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Fuzzy support vector machine (FSVM) is a part of machine learning with its good classification effect. So far, there are two most commonly used FSVM models: FSVM on account of class core and fuzzy support vector machine on account of hyperplane that is over class core. Each has its own problems: FSVM on account of class core are dependent on the geometric shape of sample sets. Although FSVM on account of hyperplane that is over class core can solve the above problems to some extent. However, this algorithm has low generalization ability and high time complexity. Therefore, Inspired by these two common models, the paper proposes an improved membership function method. By analyzing and calculating the potential support vector sample points, adjustment factor is obtained, which drives the class core to adjust along the direction away from the outliers. In this way, membership of noise and outliers are reduced and the membership of support vector will also increase to some extent. In this paper, a new experimental comparison method is used, which can make the comparison of classification effect more obvious and convincing. The experimental part compares the proposed FSVM model with the above two FSVM models. It shows that the proposed algorithm improves the stability and classification accuracy to some extent.

Transactions in web data are huge amounts of data, often consisting of fuzzy and quantitative values. Mining fuzzy association rules can help discover interesting relationships between web data. The quality of these rules depends on membership functions, and thus, it is essential to find the suitable number and position of membership functions. The time spent by users on each web page, which shows their level of interest in those web pages, can be considered as a trapezoidal membership function (TMF). In this paper, the optimization problem was finding the appropriate number and position of TMFs for each web page. To solve this optimization problem, a learning automata-based algorithm was proposed to optimize the number and position of TMFs (LA-ONPTMF). Experiments conducted on two real datasets confirmed that the proposed algorithm enhances the efficiency of mining fuzzy association rules by extracting the optimized TMFs.

The safety of such a high-security structure as a deep-water explosion test vessel in service is still in the exploration stage. The reliability of the vessel needs to be analyzed in order to prevent the underwater explosion shock wave and other explosion products on the test equipment causing great damage to the experimental personnel. The safety of such a high-security structure as a deep-water explosion test vessel in service has gradually attracted the attention of scholars. The reliability of the vessel needs to be analyzed in order to prevent the shock wave of underwater explosion and other explosion products on the test equipment causing great damage to the experimental personnel. In this paper, the dynamic response test data of a deepwater explosion test vessel in service under different conditions and the Elman neural network are used to establish the dynamic response prediction model of the deepwater explosion test vessel, and using the established model to make dynamic response prediction in the next experiment; the vessel yield strength and modulus of elasticity are taken as random variables, and the container dynamic strain prediction interval is the interval variable, the random-interval reliability model is established by using the interval variable and random variable. The random variables of the model are transformed into interval variables, and the interval variables are fuzzified using the affiliation function to calculate the reliability index. Since the interval variable obtained from the model will change with the change of the container dynamic test data, the interval reliability index calculated by the stochastic-interval reliability analysis model can quantify the reliability of the container and can be used as a reference for the subsequent use of the container by reducing the reliability index to calculate the service life and drug filling amount.

This paper presents a low power CMOS analog integrated circuit of a Takagi–Sugeno fuzzy logic controller with voltage/voltage interface, small chip area, relatively high accuracy and medium speed, which is composed of several improved functional blocks. Z-shaped, Gaussian and S-shaped membership function circuits with compact structures are designed, performing well with low power, high speed and small areas. A current minimization circuit is provided with high accuracy and high speed. A follower-aggregation defuzzification block composed of several multipliers for center of gravity (COG) defuzzification is presented without using a division circuit. Based on these blocks, a two-input one-output singleton fuzzy controller with nine rules is designed under a CMOS 0.6 μm standard technology provided by CSMC. HSPICE simulation results show that this controller reaches an accuracy of ±3% with power consumption of only 3.5 mW (at ±2.5 V). The speed of this controller goes up to 0.625M Fuzzy Logic Inference per Second (FLIPS), which is fast enough for real-time control.

