ABSTRACT Reliability is one of the most important factors for assessing the performance of the network. Packets should pass through the most reliable path. This paper presents a technique for selecting the most reliable path for communication between node pairs of a

**Usability Evaluation of Object Oriented Software System using Fuzzy Logic Approach**

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Abstract The growth in demand for interactive software system has increased greatly in recent years. But, most of the developed systems are failing due to not providing suitable interface. User interface is the only way by which user can interact with software system.

**Related**

^{1}Department of Industrial Engineering and Management, Jerusalem College of Technology-Machon Lev, Jerusalem 91160, Israel^{2}Department of Information Technology and Computer Engineering, Vinnytsia National Technical University, Vinnitsia 21021, Ukraine^{3}Department of Mechanical Engineering, Afeka-Tel Aviv Academic College of Engineering, Tel Aviv 69107, Israel

Copyright © 2012 Alexander Rotshtein et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Fuzzy sets membership functions integrated with logistic map as the chaos generator were used to create reliability bifurcations diagrams of the system with redundancy of the components. This paper shows that increasing in the number of redundant components results in a postponement of the moment of the first bifurcation which is considered as most contributing to the loss of the reliability. The increasing of redundancy also provides the shrinkage of the oscillation orbit of the level of the system’s membership to reliable state. The paper includes the problem statement of redundancy optimization under conditions of chaotic behavior of influencing parameters and genetic algorithm of this problem solving. The paper shows the possibility of chaos-tolerant systems design with the required level of reliability.

#### 1. Introduction

The classical reliability theory [1, 2] is based on the probabilistic approach. Essential limitations of this approach are connected with “the problem of the source data” which depend on many factors and which may not correspond to the real conditions of the system’s functioning. Besides, the statistical data used in the probabilistic reliability models fix only the facts of real failures and do not contain the information about the causes of these failures. Whereas the causes of these failures are connected with the elements’ variables (temperature, humidity, tension, etc.), which become more (or less) than a certain critical level. So, we can affirm that the probabilistic theory [1, 2] models the reliability in the space of events effects (i.e., failures) and suits badly for the reliability modelling in the space of events causes (i.e., variables).

The alternative for the probabilistic modeling of the reliability is the approach based on the fuzzy logic [3] and related possibility theory [4]. In this case the classical “failure probability” is replaced by “failure possibility” which is modeled by the membership function of the system (or the element) variables to the reliable state (Figure 1).

**Figure 1: **Relationship of the probability theory and fuzzy logic in reliability estimation.

The explicit dependence of the membership function on the variables (failure causes) makes convenient the integration of the fuzzy model of reliability with the technique of time series [5], which allows observing the change of the reliability level in the real time.

The chaos theory is a new approach to the analysis of nonlinear time series [6]. It uses the conceptual apparatus of the theory of nonlinear oscillations [7] and purposes to study the phase portrait of the dynamical system with its intrinsic states of stability (attractors) and bifurcations, that is, “jumps” between stable states. Unlike the classical oscillation theory [7] where the phase portrait is formed on the base of the system description by means of differential equations, the chaos theory [6] offers the methods of the phase-portrait extraction from the experimental data, that is, directly from the time series.

The integration of fuzzy reliability model with the phase portraits of variables creates preconditions for the construction of phase portrait reflecting *the system reliability dynamics*. The pattern of bifurcations which may be interpreted as failure instants is of particular interest.

The works on the fuzzy reliability theory began in 90s of the last century. The first specialized collection of papers in this field is the edited volume [8]. The first monographs containing the approaches to the construction of fuzzy reliability theory are [9–11]. In the works [12, 13] there is a fuzzy algorithmic approach to reliability modeling based on the algebra of regular algorithms [14] and expert assessments of the performance correctness of operators and conditions by means of membership functions [3]. The problem of reliability optimization of the control resources based on fuzzy algorithmic approach is solved in [15].

An approach to the online reliability evaluation based on the integration of fuzzy logic and forecasting methods of time series (exponential smoothing and Kalman filtering) is proposed in [16].

The idea of chaos theory application in the reliability modeling appears in [17]. Two real data bases about software failures are processed by the methods of chaos theory in the paper [18]. It was shown that the deterministic model of failures is more adequate to the experimental data than the traditional stochastic models, for example, the modified Poisson’s law, and so forth. The results of the work [18] can be considered as a new approach (alternative to the statistical) to the data processing about the failures on the level of elements. We do not know any publications about the chaos theory applications to the reliability modeling of the system taking into account its structure.

In this connection there are following the questions.(1)How does the system structure influence the phase portrait of reliability?(2)Is it possible to solve the redundancy optimization problem with deterministic (chaotic) order of the occurrences of failures?

As far as the failures are connected with the oscillations of variables, then the answers for these questions should be searched on the base of integration of the fuzzy logic and chaos theory.

In this paper we use the fuzzy algorithmic approach to parametric reliability modeling proposed in [12, 13], and the simple generator of chaotic oscillations of variables in the form of logistic function [19]. The further description is organized in the following way.

Section 2 describes the principles of reliability dynamics modelling by means of the composition of membership function and a generator of chaos.

Section 3 examines the fuzzy reliability model of an element with a multiple redundancy. We consider the results of computer experiment on the analysis of reliability level bifurcations depending on the multiplicity of redundancy.

Section 4 considers the redundancy optimization problem under the conditions of chaotic oscillations of the parameters of the elements of systems.

#### 2. Basic Principles

The fuzzy chaotic approach to the reliability dynamics modeling is based on the following principles.

