# Rule Based Fuzzy Inference

## Top PDF Rule Based Fuzzy Inference:

### Compositional Rule of Inference and Adaptive Fuzzy Rule Based Scheme with Applications

Daily stock trading data of DSE (Dhaka Stock Exchange) have been collected from the website of stockbangldesh.com. Which contain opening, closing, high, low and quantity of stocks traded in a particular day. Data taken from DSE are used to convert generalized price and quantity Eq. (5.1). This generalized data are then fuzzified by fuzzy numbers. Table 2 shows the parameters of generalized prices and quantities. One of the most difficult tasks is to set the value of parameter of membership function. A statistical study has been made by taking more than 100 records of each company. The parameter value is accepted by the experts and general traders. Theorem 4.1, 4.2, 4.3, 4.6 and 4.7 claim that small changes or deviation of membership function, that is, the parameter value results in small change of conclusion.

### Experience-based Rule Base Generation and Adaptation for Fuzzy Interpolation

Fuzzy inference is one of the most advanced technologies in control field. It has been widely applied to solve real world problems due to its simplicity and effectiveness in represent- ing and reasoning on human natural language. Examples of such applications include the subway control system in the city of Sendai [1], and the home heating control system [2], amongst others. A typical fuzzy inference system consists of mainly two parts, a rule base (or knowledge base) and an inference engine. A number of inference engines have been developed, with the Mamdani method [3] and the TSK method [4] being the most widely used. The Mamdani model is a particular implementation of the Compositional Rule of Inference [5], which is more intuitive and commonly utilised to deal with human natural language. The TSK approach however can produce crisp values as output and thus is more convenient to be employed when crisp values are required. The traditional fuzzy inference approaches require the entire domains of input variables to be fully covered by rules in a given rule base. Otherwise, no rule can be fired when a given observation does not overlap with any rule antecedent.

### Rule Weight Base Behavioural Modeling of Steam Turbine Using Genetically Tuned Adaptive Network Based Fuzzy Inference System

ABSTRACT: In view nonlinearities, steam turbine complex structure of dynamic modelling, selection of suitable configuration of adaptive network based fuzzy inference system (ANFIS) and minimizing the modelling error, a rule weight base behavioural system modelling of steam turbine (genetically tuned ANFIS) model has proposed to solve the problem through the assessment of enthalpy and power output of the system. The accuracy and performance of enthalpy estimation over wide range of operation data has estimated with reference to integral square error (ISE) criterion. This technique is useful in order to adjust model parameters over full range of input output operational data. From this work, it is clearly evident that the error obtained from conventional ANFIS structure is much higher than that of obtained from ANFIS structure after genetically tuning.

### A NEW CLUSTERING-BASED APPROACH FOR MODELING FUZZY RULE-BASED CLASSIFICATION SYSTEMS

Subtractive clustering is used for extracting rules from data [13]. Zhao et al. proposed a two-stage approach to extract compact Takagi-Sugeno (TS) fuzzy models using subtractive clustering and particle swarm optimization (PSO) from numeric data [15]. Subtractive clustering was employed to extract a fuzzy rules base and the PSO algorithm is used to search the optimal rule parameters simultaneously. Eftekhari and Katebi proposed a hybrid approach for building optimal fuzzy model from data for nonlinear dynamical systems [16]. This approach was a combination of a genetic algorithm, subtractive clustering and unscented filter. Subtractive clustering has been used to construct rule base and unscented filter has been employed for optimization of model parameters. Demirli et al. used the subtractive clustering method as a system identification tool to model job sequencing problems from an existing sequence (output data) and job attribute data (input data) [26]. Torun and Tohumoglu developed a new systematic way in order to obtain optimized fuzzy inference system for classification [12]. Subtractive clustering has been used to construct rule base and simulated annealing is employed for optimization of classifier parameters. Elmzabi et al. proposed a method in order to generate the Mamdani fuzzy inference systems [27]. This method used the results of the subtractive clustering in order to generate the Mamdani fuzzy rules and the genetic algorithms for the parameters optimization of these rules. Zhang and Lu proposed a method for creating ensembles of classifiers via Fuzzy C-Mean (FCM) clustering [28]. Radha and Rajagopalan in [18] and Chen in [29] proposed methods that used FCM to generate fuzzy rules from data to deal with data classification problem. Hossen et al. proposed a novel modified adaptive fuzzy inference system, which automatically generates fuzzy membership functions via the FCM clustering and fuzzy rules from the modified Apriori algorithm based on input-output data sets [30]. Zhang et al in [19] and Zhang and Liu in [20] proposed an enhanced clustering algorithm, IFCM, which originates from traditional FCM algorithm and can process with interval sets. They showed that the IFCM algorithm can be used to extract fuzzy rules for an interval type-2 fuzzy logic system.

