A GA-based Fuzzy Mining Approach to Achieve a Trade-off Between Number of Rules and Suitability of Membership Functions

Data mining is most commonly used in attempts to induce association rules from transaction data. Transactions in real-world applications, however, usually consist of quantitative values. This paper thus proposes a fuzzy data-mining algorithm for extracting both association rules and membership functions from quantitative transactions. We present a GA-based framework for finding membership functions suitable for mining problems and then use the final best set of membership functions to mine fuzzy association rules. The fitness of each chromosome is evaluated by the number of large 1-itemsets generated from part of the previously proposed fuzzy mining algorithm and by the suitability of the membership functions. Experimental results also show the effectiveness of the framework.     

A multi-level ant-colony mining algorithm for membership functions

Fuzzy data mining is used to extract fuzzy knowledge from linguistic or quantitative data. It is an extension of traditional data mining and the derived knowledge is relatively meaningful to human beings. In the past, we proposed a mining algorithm to find suitable membership functions for fuzzy association rules based on ant colony systems. In that approach, precision was limited by the use of binary bits to encode the membership functions. This paper elaborates on the original approach to increase the accuracy of results by adding multi-level processing. A multi-level ant colony framework is thus designed and an algorithm based on the structure is proposed to achieve the purpose. The proposed approach first transforms the fuzzy mining problem into a multi-stage graph, with each route representing a possible set of membership functions. The new approach then extends the previous one, using multi-level processing to solve the problem in which the maximum quantities of item values in the transactions may be large. The membership functions derived in a given level will be refined in the subsequent level. The final membership functions in the last level are then outputted to the rule-mining phase to find fuzzy association rules. Experiments are also performed to show the performance of the proposed approach. The experimental results show that the proposed multi-level ant colony systems mining approach can obtain improved results.     

Genetic-Fuzzy Data Mining With Divide-and-Conquer Strategy

Data mining is most commonly used in attempts to induce association rules from transaction data. Most previous studies focused on binary-valued transaction data. Transaction data in real-world applications, however, usually consist of quantitative values. This paper, thus, proposes a fuzzy data-mining algorithm for extracting both association rules and membership functions from quantitative transactions. A genetic algorithm (GA)-based framework for finding membership functions suitable for mining problems is proposed. The fitness of each set of membership functions is evaluated by the fuzzy-supports of the linguistic terms in the large 1-itemsets and by the suitability of the derived membership functions. The evaluation by the fuzzy supports of large 1-itemsets is much faster than that when considering all itemsets or interesting association rules. It can also help divide-and-conquer the derivation process of the membership functions for different items. The proposed GA framework, thus, maintains multiple populations, each for one item's membership functions. The final best sets of membership functions in all the populations are then gathered together to be used for mining fuzzy association rules. Experiments are conducted to analyze different fitness functions and set different fitness functions and setting different supports and confidences. Experiments are also conducted to compare the proposed algorithm, the one with uniform fuzzy partition, and the existing one without divide-and-conquer, with results validating the performance of the proposed algorithm.     

A genetic-fuzzy mining approach for items with multiple minimum supports

Data mining is the process of extracting desirable knowledge or interesting patterns from existing databases for specific purposes. Mining association rules from transaction data is most commonly seen among the mining techniques. Most of the previous mining approaches set a single minimum support threshold for all the items and identify the relationships among transactions using binary values. In the past, we proposed a genetic-fuzzy data-mining algorithm for extracting both association rules and membership functions from quantitative transactions under a single minimum support. In real applications, different items may have different criteria to judge their importance. In this paper, we thus propose an algorithm which combines clustering, fuzzy and genetic concepts for extracting reasonable multiple minimum support values, membership functions and fuzzy association rules from quantitative transactions. It first uses the k-means clustering approach to gather similar items into groups. All items in the same cluster are considered to have similar characteristics and are assigned similar values for initializing a better population. Each chromosome is then evaluated by the criteria of requirement satisfaction and suitability of membership functions to estimate its fitness value. Experimental results also show the effectiveness and the efficiency of the proposed approach.     

Mining fuzzy temporal association rules by item lifespans

Data mining is the process of extracting desirable knowledge or interesting patterns from existing databases for specific purposes. In real-world applications, transactions may contain quantitative values and each item may have a lifespan from a temporal database. In this paper, we thus propose a data mining algorithm for deriving fuzzy temporal association rules. It first transforms each quantitative value into a fuzzy set using the given membership functions. Meanwhile, item lifespans are collected and recorded in a temporal information table through a transformation process. The algorithm then calculates the scalar cardinality of each linguistic term of each item. A mining process based on fuzzy counts and item lifespans is then performed to find fuzzy temporal association rules. Experiments are finally performed on two simulation datasets and the foodmart dataset to show the effectiveness and the efficiency of the proposed approach.     