The objective of the work is to predict heart disease using computing techniques like an oppositional firefly with BAT and rule-based fuzzy logic (RBFL). The system would help the doctors to automate heart disease diagnosis and to enhance the medical care. In this paper, a hybrid OFBAT-RBFL heart disease diagnosis system is designed. Here, at first, the relevant features are selected from the dataset using locality preserving projection (LPP) algorithm which helps the diagnosis system to develop a classification model using the fuzzy logic system. After that, the rules for the fuzzy system are created from the sample data. Among the entire rules, the important and relevant group of rules are selected using OFBAT algorithm. Here, the opposition based learning (OBL) is hybrid to the firefly with BAT algorithm to improve the performance of the FAT algorithm while optimizing the rules of the fuzzy logic system. Next, the fuzzy system is designed with the help of designed fuzzy rules and membership functions so that classification can be carried out within the fuzzy system designed. At last, the experimentation is performed by means of publicly available UCI datasets, i.e., Cleveland, Hungarian and Switzerland datasets. The experimentation result proves that the RBFL prediction algorithm outperformed the existing approach by attaining the accuracy of 78%.

In this paper, we sought to determine whether fractal parameters alone are good enough in classifying astronomical images. A fuzzy membership function which follows the model of a parabola was chosen for the purpose and the success rate was found to be 73.45%. Also, we have investigated how the grade of membership functions affect the performance of a neural network classifier. For this we included the parameter, spectral flatness measure in addition to fractal dimension and the grades of both the parameters were given as input features to the neural net. It could be observed that when grades were given as inputs to the classifier, performance of the classifier has increased to 80.53%.

This paper presents a method to measure the similarity between different fuzzy concepts in order identify the user's fuzzy requests in a fuzzy semantic networks.

Tandem queueing models play an important role in many real world systems such as computer systems, production lines, and service systems. This paper proposes a procedure to construct the membership functions of the performance measures in tandem queueing systems, in that the arrival rate and service rates are fuzzy numbers. The basic idea is to transform a fuzzy tandem queue to a family of crisp tandem queues by applying the α -cut approach. Then on the basis of α -cut representation and the extension principle, a pair of mathematical programs is formulated to describe this family of crisp tandem queues, via which the membership functions of the performance measures are derived. Two numerical examples are solved successfully to demonstrate the validity of the proposed approach. Since the performance measures are expressed by membership functions rather than by crisp values, the fuzziness of input information is completely conserved. Thus the proposed approach for fuzzy systems can represent the system more accurately, and more information is provided for designing queueing systems. The successful extension of tandem queues to fuzzy environments permits tandem queueing models to have wider applications.

A fundamental problem in fuzzy analysis is that the membership function is specified subjectively. In other words, the modelers specify the membership function form and assign the values of the parameters in membership function via their working experiences. Different from its probabilistic counterpart, fuzzy mathematical theory does not provide convenient parameter estimation approach. In this paper, we first review Liu's non-classical credibility measure theory (i.e., (∨,·)-credibility measure theory) in Liu⁷, because the fuzzy theory initiated by Zadeh¹⁰ contains a critical weakness: non self-duality property for possibility measure. We establish a parameter estimation of the membership function in terms of maximum entropy principle on the ground of self-dual credibility measure theory. Furthermore, based on the data assimilated membership function, we can calculate membership grades on the fuzzy environmental index, using PM¹⁰ air pollution as an illustration. We treat the calculated membership grades as spatially distributed random quantity, and therefore perform the standard ordinary kriging approach for generating the predicted environmental index map, for PM¹⁰ prediction map.

Since fuzzy linear regression was introduced by Tanaka et al., fuzzy regression analysis has been widely studied and applied in various areas. Diamond proposed the fuzzy least squares method to eliminate disadvantages in the Tanaka et al method. In this paper, we propose a modified fuzzy least squares regression analysis. When independent variables are crisp, the dependent variable is a fuzzy number and outliers are present in the data set. In the proposed method, the residuals are ranked as the comparison of fuzzy sets, and the weight matrix is defined by the membership function of the residuals. To illustrate how the proposed method is applied, two examples are discussed and compared in methods from the literature. Results from the numerical examples using the proposed method give good solutions.