### A Fuzzy Rule-Based Expert System for Diagnosing Asthma

The approach considered for generating the fuzzy expert system explained in this paper represents the knowledge of diagnosing asthma by including symp- tom data history data and lab data in the modular structure of the knowledge-base. The fuzzy inference engine designed for this system involves the modules of symptoms; allergic rhinitis, genetic factors, symptom hyper-responsiveness, medical factors, environmental factors, short term drug use and laboratory data, during the process of diagnosing, respectively. The knowledge in these modules is presented as production rules. Meta rules are considered in the knowledge- base, which presents relevant questions for patients in the user interface. To handle the uncertainty of laboratory data in the module of the lung function test and some vague variables in other modules such as allergic rhinitis, fuzzy techniques have been considered for inference of uncertain rules.

### Fuzzy Rule based Novel Approach to Spam Filtering

The fuzzy classification contains fuzzy inference system and a set of rules. The proposed fuzzy rule based classification shown in figure 3.This work has a list spam words and spam mail addresses are in the database with its ranked value. The spam words and sender mail address are extracted from the subject, content and from address fields of an email. The spam words and spam mail address are assigned a value and categorized in to five i.e. weak (W), very weak (VW), moderate (M), strong (S), and very strong (VS). Email contains many spam words. This work extracted spam words and sender address of spammers from 100 mails. Attention, Dear Lucky Winner, Information, Job Opportunities, Notification, Congratulations, and Business Partnership are the few most attracted words used by the spammers in the subject and content fields to cheat the users. The internet user

### Self-Tuning Method of PID Parameters Based on Belief Rule Base Inference

values of PID parameters [7]. Comparing with tradi- tional ES-PID, FI-PID can capture more useful infor- mation with uncertainty in expert’s knowledge and has better generalization capability. However, simi- lar with ES-PID, it also suffers from some difficulties including poor online learning and updating abilities and incompleteness of fuzzy rule base and so on [10]. ANN-PID uses the hidden layer network structure to construct the connection between the input layer (control variables) and the output layer (PID parame- ters), and online optimizes network weights to obtain desired values of PID parameters which is a kind of typical adaptive PID control [20]. However, the neural network is a black box system, in which, the physical meanings of network nodes are obscure and even hard to understand for control engineers. Although, when objective functions are given, so many optimization strategies can be used to online adjust the networks weights, the optimized results are easy to fall into local minimum in training process because of the improper initial values of weights or other reasons [15].

### Curvature-based sparse rule base generation for fuzzy rule interpolation

The second class of the FRI approaches is based on the analogical reasoning mechanism [105] and therefore, referred to as “analogy based fuzzy rule interpolation" (intermediate-rule based). Instead of directly inferring conclusions, this class works by first creating an interme- diate rule such that its antecedent is as “close" (given a fuzzy distance metric) to the given observation as possible (given a fuzzy distance metric or other measures based on certain similarity principles). Then, a conclusion is derived from the given observation by firing the generated intermediate rule through the analogical reasoning mechanism. That is, the shape distinguishability between the resultant fuzzy set and the consequence of the intermediate rule is analogous to the shape distinguishability between the observation and the antecedent of the generated intermediate rule. A number of ways to create an intermediate rule and then to infer a conclusion from the given observation by that rule have been developed, such as the weighted fuzzy interpolative reasoning [22], and another approach based on the areas of fuzzy sets and uses the weighted average method to infer the FRI results [99]. The most important methods in this class are the HS approach based on scale and move transformation [23] and its extensions [106, 107]. The HS approaches introduce the general concept of representative values (RVs), and then use this to interpolate fuzzy rules involving arbitrary polygonal fuzzy sets, by means of scale and move transformations. The HS approaches not only guarantee the uniqueness, normality, and convexity of the interpolated fuzzy sets, but can also handle the interpolation of multiple antecedent variables with different types of fuzzy membership function. The HS methods not only inherit the common advantages of fuzzy interpolative reasoning (helping reduce rule base complexity and allowing inferences to be performed within simple and sparse rule bases), but also have two other advantages compared to the existing fuzzy interpolation methods. Firstly, they provide a degree of freedom to choose various RV definitions to meet different application requirements. Secondly, they can handle the interpolation of multiple rules, with each rule having multiple antecedent variables asso- ciated with arbitrary polygonal fuzzy membership functions. This makes the interpolation inference a practical solution for real-world applications.