A continuous ant colony system framework for fuzzy data mining

The goal of data mining is to find out interesting and meaningful patterns from large databases. In some real applications, many data are quantitative and linguistic. Fuzzy data mining was thus proposed to discover fuzzy knowledge from this kind of data. In the past, two mining algorithms based on the ant colony systems were proposed to find suitable membership functions for fuzzy association rules. They transformed the problem into a multi-stage graph, with each route representing a possible set of membership functions, and then, used the any colony system to solve it. They, however, searched for solutions in a discrete solution space in which the end points of membership functions could be adjusted only in a discrete way. The paper, thus, extends the original approaches to continuous search space, and a fuzzy mining algorithm based on the continuous ant approach is proposed. The end points of the membership functions may be moved in the continuous real-number space. The encoding representation and the operators are also designed for being suitable in the continuous space, such that the actual global optimal solution is contained in the search space. Besides, the proposed approach does not have fixed edges and nodes in the search process. It can dynamically produce search edges according to the distribution functions of pheromones in the solution space. Thus, it can get a better nearly global optimal solution than the previous two ant-based fuzzy mining approaches. The experimental results show the good performance of the proposed approach as well.     

An improved approach to find membership functions and multiple minimum supports in fuzzy data mining

Fuzzy mining approaches have recently been discussed for deriving fuzzy knowledge. Since items may have their own characteristics, different minimum supports and membership functions may be specified for different items. In the past, we proposed a genetic-fuzzy data-mining algorithm for extracting minimum supports and membership functions for items from quantitative transactions. In that paper, minimum supports and membership functions of all items are encoded in a chromosome such that it may be not easy to converge. In this paper, an enhanced approach is proposed, which processes the items in a divide-and-conquer strategy. The approach is called divide-and-conquer genetic-fuzzy mining algorithm for items with Multiple Minimum Supports (DGFMMS), and is designed for finding minimum supports, membership functions, and fuzzy association rules. Possible solutions are evaluated by their requirement satisfaction divided by their suitability of derived membership functions. The proposed GA framework maintains multiple populations, each for one item’s minimum support and membership functions. The final best minimum supports and membership functions in all the populations are then gathered together to be used for mining fuzzy association rules. Experimental results also show the effectiveness of the proposed approach.     

Integrating fuzzy knowledge by genetic algorithms

We propose a genetic algorithm-based fuzzy knowledge integration framework that can simultaneously integrate multiple fuzzy rule sets and their membership function sets. The proposed approach consists of two phases: fuzzy knowledge encoding and fuzzy knowledge integration. In the encoding phase, each fuzzy rule set with its associated membership functions is first transformed into an intermediary representation and then further encoded as a string. The combined strings form an initial knowledge population, which is then ready for integration. In the knowledge-integration phase, a genetic algorithm is used to generate an optimal or nearly optimal set of fuzzy rules and membership functions from the initial knowledge population. Two application domains, the hepatitis diagnosis and the sugarcane breeding prediction, were used to show the performance of the proposed knowledge-integration approach. Results show that the fuzzy knowledge base derived using our approach performs better than every individual knowledge base     

Genetic-fuzzy mining with multiple minimum supports based on fuzzy clustering

Data mining is the process of extracting desirable knowledge or interesting patterns from existing databases for specific purposes. Most of the previous approaches set a single minimum support threshold for all the items and identify the relationships among transactions using binary values. In real applications, different items may have different criteria to judge their importance. In the past, we proposed an algorithm for extracting appropriate multiple minimum support values, membership functions and fuzzy association rules from quantitative transactions. It used requirement satisfaction and suitability of membership functions to evaluate fitness values of chromosomes. The calculation for requirement satisfaction might take a lot of time, especially when the database to be scanned could not be totally fed into main memory. In this paper, an enhanced approach, called the fuzzy cluster-based genetic-fuzzy mining approach for items with multiple minimum supports (FCGFMMS), is thus proposed to speed up the evaluation process and keep nearly the same quality of solutions as the previous one. It divides the chromosomes in a population into several clusters by the fuzzy k-means clustering approach and evaluates each individual according to both their cluster and their own information. Experimental results also show the effectiveness and the efficiency of the proposed approach.     

