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The core of big data is intelligence still. Facing the challenge of big data, AI needs a deep and united theory, especially, a deep and united cognition math. There were three branches of cognition math emerging in 1982. One of them is Factor space theory initiated by the first author. Factor is factor, i.e. the initiator of fact, the quality-root...
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... Factor space is the coordinate space with dimensions named by factors, which is generalization of Cartesian coordination for describing things and thinking [31]. Factor Space Theory provides a general coordinate system to describe the real world and a theoretical basis for knowledge representation, fuzzy information processing, artificial intelligence theory and data science [32][33][34][35][36][37][38][39][40][41][42]. It can give us constructive guidance on feature selection, model construction and comprehensive integration. ...
... The concept of Factor Space was first proposed by Wang [31], then developed mainly by Wang and Li [32], Wang [33], Li et al. [34], Li et al. [35], Yen and Li [36], Li et al. [37], Zhang and Li [38], Tan and Wang [39], Wang et al. [40],Wang et al. [41] and Wang [42]. In recent years, it has been widely used in knowledge representation, data organization, and feature analysis etc. [40][41][42]. ...
... The concept of Factor Space was first proposed by Wang [31], then developed mainly by Wang and Li [32], Wang [33], Li et al. [34], Li et al. [35], Yen and Li [36], Li et al. [37], Zhang and Li [38], Tan and Wang [39], Wang et al. [40],Wang et al. [41] and Wang [42]. In recent years, it has been widely used in knowledge representation, data organization, and feature analysis etc. [40][41][42]. ...
The power load forecasting plays an important role in the economical and safe operation of the modern power system. However, the characteristics of power load such as non-stationarity, nonlinearity, and multiple quasi-periodicities make power load forecasting a challenging task. The present work focuses on developing a multi-model ensemble forecasting strategy by using prediction phase space construction, similar scenario improved support vector machine, and variable-weighted ensemble method, based on the Factor Space Theory. Firstly, the concept of “Prediction Scenario” is proposed to describe the “Internal historical facts in time series form” and the “External space–time environment composed of external influence factors” of power load forecasting. Next, the candidate input features for power load forecasting are selected based on the correlation analysis between the power load to be predicted, its historical load, and external influence factors. Then, based on the Factor Space Theory, the feature description of the “Prediction Scenarios” is studied and a series of prediction phase space are constructed by randomly selecting some strongly correlated features. An improved support vector machine is proposed based on similar historical scenario screening to set up the unit prediction sub models in each corresponding prediction phase space. The performance of these models is tested by simulation experiments and the variable weight of each model is designed based on the results. Finally, the power loads are forecasted by variable weighted ensemble of multiple models in different prediction phase spaces. The results of mid-Atlantic region load forecasting analysis suggest that the proposed method has better performance in almost cases, comparing with Support Vector Machine, Recurrent Neural Network, Self-partitioning Local Neuro Fuzzy method, Random Forest, Ensemble Neuro-fuzzy method and other state of art forecasting methods.
... Wu Hao et al. used the analysis system to simulate and study the uncertainty of the magnetic velocity induction system [15]; Wang Xuechao et al. analyzed the uncertainty in the process of determining environmental related sustainable development goals [16]; Karamustafa merve et al. applied safety and critical effect analysis to the uncertainty analysis of occupational risk assessment [17]; Nazeer Irfan et al. studied the uncertainty in national trading systems by using the connection control of fuzzy correlation graph [18]; Mejdal Sara and other ontology based search engines have established a search simulation model from related system functions [19]; Li Hongchao et al. studied the achievable dynamic response uncertainty of undamped mass chain system [20]. Wang Peizhaung, Shi Yong, Tien JM et al. studied cognition math based on Factor Space, Business data mining, Optimization based data mining and Internet of things et al. [21][22][23][24][25]. Most of these studies are based on the system characteristics of their respective fields. ...
In the process of system operation, the ability to complete the predetermined function is changing, which is uncertain for the system designer. In order to study the uncertainty of system function state, the causes of uncertainty are analyzed with the help of system fault evolution process and space fault network theory, and the methods to deal with and express uncertainty are studied. Firstly, human, man-made system and natural system are defined; Secondly, the four elements of evolution structure are obtained through space fault network; the causes of uncertainty are factor, data and cognition; the method to deal with uncertainty is analyzed by using four factors; finally, a method to represent the uncertainty of system function state is proposed. According to the research, man-made system is a system established by man according to his subjective cognition, which can complete the predetermined function, that is, man's cognition determines man-made system. Due to the loss of factor flow and data flow in the transmission process, people's cognition of natural system is limited. There must be differences between man-made system and natural system, which is the uncertainty of system function state.
