Rule-based classifier, that extract a subset of induced rules to efficiently learn/mine while preserving the discernibility information, plays a crucial role in human-explainable artificial intelligence. However, in this era of big data, rule induction on the whole datasets is computationally intensive. So far, to the best of our knowledge, no known method focusing on accelerating rule induction has been reported. This is first study to consider the acceleration technique to reduce the scale of computation in rule induction. We propose an accelerator for rule induction based on fuzzy rough theory; the accelerator can avoid redundant computation and accelerate the building of a rule classifier. First, a rule induction method based on consistence degree, called Consistence-based Value Reduction (CVR), is proposed and used as basis to accelerate. Second, we introduce a compacted search space termed Key Set, which only contains the key instances required to update the induced rule, to conduct value reduction. The monotonicity of Key Set ensures the feasibility of our accelerator. Third, a rule-induction accelerator is designed based on Key Set, and it is theoretically guaranteed to display the same results as the unaccelerated version. Specifically, the rank preservation property of Key Set ensures consistency between the rule induction achieved by the accelerator and the unaccelerated method. Finally, extensive experiments demonstrate that the proposed accelerator can perform remarkably faster than the unaccelerated rule-based classifier methods, especially on datasets with numerous instances.
Optimising the attribute order in Fuzzy Rough Rule Induction
Department of Mathematics, Computer Science and Statistics, Ghent University（数学、计算机科学与统计学系，根特大学）；Faculty of Economics, University of Catania（经济学院，卡塔尼娅大学）；Institute of Computing Science, Poznań University of Technology（计算科学研究所，波兹南技术大学）；Systems Research Institute, Polish Academy of Sciences（系统研究所，波兰科学院）
Several research initiatives have been proposed for computing similarity between two Fuzzy Sets in analysis through Fuzzy Rough Sets. These techniques yield two measures viz. lower similarity and upper similarity. While in most applications only one entity is useful to further analysis and for drawing conclusions. The aim of this paper is to propose novel technique to combine Fuzzy Rough Set based lower similarity and upper similarity using Fuzzy Inference Engine. Further, the proposed approach is applied to the problem computing sentence similarity and have been evaluated on SICK2014 dataset.
Northwest A & F University（西北农林科技大学）；Northwest Normal University（西北师范大学）
In this paper, we mainly construct three types of $L$-fuzzy $β$-covering-based rough set models and study the axiom sets, matrix representations and interdependency of these three pairs of $L$-fuzzy $β$-covering-based rough approximation operators. Firstly, we propose three pairs of $L$-fuzzy $β$-covering-based rough approximation operators by introducing the concepts such as $β$-degree of intersection and $β$-subsethood degree, which are generalizations of degree of intersection and subsethood degree, respectively. And then, the axiom set for each of these $L$-fuzzy $β$-covering-based rough a…
In order to involve user knowledge in determining equality of sets, which may not be equal in the mathematical sense, three types of approximate (rough) equalities were introduced by Novotny and Pawlak ([8, 9, 10]). These notions were generalized by Tripathy, Mitra and Ojha ([13]), who introduced the concepts of approximate (rough) equivalences of sets. Rough equivalences capture equality of sets at a higher level than rough equalities. More properties of these concepts were established in [14]. Combining the conditions for the two types of approximate equalities, two more approximate equaliti…
Northwest A & F University（西北农林科技大学）；Northwest Normal University（西北师范大学）
Since Bustince et al. introduced the concepts of overlap and grouping functions, these two types of aggregation functions have attracted a lot of interest in both theory and applications. In this paper, the depiction of $(O,G)$-granular variable precision fuzzy rough sets ($(O,G)$-GVPFRSs for short) is first given based on overlap and grouping functions. Meanwhile, to work out the approximation operators efficiently, we give another expression of upper and lower approximation operators by means of fuzzy implications and co-implications. Furthermore, starting from the perspective of constructio…
Department of Electrical and Computer Engineering, University of Alberta（阿尔伯塔大学电气与计算机工程系）；Department of Computer Science and Technology, Nanjing University（南京大学计算机科学与技术系）；School of Computer, Jiangsu University of Science and Technology（江苏科技大学计算机学院）；School of Artificial Intelligence and Computer Science, Nantong University（南通大学人工智能与计算机科学学院）
University of Macau（澳门大学）；Zhuhai Institutes of Advanced Technology of the Chinese Academy of Sciences（中国科学院珠海先进技术研究院）；Techno India College of Technology（印度Techno印度科技学院）；Universidad Internacional de La Rioja（拉里奥哈国际大学）；University of Granada（格拉纳达大学）