### DESIGNING FORWARD CHAINING INFERENCE ENGINE FOR FUZZY RULE BASED EXPERT SYSTEM FOR CYBER SECURITY

The fuzzy set theory was introduced by Zadeh. Fuzzy logic is a multi-value logic which permits intermediate values to be defined between conventional ones like true/false, low/high, good/bad etc. In a classical set theory, an element may either belong to set or not. In fuzzy set theory, an element has a degree of membership. A degree of membership function can be described as an interval [0, 1].

### An Application of Fuzzy Inference System Composed of Double-Input Rule Modules to Control Problems

M ANY studies on self-tuning fuzzy systems[1], [2] have been made. The aim of these studies is to construct automatically fuzzy reasoning rules from input and output data based on the steepest descend method. Obvious drawbacks of the steepest descend method are its large com- putational complexity and getting stuck in a shallow local minimum. In order to overcome them, some novel methods have been developed as shown in the references[3], [4], [5], [6], [7]. The SIRMs (Single-Input Rule Modules) model aims to obtain a better solution by using fuzzy inference system composed of SIRMs[8], where output is determined as the weighted sum of all modules. However, it is known that the SIRMs model does not always achieve good performance in non-linear problems. Therefore, we have proposed the SNIRMs (Small Number of Input Rule Modules) model as a generalized SIRMs model, in which each module is composed of small number of input variables[9]. DIRMs (Double-Input Rule Modules) model is an example of such models and each module of DIRMs model is composed of two input variables. It is well known that EX-OR problem with two input variables can be approximated by DIRMs model but not by SIRMs model[10]. Further, there exists the difference of the ability between DIRMs and SIRMs models as shown later in the paper. Then, does there exist such example in control problems? In this paper, we consider the

### Curvature-Based Sparse Rule Base Generation for Fuzzy Rule Interpolation

Fuzzy rule base generation has been intensively studied in the literature. It is usually implemented in one of two ways: data-driven (extracting rules from data) [15] and knowledge-driven (generating rules from human expert knowledge) [16]. Both approaches may suffer from the ‘curse of dimensionality’. In ad- dition, the knowledge-driven method may be further negatively affected by the limited availability of ex- pert knowledge. Data-driven rule base generation was proposed to minimise the involvement of human ex- pertise. The success of data-driven approaches is built upon a large quantity of training data. These ap- proaches usually only target dense rule bases that are used for traditional fuzzy inference approaches. How- ever, redundancy often exists in fuzzy rule-based mod- els that are acquired from numerical data. This re- sults in unnecessary structural complexity and reduces the interpretability of the system. In order to reduce the complexity of such rule bases, various rule base reduction approaches have been developed to min- imise the redundancy [17,18,19,20]. Most of such ap- proaches are based on certain similarity measures; therefore, they are likely to cause performance deteri- oration along with the size reduction of the rule base.