... The spatial correlation theory of factors proposed by Professor Wang Peizhuang [7], including factors; The left matching; The relation and operation of factors: zero factor, factor equality, sub-factor, factor combination, factor disjunction, independent factor, factor remainder, atomic factor, etc. Factor space and characteristics: attribution, explanatory, descriptive; The connotation and denotation of concept and the description frame of concept; Factor spectrum and factor vine; Ontology and factor knowledge graph and knowledge growth; Factor coding; Library; Factors of the space of the state, and so on, in this is not a description (see Mr. Wang's famous works chapter 1-Chapter 5 theoretical content [8]). ...
The factor space theory proposed by Professor Peizhuang Wang, after nearly 40 years of theoretical research by Mr. Wang and in-depth exploration and research by many other scholars, has formed a relatively complete theoretical system and has certain practical methods. However, the engineering and universal application system of factor space has not been completely constructed. The text data is found in large Numbers in this paper, based on the current document the reality of this type of unstructured data, to study and put forward factors space engineering concept and the process method of space engineering research direction to factors, application for Mr. Wang's theory of factors space exploration methods and way to solve the scientific, so that the space can be ground to take root, carry forward. Given prison mobsters education reform is long-term proposition of criminal execution theory and practice research, evidence-based rehabilitation practice test is effective method, but for evidence-based transformation, the biggest bottleneck is the evidence of the evidence-based library is lack of scientific recognition, expression, and evidence to construction and retrieval, etc., I am responsible for the large data of evidence-based rehabilitation research, The author actively explores the application of factor space engineering research to the evidence factor space system of evidence-based reform of criminals and applies factor space engineering theory to evidence-based evidence research practice.
... The application systems built on the relational database, such as Train Ticket System, Bank System, Salary Distribution System, and B Xiangfu Meng marxi@126.com 1 Supermarket Sales System, only store the data directly associated with the system while the information and knowledge which are inter-related to the system would not be considered. As a result, the existing application systems may lead to the systems being unable to make intelligent reasoning (such as causal induction between different attributes/events) due to insufficient knowledge and data. ...
... Therefore, it is urgent to design a data model and theory that can uniformly represent, query, and reason for the knowledge that conforms to human cognition. The famous Chinese mathematician Professor Peizhuang Wang from Beijing Normal University first proposed the Factor Space theory in the 1980s [1][2][3], the same time with Rough Set [4]. He systematically explained that factors and factor space can be the foundation and principles to describe and represent the knowledge hierarchy in the real world; this reveals the essence of data science and intellectual reasoning. ...
... For example, let a factor to be f = color, 4 , v 5 } represents 5 cars, I(f ) = {red, white, black} denotes the colors of car. The factor "color" maps a car into its body color, such as f (d 1 ...
Factor space theory was first proposed in the 1980s with the rough set theory. After 30 years of development, factor space theory has established its completed theoretical architecture in mathematics; it has been proved very useful in causal analysis, intelligent reasoning and decision making. This paper proposes a Factor Query Language (FQL)—an SQL-like query language for operating the Factor Pedigree to make the factor space theory easily and widely used. First, the concepts associated with factor and factor space are presented. The factor pedigree which builds by knowledge increase and concept partitioning is presented; an XML specification–based storage method is also proposed for storing the factor pedigree. Next, the FQL (including FQL statements for insert, delete, update and select operations) is proposed. Two kinds of node encoding of factor pedigree strategies (interval-based encoding and prime + binary string-based encoding) are designed. They can facilitate the FQL query performance efficiently. The Factor Base Management System (FBMS) architecture and module functions are also presented.
... Hui Sun 1148429357@qq.com extensive attention in the academic and industrial circles and has been extensively discussed and studied by experts at home and abroad [1][2][3][4][5][6]. ...
... Step 3 i* = 3 can be obtained by returning to Table 5 and using i* = argmin i {s i /τ ij }, thus the pivot point coordinates (3,3) can be obtained. ...
... Step 3 i* = 3 can be obtained by returning to Table 5 and using i* = argmin i {s i /τ ij }, thus the pivot point coordinates (3,3) can be obtained. ...
All the classification solutions in artificial intelligence can be summed up as explicit factor implicit problem, and the explicit factor implicit problem should be solved by linear programming. The simplex linear programming algorithm is simple and fast, but it is not a polynomial algorithm. Whether it can be improved into a “strong polynomial algorithm”, that is, in any case, the number of operations of this algorithm is a polynomial function of the number of equations and variables, is a trans-century international mathematical problem that has been unsolved for decades. This question, which involves the mathematical boundaries of ai development, is crucial. The method of solving programming problem from the demand and specialty of artificial intelligence is called factor programming. This paper will introduce the basic ideas of factor explicit and implicit programming and factor programming, and write programs for some of the algorithms, and prove the theorem of triangular matrix optimization.