In the advent of the novel coronavirus epidemic since December 2019, governments and authorities have been struggling to make critical decisions under high uncertainty at their best efforts. Composite Monte-Carlo (CMC) simulation is a forecasting method which extrapolates available data which are broken down from multiple correlated/casual micro-data sources into many possible future outcomes by drawing random samples from some probability distributions. For instance, the overall trend and propagation of the infested cases in China are influenced by the temporal-spatial data of the nearby citi…
Fuzzy rough set (FRS) has a great effect on data mining processes and the fuzzy logical operators play a key role in the development of FRS theory. In order to further generalize the FRS theory to more complicated data environments, we firstly propose four types of fuzzy neighborhood operators based on fuzzy covering by overlap functions and their implicators in this paper. Meanwhile, the derived fuzzy coverings from an original fuzzy covering are defined and the equalities among overlap function-based fuzzy neighborhood operators based on a finite fuzzy covering are also investigated. Secondl…
Changsha University of Science and Technology（长沙理工大学）；Hunan University（湖南大学）
In practical situations, interval-valued fuzzy sets are frequently encountered. In this paper, firstly, we present shadowed sets for interpreting and understanding interval fuzzy sets. We also provide an analytic solution to computing the pair of thresholds by searching for a balance of uncertainty in the framework of shadowed sets. Secondly, we construct errors-based three-way approximations of interval-valued fuzzy sets. We also provide an alternative decision-theoretic formulation for calculating the pair of thresholds by transforming interval-valued loss functions into single-valued loss f…
Memorial University of Newfoundland（纽芬兰纪念大学）；University of Windsor（温莎大学）；Shahid Bahonar University of Kerman（克尔曼沙希德·巴霍纳尔大学）；Gwangju Institute of Science and Technology（光州科学技术院）
Feature selection and attribute reduction are crucial problems, and widely used techniques in the field of machine learning, data mining and pattern recognition to overcome the well-known phenomenon of the Curse of Dimensionality, by either selecting a subset of features or removing unrelated ones. This paper presents a new feature selection method that efficiently carries out attribute reduction, thereby selecting the most informative features of a dataset. It consists of two components: 1) a measure for feature subset evaluation, and 2) a search strategy. For the evaluation measure, we have …
Meghnad Saha Institute of Technology（梅格纳德·萨哈理工学院）；Netaji Subhas Open University（苏巴斯·钱德拉·鲍斯开放大学）；St. Xavier’s College（圣沙勿略学院）
In India financial markets have existed for many years. A functionally accented, diverse, efficient and flexible financial system is vital to the national objective of creating a market driven, productive and competitive economy. Today markets of varying maturity exist in equity, debt, commodities and foreign exchange. In this work we attempt to generate prediction rules scheme for stock price movement at Bombay Stock Exchange using an important Soft Computing paradigm viz., Rough Fuzzy Multi Layer Perception. The use of Computational Intelligence Systems such as Neural Networks, Fuzzy Sets, G…
Fuzzy Granule Density-Based Outlier Detection with Multi-Scale Granular Balls
College of Computer Science and Software Engineering, Shenzhen University（深圳大学计算机与软件学院）；National Engineering Laboratory for Big Data System Computing Technology, Shenzhen University（深圳大学大数据系统计算技术国家工程实验室）；School of Artificial Intelligence and Computer Science, Nantong University（南通大学人工智能与计算机科学学院）；Faculty of Data Science, City University of Macau（澳门城市大学数据科学学院）；Department of Electrical and Computer Engineering, University of Alberta（阿尔伯塔大学电气与计算机工程系）；Systems Research Institute, Polish Academy of Sciences（波兰科学院系统研究所）；Department of Electrical and Computer Engineering, King Abdulaziz University（阿卜杜勒阿齐兹大学电气与计算机工程系）；Department of Computer Engineering, Istinye University（伊斯提尼耶大学计算机工程系）
School of Computing Sciences and Engineering, VIT University（VIT大学计算科学与工程学院）
Emergences of computers and information technological revolution made tremendous changes in the real world and provides a different dimension for the intelligent data analysis. Well formed fact, the information at right time and at right place deploy a better knowledge.However, the challenge arises when larger volume of inconsistent data is given for decision making and knowledge extraction. To handle such imprecise data certain mathematical tools of greater importance has developed by researches in recent past namely fuzzy set, intuitionistic fuzzy set, rough Set, formal concept analysis and …
