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Outline of a Computational Theory for Linguistic Dynamic Systems Toward Computing with Words
... Much useful information is hidden in the accumulated voluminous data, but it is very hard for us to obtain it. In order to mine knowledge from the rapidly growing volumes of digital data, researchers have proposed many methods other than classical logic, for example, fuzzy set theory [1], rough set theory [2], computing with words [3], [4], [5], [6], [7], granular computing [8], [9], [10], [11], [12], computational theory for linguistic dynamic systems [3], etc. ...
... Much useful information is hidden in the accumulated voluminous data, but it is very hard for us to obtain it. In order to mine knowledge from the rapidly growing volumes of digital data, researchers have proposed many methods other than classical logic, for example, fuzzy set theory [1], rough set theory [2], computing with words [3], [4], [5], [6], [7], granular computing [8], [9], [10], [11], [12], computational theory for linguistic dynamic systems [3], etc. ...
... It seems that a covering based granular computing is more reasonable than a binary relation based one [8]. Furthermore, there seems a need and possibility to apply the covering generalized rough set theory to the computational theory for linguistic dynamic systems [3], software watermarking and software obfuscation [39]. Our work on conflict analysis [38] is a start in these directions and they need further study. ...
Rough sets, a technique of granular computing, deal with the vagueness and granularity in information systems. They are based on equivalence relations on a set, or equivalently, on a partition on the set. Covering is an extension of a partition and a more feasible concept for coping with incompleteness in information, thus the classical rough sets based on partition are extended to covering based rough sets. When a covering is introduced, there are more than one possibility to define the upper approximation. It is necessary to study the properties of these different types of upper approximations and the relation- ships among them. This paper presents three kinds of covering generalized rough sets and explores the relationships among them. The main results are conditions under which two different types of upper approximation operations are identical.
... To deal with large complex systems effectively with linguistic human knowledge, the theory of linguistic dynamic system is introduced by Wang [1]- [4], which is suitable for modeling, analysis and synthesis of knowledgebased systems, expert systems etc. Since then many efforts have been made on this area. ...
... To effectively study LDS, Wang defined two types of LDS systems, type-I LDS and type-II LDS [4]. ...
The theory of linguistic dynamic system (LDS) focuses on modeling, analysis, control and evaluation of complex systems at a linguistic level through computing with words. The concepts, frameworks and methods in conventional dynamic systems (CDS) are adopted in research of LDS. This paper is concerned about linguistic controller design of LDS upon cell mapping concept. In view of the studies of controller design for type-I and type-II LDS and optimal fuzzy controller design and tuning methods based on cell-to-cell mapping, two approaches to construct optimal linguistic controller for LDS using cell-to-cell mapping techniques are outlined in this paper.
... Although much useful information is hidden in the accumulated voluminous data, it is very difficult to obtain. To mine knowledge from the rapidly growing volumes of digital data, researchers have proposed many methods besides classical logic, such as fuzzy set theory [44], rough set theory [21,22,24], computing with words [36,45], granular computing [1,14,15,42], computational theory for linguistic dynamic systems [37], and so on. ...
... that a covering based granular computing is more appropriate than a binary relation based one [14]. Furthermore, possibilities exist for applying the covering generalized rough set theory to computational theory for linguistic dynamic systems [36]. The relationships between covering rough sets and binary relation based rough sets [40,41,47,61] is a future topic to be explored [23,62]. ...
As a technique for granular computing, rough sets deal with the vagueness and granularity in information systems. Covering-based rough sets have been proposed to generalize this theory for wider application. Three types of covering-based rough sets have been studied for different situations. To make the theory more complete, this paper proposes a fourth type of covering-based rough sets. Compared with the existing ones, the new type shows its special characteristic in the interdependency between its lower and upper approximations. We carry out a systematical study of this new theory. First, we discuss basic properties such as normality, contraction, and monotone. Then we investigate the conditions for this type of covering-based rough sets to satisfy the properties of Pawlak’s rough sets and study the interdependency between the lower and upper approximation operations. In addition, axiomatic systems for the lower and upper approximation operations are established. Lastly, we address the relationships between this type of covering-based rough sets and the three existing ones.