... Reference [5] introduced advances in big data analytics. Wang et al. asserted that factor space is the theoretical base of data science [6] and is the best framework for cognition math [7]. Factor space was proposed by Wang in 1982 [8], which provided a general coordinate system with dimensions named by factors to describe the real world and was a generalization of Cartesian coordination for describing things and thinking. ...
The determining degree-based classification methods, new types of classification methods built in the frame of factor space theory, mainly include factorial analysis, improved factorial analysis and set subtraction and rotation calculation (S&R). This paper first compares the three methods to present a comprehensive understanding of them and claims that whether to reuse dominant factors and to use synthetic partitioning are the main differences between factorial analysis and S&R. Furthermore, this paper introduces S&R definitively and concisely through an example. Based on the investigation, we propose a novel method for classification problems with interval-valued attributes that uses a determining degree to discretize interval values, and takes S&R as one of its steps. Experimental results show that this method is effective and reasonable.
... But obviously, the analytic hierarchy process has not been able to do this. The regression model [15,16], maximum entropy model [17,18], ant colony theory [19], factor space theory [20][21][22], and other theories or models are not suitable to evaluate the engineering geological practice route due to their own characteristics. ...
Engineering geological practice and investigation are important measures for geological fluid and engineering geological research; the practice route has an important impact on the achievement of research objectives. In this study, the practice route is mainly affected by four primary indicators: abundance of geological resources, rationality of the practice route, effect of practice, and the accommodation conditions. The four primary indicators include 13 secondary indicators, and each secondary indicator can be divided into positive and negative random variables, which is the specific content of the evaluation. In order to collect the feedback data of participants on the practice route, a questionnaire was constructed based on indicators at all levels. According to the results of the questionnaire, the mean and standard deviation of each random variable are counted and the distribution law of probability density is fitted. A performance function is constructed to represent the approval status of participants for each indicator. Considering the influence of 26 random variables, a multifactor evaluation method for the engineering geology practice route is proposed based on the reliability analysis method. This method can be used to analyze the approval status of random factors, search for the shortcomings of the route, and provide an effective method to improve the rationality of the route. The conclusion shows that this study provides a solution to evaluate fuzzy problems in engineering geological practice, especially if the problems are difficult to be quantified through experiment or measurement.
... 察"的人工智能关注的"意识"，都无法在其基础上 建立起智能数学。 心理学的"意识"中，研究对象的原像仍在物质 世界中。例如，"群体欲"这一原意识，其原像就是 物质世界中的某种"集合"。 人工智能关注的"意识"，更是离不开物质世 界，因为其依托的"信息"是指客体所呈现的"状态 及其变化方式"。这里的"客体" 或许从"概念""知识"和"意识"这三个基元 素出发，能一步一步地生长出智能数学的版图。 传统逻辑认为，词项的含义即概念。例如"商 品"一词，其含义"为交换而生产的劳动产品"即为 概念。概念是事物特有属性的反映。 概念史研究者们认为，概念是思想的出口。通过 对历史中"主导概念"的形成、演变、运用及社会文 化影响的分析，可揭示历史变迁的特征。 不言而喻，"概念"是头脑思维活动中的重要成 分，而且是接触外部世界后产生。人类共识性的"概 念"，可以通过语言进行交流；一些非共识性的"概 念"，内中有部分共识性成分，也能进行交流；完全 个性化的"概念"，常常在个人思维活动中发挥重要 作用。"财产"是一个共识性较高的概念，"风险" 是一个非共识性概念，而"某人对我很好"则是一个 完 全 个 性 化 的 概 念 。 一 些 概 念 很 简 单 （ 例 如 "水"）；一些概念则非常复杂（例如"文化"）。 显然，思维活动中的"概念"，远比数理逻辑中 的"概念"复杂，并非都可以用内涵和外延来表达， 也不是用"对合性" [8] 对内涵和外延加以约束就能解 决问题。 从智能数学研究的需要出发，本文给出"概念" 的定义如下： [11] ，因此，可用因 素空间理论描述概念。 "概念"，是人脑区分万物差异的一种表达。婴儿 生存的本能把母亲从万物中区分出来，在脑海中形成 "母亲"这一概念。认知的需求，概念由粗变细。古 人用甲骨文 将牛从动物中区分出来。 这一表达， 是一个概念。为了进一步认知牛，细分又出现了耕 牛、奶牛和野牛等等概念。 因素空间理论采用"内涵"（Intension）的方式 来描述概念。此处的"内涵"，是在因素空间中定义 的 [12] [16] 是首个研制成功的智联网演示系统。考生以 购买服务的方式，通过智联网获得信息和咨询，并由 数学模型处理后提供决策参考，有效规避填报失误的 风险。