### TSK Inference with Sparse Rule Bases

A dense TSK fuzzy rule base was generated based on the given model first, by which the entire input domain is fully covered. In order to do so, a training data set com- prised of 500 data points have been randomly generated from Equation 22. Then, a linear regression-based Matlab TSK rule base generation approach [19] was em- ployed to derive a normal TSK fuzzy rule base that partitions each antecedent vari- able domain by 7 fuzzy sets. The surface view of fuzzy partition of TSK model is also illustrated in Fig. 5. As there are two input variables, this leads to 49 fuzzy rules in total, as listed in Table 1 and shown in Fig. 4. Briefly, the employed data-driven approach first grid partitions the given input domain into sub-regions. Then, for each sub-region, a linear regression approach, the least-squares approach, is employed to represent the data in an initial fuzzy rule. After that, linear quadratic estimation (Kalman Filter) algorithm is used to fine tune the rules’ parameters until the satis- factory solution is found. The data-driven approach for TSK rule base generation is beyond the scope of this paper, and thus details are omitted here, however, more information can be found in [20].

### Adaptive Neuro Fuzzy Inference System Based Solar Energy Planning

optimization routines can be applied in order to adjust the parameters to reduce some error measure (performance index). This error measure is usually defined by the sum of the squared difference between actual and desired outputs. ANFIS uses a combination of least squares estimation and back propagation for membership function parameter estimation. Fig.4 shows Sugeno’s fuzzy logic model. Fig.5 shows the architecture of the ANFIS, comprising by input, fuzzification, inference and defuzzification layers. The network can be visualized as consisting of inputs, with N neurons in the input layer and F input membership functions for each input, with F*N neurons in the fuzzification layer. There are FN rules with FN neurons in the inference and defuzzification layers and one neuron in the output layer. For simplicity, it is assumed that the fuzzy inference system under consideration has two inputs x and y and one output z as shown in Fig.5. For a zero-order Sugeno fuzzy model, a common rule set with two fuzzy if-then rules is the following:

### Fuzzy integral for rule aggregation in fuzzy inference systems

Herein, we proposed and started to explore the NDFI and gFI extensions for rule aggregation in a FIS. We discussed how these extensions fit into existing FISs, reviewed efficient discrete algorithms and analyzed their computational complexities. Furthermore, we showed, via the toy tipping example, how to pick FMs that turn the CI into existing FIS aggregation operators, we discussed imputation methods (from the densities) and opened the door for learning. The example and Table 1 gave the reader a feel for the inner workings and differences between the gFI and NDFI and it helps with understanding when and where to use one extension over the other. We also highlighted that the NDFI “aggregates in place” (per-element) while the gFI is based on the EP. Ultimately, this makes a big difference, in terms of output, and it is a choice the user must make.

### An Extended Takagi-Sugeno-Kang Inference System (TSK+) with Fuzzy Interpolation and Its Rule Base Generation

Centroid-based clustering algorithms are traditionally emp- loyed in TSK fuzzy modelling to group similar objects together for rule extraction (Chen and Linkens (2004)), which is also the case in this work. However, differing from exist- ing TSK-style rule base generation approaches, the proposed system is workable with dense data sets, sparse data sets and unevenly distributed data sets. Therefore, a two-level cluster- ing scheme is applied in this work. The first level of clustering divides the given (dense/sparse) data set into multiple sub- data sets using sparse K-Means clustering algorithm (Witten and Tibshirani (2010)). Based on the feature of the sparse K-Means clustering, those divided sub-data sets are gener- ally considered being dense. The second level of clustering is applied on each obtained dense sub-data set to generate rule clusters for TSK fuzzy rule extraction by employing the standard K-Means clustering algorithm (MacQueen (1967)). Note that the number of clusters has to be pre-defined for both sparse K-Means and the standard K-Means, which is discussed first below.