##### 2.1. Fuzzy Correctness

According to this principle introduced in [12, 13], there is not a crisp boundary between “correct” and “incorrect” (0) results of the functioning of a system and its elements. For the formal evaluation of the correctness level it is used the multidimensional (by the number of variables) membership function which depends on the measured parameters (input variables). The correctness of each variable is determined by the membership function of the variable to the correct value.

The function can be interpreted as the *correctness distribution of the variable *: extreme cases correspond to the maximal (minimal) level of the correctness of the variable . Pay attention that the correctness distribution satisfies the axioms of fuzzy sets theory [3], in contrast to the probabilistic distributions used in the classical reliability theory [1, 2].

The typical correctness distributions (membership functions) are represented in Figure 2. They correspond to three possible cases of fuzzy boundaries between “correct” and “incorrect” (0):(a)correct —incorrect (0),(b)incorrect (0)—correct —incorrect (0),(c)incorrect (0) correct .

**Figure 2: **The typical correctness distributions.

##### 2.2. Integration of Membership Functions and Time Series

It is assumed that for the variable it is known the time series of its values in discrete moments of time (). Putting these values in the membership function , we receive the dynamics of the correctness level of the variable in the form of the function , Figure 3.

**Figure 3: **Integration of membership functions and time series.

##### 2.3. Chaos Generator

Chaos means the oscillations which seem random but in truth they are generated by the deterministic nonlinear model. In [6] about 40 models of the chaos generators are described. Each model contains variables whose values must be fitted on the base of the experimental data. Algorithm of the chaos generation is explained by means of iterative Lamerey diagram, widely used in the classical theory of nonlinear oscillations [7].

It is assumed that there is a known function , connecting two neighboring elements of time series: and . Iterative diagram consists of this function and the bisector (Figure 4). Choosing the initial point by means of vertical and horizontal lines we obtain the points on the axis as follows:

**Figure 4: **Iterative Lamerey diagram.

The most popular generator of chaos is given by the logic map [19] as follows: where is the control parameter determining the nature of chaotic orbits.

Using the iterative equation (2) we can generate the consequence for the given parameter and initial point .For example, if = 0.25 and , then we find that. If = 0.25 and , then.

With the corresponding values of the parameter it is possible to get different types of attractors (Figure 5) by means of iteration algorithm (Figure 4):

**Figure 5: **Different types of logistic map attractors: (a) stable focus, (b) stable orbit, (c) double orbit, and (d) chaotic orbit.

(a) stable focus (), (b) stable orbit (), (c) double orbit (), and (d) chaotic orbit ().

Increasing gradually the parameter , it is possible to observe the moments of bifurcations, that is, transitions from one type of the attractor to another. Figure 6 shows that in the moment there is a jump from one stable state to two other stable states. In the moment the number of stable states is doubled, and so forth. The moment corresponds to the complete chaos [19]. The described chaos generator will be used further for the integration with the fuzzy reliability model.

**Figure 6: **Bifurcation diagram of logistic map.

#### 3. Fuzzy Chaotic Reliability Model

We consider the simple system with redundancy which is modeled by fuzzy algorithmic approach proposed in [12, 13] and logistic function (2).

##### 3.1. Element with Redundancy

The element with redundancy is presented in Figure 7 in the form of the parallel circuit where the primary element () has of redundant elements . All the elements are supposed to be homogeneous.

**Figure 7: **Element with redundancy.

The quality of the element functioning depends on the variable which varies during the time: . To evaluate the reliability of the element it is used: is a membership function which determines correctness distribution of variable during the functioning of .

The parallel circuit (Figure 7) assumes that the failure of the system requires the failure of all elements similar to . That is why the correctness of the element with redundancy functioning is evaluated by the following formula:

##### 3.2. Reliability Bifurcation

The model (3) allows observing the dynamics of the system reliability level, that is, of the correctness function during the chaotic oscillations of the variable according to the logistic map (2).

The purpose of the computer experiment consisted of the research of bifurcations of the correctness level with different correctness distributions of the element and different redundancy rates ().

The experiment is carried out with two correctness distributions shown in Figure 8: triangle (a) and threshold (b). During the chaos generation the parameter of the logistic map (2) was changed in the range from 2.5 to 4. For each distribution (Figure 8) we obtained 4 bifurcation diagrams, each of them corresponds to different redundancy rates . The results are represented in Figures 9 and 10, where the horizontal axis is the chaos parameter (), and vertical axis is the reliability level .

**Figure 8: **Correctness distributions of variable in the experiment.

**Figure 9: **Reliability bifurcations for triangle correctness distribution.

**Figure 10: **Reliability bifurcations for threshold correctness distribution.

Figures 9 and 10 show that in spite of the chaos growth (parameter ) by the increasing of redundancy rate (), it is possible(a)to postpone the moment of the first bifurcation which is associated with the reliability loss and(b)to decrease the diameter of an orbit around which there are oscillations of the level of system’s membership to the stable state.

That is why we can consider a redundancy optimization problem under chaotic oscillations of the parameters of elements.

#### 4. Redundancy Optimization under Chaosof Parameters

We consider a sequential system where each element has some level of redundancy. This system is described by the series-parallel structure (Figure 11), where is a component which depends on the variable , is the redundancy rate of the component , and is the vector of the redundancy rates , .

**Figure 11: **Sequential system with redundancy of elements.

It is supposed to be known that** is correctness distribution of variable during the element functioning,** is the range of possible values of the variable and** is mean cost of one redundant component like .

For the system in the Figure 11 taking into account (3) we have

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