台风灾害风险分析智联网 [17] 中出现了柔性知识 捕获器，以在温州地区开展台风灾害水产养殖保险的 可行性需求调查为例，对智联网平台的理念和模型进 行了成功的验证。智联网支撑的"优秀论文"评选系 统 [18] 能评出共识性最高的优秀论文，多次用于中国风 险分析与管理精英杯优秀论文的评选。内涝风险分析 智联网服务平台 [19] 使用属性拼图技术对原始的经验信 息进行优化整合，再通过"雨强-水深"模糊关系模 型，在线实现基于降雨强度，估计易涝点积水深度， 进而给出积水风险值。智联网驱动的风险雷达 [20] 通过 社区居民的参与，进行风险信息搜集、动态风险评 估，实现了风险事件的动态追踪。该项发明已由北京 崇安智联科技服务有限责任公司申请了名为"一种社 区安全风险雷达智联网服务系统"的发明专利。海洋 环境风险管理智联网平台 [21] 通过去中心化信息收集的 技术，完成了围填海造地项目对天津自然灾害抵御能 力的影响评价。地震宏观异常的智联网服务平台 [22] 将 众多一线地震工作者对地震宏观异常群强度的目视判 断，以模糊隶属函数的曲线方式输入，在智联网中建 立以模糊关系矩阵表达的共识性宏观异常群测度空 间，有望为震前宏观异常辅助地震预报提供帮助。风 险时效性评价的智联网服务平台 [23] 是一个因素藤智联 网，被用于对北京延庆区果树冰雹灾害概率风险的时 效性进行评价。风险沟通智联网服务平台 [24] 提供了洪 水灾害风险沟通的便捷渠道，并尝试用于宁波市洪水 灾害的风险管理。四川省三台县永和堰灌区综合风险 评 估 智 联 网 信 息 系 统 [25] [26] ( 2 2 2 2 2 2 2 2 2 2 1 1 2 2 2 2 2 2 ...
In this paper, we for the first time propose an framework of intelligent mathematics, which consists of factor space, information diffusion, and internet of intelligences. This paper demonstrates how to use intelligent mathematics to describe earthquake risk perception. The concept of earthquake risk is described in the factor space, and the knowl- edge of earthquake risk is formed in association learning based on information diffusion. Different knowledge sys- tems precipitate different acquired consciousnesses. The security instinct affects the perception of risk. For a region, the risk consciousnesses of the stakeholders could be integrated with the internet of intelligences to form a consen- sus of the earthquake risk perception.
... A lot of theoretical papers before 2012 can be found in the reference [3, 6-11, 13, 16, 19, 20,24,26,31,34,35]. Since 2012, FS has turned to the data science [1,2,12,[21][22][23]27,28,30,37,38]. We have mentioned that a factor causes something. ...
... Gene was called the factor by G. Mendel; factor is the generalization of gene, which is the key to opening the door of ontology and cognition, said Wang, who gives special emphasize from philosophy: Anything is united in the opposite of quality and quantity; factor is the root of quality, as gene is the root of biological attributes. Without the string of factors, attributes are like broken strings of pearls sprinkled over a floor [28]. By means of factors, things are organized and concepts are generated. ...
Conceptual generation is a key point and basic problem in artificial intelligence, which has been probed in the Formal Concept Analysis (FCA) established by G. Wille. Factors Space (FS) is also a branch of cognition math initiated by P.Z. Wang at the end of last century, which has been applied in information processing with fuzzy concepts effectively. This paper briefly introduces the historic background of FS and its relationship with FCA. FS can be seen as a good partner of FCA on conceptual description and structure extraction; combining FCA with FS, we can get more clear and simple statements and more fast algorithms on conceptual generation.
Artificial intelligence technology has made important progress in machine learning and problem-solving with relatively determined boundary conditions. However, the more common open problems with uncertain boundary conditions in management practice still depend on the experience mastered by individuals. The combination of Extenics, Factor Space, and knowledge management will potentially solve this kind of problem intelligently to a extent. Based on Extenics and factor space theory, this paper studies the Extension model of open problems, explores the intelligent expansion mechanism of factor knowledge in big data environment, and constructs the double integration of multi granularity factor knowledge space and expert experience knowledge. We try to make Extenics and factor space theory complement each other in the field of problem solving, reveal the knowledge expansion mechanism of open problem solving in the big data environment, provide a novel theoretical perspective and method basis for knowledge based intelligent service on factor mining. This paper will also provide theoretical research directions for building a new generation of problem-oriented new factor knowledge base, promote the deep integration of knowledge management and artificial intelligence leading to a new direction of knowledge engineering based on factor space and Extenics.