一种基于遗传算法的模糊关联规则挖掘方法

文中提出了一种基于遗传算法的生成隶属度函数的方法,该方法通过遗传算法对初始种群进行优化,获得一个适应度较高的隶属度函数编码,然后再根据机场噪声数据的实际标准对优化后得到的隶属度函数进行修正,进而得到梯形分布的隶属度函数编码.最后通过得到的隶属度函数对数据进行模糊化,并采用FP-trees算法生成模糊关联规则.该文针对数量型属性提出了这种方法,它的优点是能够使通过遗传算法得到的较优的隶属度函数更加适用于实际的数据集.     

An effective parallel approach for genetic-fuzzy data mining

Data mining is most commonly used in attempts to induce association rules from transaction data. In the past, we used the fuzzy and GA concepts to discover both useful fuzzy association rules and suitable membership functions from quantitative values. The evaluation for fitness values was, however, quite time-consuming. Due to dramatic increases in available computing power and concomitant decreases in computing costs over the last decade, learning or mining by applying parallel processing techniques has become a feasible way to overcome the slow-learning problem. In this paper, we thus propose a parallel genetic-fuzzy mining algorithm based on the master–slave architecture to extract both association rules and membership functions from quantitative transactions. The master processor uses a single population as a simple genetic algorithm does, and distributes the tasks of fitness evaluation to slave processors. The evolutionary processes, such as crossover, mutation and production are performed by the master processor. It is very natural and efficient to run the proposed algorithm on the master–slave architecture. The time complexities for both sequential and parallel genetic-fuzzy mining algorithms have also been analyzed, with results showing the good effect of the proposed one. When the number of generations is large, the speed-up can be nearly linear. The experimental results also show this point. Applying the master–slave parallel architecture to speed up the genetic-fuzzy data mining algorithm is thus a feasible way to overcome the low-speed fitness evaluation problem of the original algorithm.     

Mining fuzzy β-certain and β-possible rules from quantitative data based on the variable precision rough-set model

The rough-set theory proposed by Pawlak, has been widely used in dealing with data classification problems. The original rough-set model is, however, quite sensitive to noisy data. Ziarko thus proposed the variable precision rough-set model to deal with noisy data and uncertain information. This model allowed for some degree of uncertainty and misclassification in the mining process. Conventionally, the mining algorithms based on the rough-set theory identify the relationships among data using crisp attribute values; however, data with quantitative values are commonly seen in real-world applications. This paper thus deals with the problem of producing a set of fuzzy certain and fuzzy possible rules from quantitative data with a predefined tolerance degree of uncertainty and misclassification. A new method, which combines the variable precision rough-set model and the fuzzy set theory, is thus proposed to solve this problem. It first transforms each quantitative value into a fuzzy set of linguistic terms using membership functions and then calculates the fuzzy β-lower and the fuzzy β-upper approximations. The certain and possible rules are then generated based on these fuzzy approximations. These rules can then be used to classify unknown objects. The paper thus extends the existing rough-set mining approaches to process quantitative data with tolerance of noise and uncertainty.     

一种用模糊－神经技术建造专家系统的方法

本文提出了一种用模糊－神经技术建造专家系统的方法（ＦＮＴ方法）。从领域专家处获取的知识是以模糊规则和隶属函数的形式表示的。根据本文提出的方法，首先将模糊规则和隶属函数用神经网络表示出来（导入）；生成的神经网络用于实现模糊推理，然后利用修改的反传算法训练神经网络，从而提高系统的精度，修改隶属函数，求精模糊规则；最后从神经网络中提取隶属函数和模糊规则（导出），帮助解释神经网络的内部表示和操作。利用本文所提出的方法建造的系统可实现快速的无匹配模糊推理，并具有较强的学习能力。     

A fuzzy coherent rule mining algorithm

In real-world applications, transactions usually consist of quantitative values. Many fuzzy data mining approaches have thus been proposed for finding fuzzy association rules with the predefined minimum support from the give quantitative transactions. However, the common problems of those approaches are that an appropriate minimum support is hard to set, and the derived rules usually expose common-sense knowledge which may not be interesting in business point of view. In this paper, an algorithm for mining fuzzy coherent rules is proposed for overcoming those problems with the properties of propositional logic. It first transforms quantitative transactions into fuzzy sets. Then, those generated fuzzy sets are collected to generate candidate fuzzy coherent rules. Finally, contingency tables are calculated and used for checking those candidate fuzzy coherent rules satisfy the four criteria or not. If yes, it is a fuzzy coherent rule. Experiments on the foodmart dataset are also made to show the effectiveness of the proposed algorithm.     