A generalized Bayesian inference nets model (GBINM) and a new approach for internal fault detection and diagnosis of three-phase induction motor is proposed. The input data set for designing and testing the fault diagnostic system are acquired through on-site experiment. The preprocessed input data and experts' rich diagnostic experience/knowledge are used to define the membership functions and fault fuzzy sets. With GBINM and the defined fault fuzzy sets, the hierarchical Bayesian fuzzy inference nets are constructed to carry out the complex motor fault diagnostic procedure. The propagation of probability is used to address the uncertainties involved in detecting and diagnosing the motor incipient faults. The immense difficulties of defining and assigning statistical parameters, required for calculating the propagation of probability are effectively solved. The validity and effectiveness of the proposed approach is witnessed clearly from the testing results obtained.

Color knowledge representation is an essential aspect for designing intelligent graphic systems. Since the mapping between low-level color numerical values and high-level semantics is crucial, the theory of fuzzy numbers is greatly needed for representing color concepts. The limited linguistic color words bring about the requirement for representing intermediate color concepts. However, there is not corresponding definitions in the fuzzy realm. To overcome this representational inadequacy, this work addresses the issue of formally defining the intermediate fuzzy concept. Since definitions of the intermediate fuzzy numbers need a well-defined order between two basic fuzzy numbers, this paper first presents a cognition based linguistic ranking method. Then two novel definitions, namely, intermediate fuzzy numbers and intermediate operations on fuzzy numbers, are presented. The definitions are of abstract ones in order for general use. Besides, the paper also presents and studies some specific intermediate fuzzy numbers and intermediate operations, which are important for modelling gradual changes between two color terms in Color Naming System.

Data mining is most commonly used in attempts to induce association rules from transaction data. Since transactions in real-world applications usually consist of quantitative values, many fuzzy association-rule mining approaches have been proposed on single- or multiple-concept levels. However, the given membership functions may have a critical influence on the final mining results. In this paper, we propose a multiple-level genetic-fuzzy mining algorithm for mining membership functions and fuzzy association rules using multiple-concept levels. It first encodes the membership functions of each item class (category) into a chromosome according to the given taxonomy. The fitness value of each individual is then evaluated by the summation of large 1-itemsets of each item in different concept levels and the suitability of membership functions in the chromosome. After the GA process terminates, a better set of multiple-level fuzzy association rules can then be expected with a more suitable set of membership functions. Experimental results on a simulation dataset also show the effectiveness of the algorithm.

This paper proposes an Enhanced Particle Swarm Optimization (EPSO) for extracting optimal rule set and tuning membership function for fuzzy logic based classifier model. The standard PSO is more sensitive to premature convergence due to lack of diversity in the swarm and can easily get trapped into local minima when it is used for data classification. To overcome this issue, BLX-α crossover and Non-uniform mutation from Genetic Algorithm (GA) are incorporated in addition to standard velocity and position updating of PSO. The performance of the proposed approach is evaluated using ten publicly available bench mark data sets. From the simulation study, it is found that the proposed approach enhances the convergence and generates a comprehensible fuzzy classifier system with high classification accuracy for all the data sets. Statistical analysis of the test result shows the suitability of the proposed method over other approaches reported in the literature.

A well-known version of minimal cost flow problem with fuzzy arc costs is focused in this study. The fuzzy arc costs is applied as in most of real-world applications, the parameters have high degree of uncertainty. The goal of this problem is to determine the minimum fuzzy cost of sending and passing a specified flow value in to and from a network. A decomposition-based solution methodology is introduced to tackle this problem. The methodology applies Zadeh’s extension principle to decompose the problem to two upper bound and lower bound problems. These problems are capable of being solved for different α-cut values to construct the fuzzy cost flow value as the objective function value. The efficiency of the proposed solution methodology is studied over some well-known examples of the minimal cost flow problem. The obtained results and the procedure applied to obtain them prove the superiority of the proposed approach comparing to the previous approaches of the literature.