Performance evaluation of various organizations especially educational institutions is a very important area of research and needs to be cultivated more. In this paper, we propose a performance evaluation for educational institutions using rough set on fuzzy approximation spaces with ordering rules and information entropy. In order to measure the performance of educational institutions, we construct an evaluation index system. Rough set on fuzzy approximation spaces with ordering is applied to explore the evaluation index data of each level. Furthermore, the concept of information entropy is u…
Medical diagnosis process vary in the degree to which they attempt to deal with different complicating aspects of diagnosis such as relative importance of symptoms, varied symptom pattern and the relation between diseases them selves. Based on decision theory, in the past many mathematical models such as crisp set, probability distribution, fuzzy set, intuitionistic fuzzy set were developed to deal with complicating aspects of diagnosis. But, many such models are failed to include important aspects of the expert decisions. Therefore, an effort has been made to process inconsistencies in data b…
Netaji Subhas Open University（内塔吉·苏巴斯开放大学）；St. Xavier’s College（圣沙勿略学院）
The Fuzzy Modeling has been applied in a wide variety of fields such as Engineering and Management Sciences and Social Sciences to solve a number Decision Making Problems which involve impreciseness, uncertainty and vagueness in data. In particular, applications of this Modeling technique in Decision Making Problems have remarkable significance. These problems have been tackled using various theories such as Probability theory, Fuzzy Set Theory, Rough Set Theory, Vague Set Theory, Approximate Reasoning Theory etc. which lack in parameterization of the tools due to which they could not be appli…
Neutrosophic theory and applications have been expanding in all directions at an astonishing rate especially after the introduction the journal entitled Neutrosophic Sets and Systems. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structure such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hes…
This paper describes application of information granulation theory, on the analysis of "lugeon data". In this manner, using a combining of Self Organizing Map (SOM) and Neuro-Fuzzy Inference System (NFIS), crisp and fuzzy granules are obtained. Balancing of crisp granules and sub- fuzzy granules, within non fuzzy information (initial granulation), is rendered in open-close iteration. Using two criteria, "simplicity of rules "and "suitable adaptive threshold error level", stability of algorithm is guaranteed. In other part of paper, rough set theory (RST), to approximate analysis, has been empl…
Recently, the relationship between matroids and generalized rough sets based on relations has been studied from the viewpoint of linear independence of matrices. In this paper, we reveal more relationships by the predecessor and successor neighborhoods from relations. First, through these two neighborhoods, we propose a pair of matroids, namely predecessor relation matroid and successor relation matroid, respectively. Basic characteristics of this pair of matroids, such as dependent sets, circuits, the rank function and the closure operator, are described by the predecessor and successor neigh…
This study describes application of some approximate reasoning methods to analysis of hydrocyclone performance. In this manner, using a combining of Self Organizing Map (SOM), Neuro-Fuzzy Inference System (NFIS)-SONFIS- and Rough Set Theory (RST)-SORST-crisp and fuzzy granules are obtained. Balancing of crisp granules and non-crisp granules can be implemented in close-open iteration. Using different criteria and based on granulation level balance point (interval) or a pseudo-balance point is estimated. Validation of the proposed methods, on the data set of the hydrocyclone is rendered.
Amirkabir University of Technology（阿米尔卡比尔理工大学）；University of Alberta（阿尔伯塔大学）
This paper pursues some applications of Rough Set Theory (RST) and neural-fuzzy model to analysis of "lugeon data". In the manner, using Self Organizing Map (SOM) as a pre-processing the data are scaled and then the dominant rules by RST, are elicited. Based on these rules variations of permeability in the different levels of Shivashan dam, Iran has been highlighted. Then, via using a combining of SOM and an adaptive Neuro-Fuzzy Inference System (NFIS) another analysis on the data was carried out. Finally, a brief comparison between the obtained results of RST and SOM-NFIS (briefly SONFIS) has…
Universiti Teknologi PETRONAS（马来西亚石油科技大学）；University California Irvine (UCI)（加州大学欧文分校）；Ipoh Specialist Hospital（怡保专科医院）
This research is about the development a fuzzy decision support system for the diagnosis of coronary artery disease based on evidence. The coronary artery disease data sets taken from University California Irvine (UCI) are used. The knowledge base of fuzzy decision support system is taken by using rules extraction method based on Rough Set Theory. The rules then are selected and fuzzified based on information from discretization of numerical attributes. Fuzzy rules weight is proposed using the information from support of extracted rules. UCI heart disease data sets collected from U.S., Switzer…