... Various theories and methods have been proposed to deal with incomplete and insufficient information in classification, concept formation, and data analysis in data mining. For example, fuzzy set theory [15], rough sets [6], computing with words [12,16,17], linguistic dynamic systems [11,12], and many others, have been developed and applied to real-world problems. The focus of this paper is on the rough set theory, a tool originated by Pawlak [6] for data mining, with the particular intention to generalize it for the possible applications in computing with words and linguistic dynamic systems for modeling and analyzing complex systems and for data mining. ...
... Various theories and methods have been proposed to deal with incomplete and insufficient information in classification, concept formation, and data analysis in data mining. For example, fuzzy set theory [15], rough sets [6], computing with words [12,16,17], linguistic dynamic systems [11,12], and many others, have been developed and applied to real-world problems. The focus of this paper is on the rough set theory, a tool originated by Pawlak [6] for data mining, with the particular intention to generalize it for the possible applications in computing with words and linguistic dynamic systems for modeling and analyzing complex systems and for data mining. ...
This paper investigates some basic properties of covering generalized rough sets, and their comparison with the corresponding ones of Pawlak’s rough sets, a tool for data mining. The focus here is on the concepts and conditions for two coverings to generate the same covering lower approximation or the same covering upper approximation. The concept of reducts of coverings is introduced and the procedure to find a reduct for a covering is given. It has been proved that the reduct of a covering is the minimal covering that generates the same covering lower approximation or the same covering upper approximation, so this concept is also a technique to get rid of redundancy in data mining. Furthermore, it has been shown that covering lower and upper approximations determine each other. Finally, a set of axioms is constructed to characterize the covering lower approximation operation.
... This is true especially when one is dealing with social, political or economical, rather than engineering or physical systems. In this paper, we outline an approach along this direction based on the theory of linguistic dynamic systems (LDS) developed by Wang [22][23][24][25][26]. ...
... Although these methodologies have been successfully used to solve many problems in large complex systems, none of them has led to a theoretical framework upon which concepts and methods for system analysis and synthesis parallel to those well known for conventional dynamic systems, such as stability analysis and control design, can be developed. In [22][23][24][25][26], Wang have used Kosko's interpretation [10] of fuzzy sets to consider LDS as mappings on fuzzy hypercubes; and by introducing cellular structures on hypercubes using equi-distribution lattices developed in number theory [8], these mappings can be approximated as cellto-cell mappings in a cellular space [6,7], in which each cell represents a linguistic term (a word) defined by a family of membership functions of fuzzy sets; in this way, LDS can be studied in the cellular space, and thus, methods and concepts of analysis and synthesis developed for conventional nonlinear systems, such as stability analysis and design synthesis, can be modified and applied for LDS; while cell-to-cell mappings provide us with a very general numeric tool for studying LDS, it is not the most effective method to handle the special cases of type-I and type-II LDS to be studied here. ...
Linguistic dynamic systems (LDS) are dynamic processes involving mainly computing with words instead of numbers for modeling and analysis of complex systems and human–machine interfaces. The goal of studying LDS is to establish a methodology of design, modeling, and analysis of complex decision-making processes bridging the machine world in numbers and the human world in words. Specifically in this paper, conventional dynamic systems are converted to different types of LDS for the purpose of verification and comparison. The evolving laws of a type-I LDS are constructed by applying the fuzzy extension principle to those of its conventional counterpart with linguistic states. The evolution of type-I LDS represents the dynamics of state uncertainty derived from the corresponding conventional dynamic process. In addition to linguistic states, the evolving laws of type-II LDS are modeled by a finite number of linguistic decision rules. Analysis of fixed points is conducted based on point-to-fuzzy-set mappings and linguistic controllers are designed for goals specified in words for type-II LDS. An efficient numerical procedure called α-cuts mapping is developed and applied to obtain extensive simulation results.
... Down-sets and up-sets are defined in the poset environment. In order to achieve this goal, many theories and methods have been proposed, for example, fuzzy set theory ( [4], [16]), computing with words ( [9], [15]), rough set theory ( [5], [14]) and granular computing ( [1], [3], [11], [13]). From the structures of these theories, two structures are mainly used, that is, algebraic structure ( [2], [10], [12]) and topological structure [17]. ...
Covering is a common type of data structure and covering-based rough set theory is an efficient tool to process this type of data. Lattice is an important algebraic structure and used extensively in investigating some types of generalized rough sets. This paper presents the lattice based on covering rough approximations and lattice for covering numbers. An important result is investigated to illustrate the paper.