When some coefficients of the constraints are uncertain with only their possible ranges being given, a conventional linear programming (LP) problem can be generalised to the one with set-inclusive constraints. We consider the case where the possible ranges are given by fuzzy sets in this paper. The set-inclusive constraints with fuzzy coefficients have been treated by a necessity measure. However, the usual necessity measure cannot express well the decision-maker’s requirement about the trade-off between the robustness level and the satisfaction level of the constraints. We extend the necessity measure to incorporate the trade-off between the robustness level and the satisfaction level of the constraints. We apply the extended necessity measure to LP problems with fuzzy coefficients. After the problem is formulated and reduced to the conventional programming problem, we propose a solution algorithm. Numerical examples are given to illustrate the proposed approach.

The optimization techniques used in commercial-off-the-shelf (COTS) selection process faces challenges to deal with uncertainty in many important selection parameters, for example, cost, reliability and delivery time. In this paper, we propose a fuzzy optimization model for selecting the best COTS product among the available alternatives for each module in the development of modular software systems. The proposed model minimizes the total cost of the software system satisfying the constraints of minimum threshold on system reliability, maximum threshold on the delivery time of the software, and incompatibility among COTS products. In order to deal with uncertainty in real-world applications of COTS selection, the coefficients of the cost objective function, delivery time constraints and minimum threshold on reliability are considered fuzzy numbers. The fuzzy optimization model is converted into a pair of mathematical programming problems parameterized by possibility (feasibility) level α using Zadeh's extension principle. The solutions of the resultant problems at different α-cuts provide lower and upper bounds of the fuzzy minimum total cost which helps in constructing the membership function of the cost objective function. The solution approach provide fuzzy solutions instead of a single crisp solution thereby giving decision maker enough flexibility in maintaining cost-reliability trade-off of COTS selection besides meeting other important system requirements. A real-world case study is discussed to demonstrate the effectiveness of the proposed model in fuzzy environment.

In this paper, we propose a multi-choice goal programming (MCGP) model of the multi-objective commercial-off-the-shelf (COTS) products selection problem. The proposed model simultaneously minimize the total cost, size, execution time and delivery time and maximize the system reliability of a modular software system subject to many realistic constraints including incompatibility among COTS products. We assume that the decision maker provides multiple aspiration levels regarding cost, size, execution time, delivery time and reliability objectives using discrete choices. To obtain efficient COTS selection plans, we use MCGP methodology to solve the COTS products selection problem. A real-world case study is discussed to demonstrate the effectiveness of the proposed model and methodology.

In this paper, we study a decision-making problem related to software creation using commercial-off-the-shelf (COTS) products in a modular software system. The optimal selection of COTS products is difficult due to the variations in various critical parameters such as cost, reliability, execution time, and delivery time. Further, it is difficult to estimate precisely the values of these parameters since sufficient data may not be available and also there could be measurement errors. We present a fuzzy 0–1 optimization model of the multiobjective COTS products selection problem using exponential membership functions that simultaneously minimize the total cost, size, execution time and delivery time and maximize the reliability of a modular software system subject to many realistic constraints. The fuzzy goals are defined for each selection criterion as per the preferences of the decision maker and are aggregated using product operator to obtain an equivalent optimization model for optimal COTS selection. A real-world case study is discussed to demonstrate the effectiveness of the proposed model and the solution methodology.

Multiple criteria linear programming and multiple criteria quadratic programming classification models have been applied in some field in financial risk analysis and credit risk control such as credit cardholders' behavior analysis. In this paper, a fuzzy linear programming classification method with soft constraints and criteria was proposed based on the previous findings from other researchers. In this method, the satisfied result can be obtained through selecting constraint and criteria boundary variable d_i*, respectively. A general framework of this method is also constructed. Two real-life datasets, one from a major USA bank and the other from a database of KDD 99, are used to test the accurate rate of the proposed method. And the result shows the feasibility of this method.