Incremental fuzzy temporal association rule mining using fuzzy grid table

Traditional temporal association rules mining algorithms cannot dynamically update the temporal association rules within the valid time interval with increasing data. In this paper, a new algorithm called incremental fuzzy temporal association rule mining using fuzzy grid table (IFTARMFGT) is proposed by combining the advantages of boolean matrix with incremental mining. First, multivariate time series data are transformed into discrete fuzzy values that contain the time intervals and fuzzy membership. Second, in order to improve the mining efficiency, the concept of boolean matrices was introduced into the fuzzy membership to generate a fuzzy grid table to mine the frequent itemsets. Finally, in view of the Fast UPdate (FUP) algorithm, fuzzy temporal association rules are incrementally mined and updated without repeatedly scanning the original database by considering the lifespan of each item and inheriting the information from previous mining results. The experiments show that our algorithm provides better efficiency and interpretability in mining temporal association rules than other algorithms.

     

AUTOMATICALLY CONSTRUCTING MEMBERSHIP FUNCTIONS AND GENERATING FUZZY RULES USING GENETIC ALGORITHMS

The most important task in designing a fuzzy classification system is to find a set of fuzzy rules from training data to deal with a specific classification problem. In recent years, many methods have been proposed to construct membership functions and generate fuzzy rules from training data for handling fuzzy classification problems. We propose a new method to generate fuzzy rules from training data by using genetic algorithms (GAs). First, we divide the training data into several clusters by using the weighted distance clustering method and generate a fuzzy rule for each cluster. Then, we use GAs to tune the membership functions of the generated fuzzy rules. The proposed method attains a higher average classification accuracy rate than the existing methods.     

模糊关联规则挖掘模型及其在分解炉中的应用

研究了模糊关联规则挖掘模型在分解炉中的应用,并阐述了模糊聚类算法和关联规则的相关内容,提出运用模糊聚类KFCM算法对实际数据进行计算,得到数据归属于不同类别的隶属度.同时,利用规则挖掘算法MFAR对模糊化的参数进行处理,得到了有价值的模糊规则,解决了实际中专家经验获取的瓶颈问题.试验表明,该方法为水泥生产环节中分解炉的温度控制提供了理论依据和生产优化指导.     

Mining Fuzzy Multiple-Level Association Rules from Quantitative Data

Machine-learning and data-mining techniques have been developed to turn data into useful task-oriented knowledge. Most algorithms for mining association rules identify relationships among transactions using binary values and find rules at a single-concept level. Transactions with quantitative values and items with hierarchical relationships are, however, commonly seen in real-world applications. This paper proposes a fuzzy multiple-level mining algorithm for extracting knowledge implicit in transactions stored as quantitative values. The proposed algorithm adopts a top-down progressively deepening approach to finding large itemsets. It integrates fuzzy-set concepts, data-mining technologies and multiple-level taxonomy to find fuzzy association rules from transaction data sets. Each item uses only the linguistic term with the maximum cardinality in later mining processes, thus making the number of fuzzy regions to be processed the same as the number of original items. The algorithm therefore focuses on the most important linguistic terms for reduced time complexity.     

A new method for constructing membership functions and fuzzy rulesfrom training examples

To extract knowledge from a set of numerical data and build up a rule-based system is an important research topic in knowledge acquisition and expert systems. In recent years, many fuzzy systems that automatically generate fuzzy rules from numerical data have been proposed. In this paper, we propose a new fuzzy learning algorithm based on the alpha-cuts of equivalence relations and the alpha-cuts of fuzzy sets to construct the membership functions of the input variables and the output variables of fuzzy rules and to induce the fuzzy rules from the numerical training data set. Based on the proposed fuzzy learning algorithm, we also implemented a program on a Pentium PC using the MATLAB development tool to deal with the Iris data classification problem. The experimental results show that the proposed fuzzy learning algorithm has a higher average classification ratio and can generate fewer rules than the existing algorithm.     

Application of fuzzy logic and variable precision rough set approach in a remote monitoring manufacturing process for diagnosis rule induction

Rough set has been shown to be a valuable approach to mine rules from a remote monitoring manufacturing process. In this research, an application of the fuzzy set theory with the fuzzy variable precision rough set approach for mining the causal relationship rules from the database of a remote monitoring manufacturing process is presented. The membership function in the fuzzy set theory is used to transfer the data entries into fuzzy sets, and the fuzzy variable precision rough set approach is applied to extract rules from the fuzzy sets. It is found that the induced rules are identical to the practical knowledge and fault diagnosis thinking of human operators. The induced rules are then compared with the rules induced by the original rough set approach. The comparison shows that the rules induced by the fuzzy rough set are expressed in linguistic forms, and are evaluated by plausibility and future effectiveness measures. The fuzzy rough set approach, being less sensitive to noisy data, induces better rules than the original rough set approach.