... In language dynamic systems (LDS) [4][5][6], word computation [7] instead of conventional numerical and symbolic computation is used to solve the problems of modeling, analysis, control and evaluation of complex systems at the language level [8], and dynamic characteristics and evaluation of the development of things are described formly. In recent years, language dynamic system has been developed to a new extent. ...
In general, evaluating an object is mainly expressed by natural language. It is not easy for people to evaluate an object with accurate mathematical methods. In this paper, partially connected type-2 fuzzy sets, linguistic dynamic systems and fuzzy comprehensive evaluation are used to evaluate an object, and the evaluation results are expressed by type-2 fuzzy sets. The method of evaluation is presented and the results indicate that this method is both feasible and effective.
... At the Internet age, more and more data are being collected and stored, thus, how to extract the useful information from such enormous data becomes an important issue in computer science. In order to cope with this issue, researchers have developed many techniques such as fuzzy set theory [40], rough set theory [18], computing with words [27,41,42,43,44], computational theory for linguistic dynamic systems [28], etc. ...
Rough set theory has been proposed by Pawlak as a tool for dealing with the vagueness and granularity in information systems. The core concepts of classical rough sets are lower and upper approximations based on equivalence relations. This paper studies arbitrary binary relation based generalized rough sets. In this setting, a binary relation can generate a lower approximation operation and an upper approximation operation. We prove that such a binary relation is unique, since two different binary relations will generate two different lower approximation operations and two different upper approximation operations. This paper also explores the relationships between the lower or upper approximation operation generated by the intersection of two binary relations and those generated by these two binary relations, respectively.
... Thus, how to solve this bottleneck problem becomes an important issue in computer science and industry. In order to cope with this issue, researchers have developed many techniques such as fuzzy set theory [40], rough set theory [14], computing with words [21,36,37,38,39], computational theory for linguistic dynamic systems [22], and granular computing [1,9,10,35,34]. ...
Rough set theory has been proposed by Pawlak as a tool for dealing with the vagueness and granularity in information systems. The core concepts of classical rough sets are lower and upper approximations based on equivalence relations , or partitions. This paper studies covering-based generalized rough sets. In this setting, a covering can also generate a lower approximation operation and an upper approximation operation, but some of common properties of classical lower and upper approximation operations are no longer satisfied. We investigate conditions for a covering under which these properties hold for the covering-based lower and upper approximation operations.
... It has been widely used in decision making [28] , pattern recognition [9] , fuzzy control [8,33,34,67] and so on. It's worth mentioning that besides the fields enumerated above, another fontal and crucial field is the complex systems, which has made many achievements in modeling, analysis, control and evaluation of complex systems [35,[52][53][54][55]62] . ...
This study proposes a fuzzy logic approach to model and simulate pedestrian dynamical behaviors, which takes full advantage of human experience and knowledge and perceptual information obtained from interactions with surrounding environments. First, the radial-based method is adopted to represent the physical space. A pedestrian’s visual field, defined as a fan-shaped area with a certain visual distance and visual angle, is divided into five sectors. Then, the motion states of a pedestrian are determined by the integration of recommendations of local obstacle-avoiding behavior, regional path-searching behavior and global goal-seeking behavior with mutable weighting factors at three different scopes. These elementary behaviors and weighting’s assignment principle are modeled as fuzzy inference systems with the input information of a pedestrian’s perception toward surrounding environments. A pedestrian is guided to avoid the front obstacles and select the lowest negative energy path by local obstacle-avoiding behavior and regional path-searching behavior, respectively. The global goal-seeking behavior makes a pedestrian has a tendency of moving in direction of his/her goal regardless of external environments. The magnitudes of weighting factors are adjusted automatically to coordinate three elementary behaviors and resolve potential conflicts. At last, the effectiveness of the proposed model is validated by simulations of crowd evacuation, unidirectional and bidirectional pedestrian flows. The simulation results are analyzed from both qualitative and quantitative aspects, which indicate that the fuzzy logic based pedestrian model can get true reappearance of self-organization phenomena such as ‘arching and clogging’, ‘faster-is-slower effect’ and ‘lane formation’, and the fundamental diagrams are in matching with a large variety of empirical and experimental data. A further study finds that walking habits have negligible influence on the fundamental diagrams of bidirectional pedestrian flow at least for densities of ρ < 3p/m2.