### Design of Host based Intrusion Detection System using Fuzzy Inference Rule

Due to technology emerges day by day, there is a need to have a security mechanism to protect the systems from unauthorised users and malicious activities. For this, the intrusion detection systems (IDS) are used. An intrusion detection system is a device or software application that collects information from a variety of network sources or computer systems for analysis in order to detect the signs of malicious activities. An intrusion is defined as a set of actions that attempts to compromise the integrity, confidentiality, or availability of the system resources [1]. Integrity refers to maintain and assure the accuracy and consistency of data over its entire life cycle. Confidentiality refers to maintain the secrecy of data into system so that unauthorized user cannot access. Availability refers to availability of information resources. There are two common approaches to develop an intrusion detection model: misuse detection model and anomaly detection model [2]. The misuse detection model refers to detection of intrusions that follow well-defined intrusion patterns. Every intrusion has some pattern e.g. number of packets, number of connection, bytes sent, duration etc. It matches the packets with the database of pattern. Whenever there is a match, alarms are raised. It is very useful in detecting known attack, but not suitable for unknown attacks. The anomaly detection model refers to detection performed by detecting changes in the patterns of utilization or behaviour of the system. Whenever there is any deviation from the normal behaviour activity, alarms are raised. Normal behaviour can be developed using different techniques such as statistical analysis, data mining algorithms, genetic algorithms, artificial neural network approach, fuzzy logic and rough set etc. The anomaly detection systems can detect new intrusions unlike the misuse detection systems. The IDSs can be network based or host based as far as the source of data is

### Image Edge Detection by Using Rule Based Fuzzy Classifier

processing such as image quality assessment, edge detection, image segmentation, etc. Many techniques have been suggested by researchers in the past for fuzzy logic- based edge detection. Devesh D. Nawgaje, et al presented a Fuzzy Inference System (FIS) approach to detect edge within color bone marrow microscopic images, which is robust with regard to variable illuminant level conditions, and takes into account color components stability degrees. They proposed a fuzzy technique which is based on the subjection of set of three pixels, part of a 2x2 window of an image to a set of fuzzy rules which help to highlight all the edges that are associated with an image[4]. Devesh D. Nawgaje, et al aimed at developing the edge detection techniques for breast cancer using Fuzzy Logic and DSP so that the disease may be detected in its early stage and proper and sooner steps may be taken thereafter. Edge detection is one of the important factors in the diagnosis of cancer [2]. Isha Jain, et al have been taken the images of moving and still vehicles and an algorithm is used for vehicle detection which is based on image processing techniques and classification of vehicles in the form of natural description( in linguistic terms) based on fuzzy logic[5].

### Hierarchical fuzzy rule based model for teaching performance evaluation

The design of fuzzy system mainly involves two operations of knowledge base derivation and the selection of the fuzzy inference process to perform the fuzzy reasoning (Cordon, et al. 1999). The successful development of a fuzzy model for a particular application domain is a complex multi-step process, in which the designer is faced with a large number of alternative implementation strategies (Garibaldi and Ifeachor, 1999). Fuzzy logic addresses such applications perfectly as it resembles human decision making with an ability to generate precise solutions from certain or approximate information. The advantage of fuzziness dealing with imprecision fit ideally into decision systems. The vagueness and uncertainty of human expressions are well modeled in the fuzzy sets and a pseudo-verbal representation, similar to an expert’s formulation, can be achieved (Hasiloglu, et al. 2003). A general scheme of a fuzzy model based on the environmental variables is shown in Figure 1.

### Fuzzy Rule based Enhanced Homomorphic Encryption in Cloud Computing

The first approach to artificial intelligence were (crisp) expert systems and models imitating the functionality of the human brain- so called artificial neural networks (ANNs). While conventional expert systems are rule based systems, which manipulate symbolic expressions based on traditional binary logic, neural nets are systems with, in most cases, real valued input and output, which can learn from sample data, but without the possibility to survey the actions inside. Fuzzy systems are rule based systems which are able to process vague, imprecise data. In this sense, fuzzy systems can be regarded as generalized rule based expert systems. This generalization requires a mathematical formulation of impreciseness and inference methods adapted to this model. To enhance the FHE based system fuzzy rule based system is being used by the generated cloud environment. This fuzzy rule based system can be worked on 27 different if-then rules and by using this cloud system will perform better and reduce the burden of the network. These rules are standard rules prepared by fuzzy rule based system and this local cloud system follows these rules and performs their actions. The proposed work is to implement Fully Homomorphic encryption environment by using .NET Environment and also to simulate a new fuzzy rule based FHE system which reduce the heavy burden of network and storage.

### Software Quality Prediction using Fuzzy Rule based System

Development of software quality, development effort etc is a common application of software metrics. A new tool as Fuzzy Logic offers a good technique for building models for software quality prediction. This paper illustrates the practice of estimation at a personal level using projects and presents the results obtained with a fuzzy rule based system and an ordinary multip