... Thus, there is an urgent need for a new generation of computational theories and tools to assist humans in extracting information from the rapidly growing volumes of digital data. Those theories and tools are the subject of the emerging field of knowledge discovery in databases (KDD).To this end, reaches have proposed many methods other than classical logic such as fuzzy set theory [7], rough set theory [3][4][5], computing with words [8][9][10][11], computational theory for linguistic dynamic systems [6], etc. ...
Rough sets, a tool for data mining, deal with the vagueness and granularity in information systems. This paper introduces new approach for tolerance space given by Järvinen [3] via a topological view .Our technique can be considered as a generalization for tolerance space.
... This new observation extends the concept of crisp set for modeling the imprecise data by enriching the modeling power. In order to face such trying situations, necessarily, researchers have developed many advance techniques such as fuzzy set theory ( [18]) Dempster -Shafer theory of evidence ( [10]), rough set theory ( [4]), computing with words ( [13], [19], [20], [21]) computational theory for linguistic dynamic systems ( [14]) and granular computing ( [2]). ...
An approach to capture impreciseness, Pawlak introduced the notion of rough sets, which is an excellent tool to capture indiscernibility of objects. An equivalence relation is the simplest formulization of the indiscernibility. The basic assumption of rough set theory is that human knowledge about a universe depends upon their capability to classify its objects. Classifications of a universe and equivalence relations defined on the universe are known to be interchangeable notions. So, for mathematical point of view, equivalence relations are considered to define rough set. An inexact set (A rough set) is represented by a pair of exact sets called the lower approximation and upper approximation of the set. The lower approximation of a rough set comprises of those elements of the universe which can be said to belong to it definitely with the available knowledge. The upper approximation comprises of those elements which are possibly in the set with respect to the available information (knowledge). In this note we introduced Covering Based Rough Sets which is an extension to the traditional (Z. Pawlak) Rough Sets. Undoubtedly Z.Pawalak's introduction of the rough set theory is born out of his long expedition in the forest chaos originated from insufficient and incomplete information system .This inspires him to search for a comprehensible theory for classification , concept formation and data analysis. The new theory upholds the mathematical approach for the study of indiscernibility of objects. Indiscernibility of object refers though the granularity of knowledge that effects the definition of universe of discourse. Indiscernibility may be described by equivalence relations. Defining the indiscernibility of object includes the objects of universe represented by a set of attributes, based on their attribute values. The principle of rough set theory enables to conceptualize , organize and analyze different types of data in data mining . In addition to this, the theory is vary much useful for dealing with uncertain and vague knowledge in the information systems. The extensive application of rough set models are found in Process control, Economics, Medical diagnosis, Biochemistry, Environmental science, Biology, Psychology, Conflict analysis and other area of knowledge ([1], [6], [8], [9], [10],[12], [15], [16], [22]).
... In order to achieve this goal, many theories and methods have been proposed, for example, fuzzy set theory [1], [2], computing with words [3], [4], rough set theory [5], [6] and granular computing [7], [8], [9], [10]. From the structures of these theories, two structures are mainly used, that is, algebraic structure [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], and topological structure [27], [28], [29], [30]. ...
Rough set theory is a very effective tool to deal with granularity and vagueness in information systems. Covering-based rough set theory is an extension of classical rough set theory. In this paper, firstly we present the characteristics of the reducible element and the minimal description covering-based rough sets through down-sets. Then we establish lattices and topological spaces in covering-based rough sets through down-sets and up-sets. In this way, one can investigate covering-based rough sets from algebraic and topological points of view.
... Various theories and methods have been proposed to deal with incomplete and insufficient information in classification, concept formation, and data analysis in data mining. For example, fuzzy set theory [1][2][3], rough set theory [4,5], computing with words [6,7], and linguistic dynamic systems [8] have been developed and applied to real-world problems. Classical rough sets were originally proposed by Pawlak as a useful tool for dealing with the fuzzy and uncertain problems in information systems and have already been an efficient tool for data pre-process and widely used in fields such as process control, economics, medical diagnosis, conflict analysis, and other fields [9][10][11][12]. ...
Rough set theory is an efficient and essential tool for dealing with vagueness and granularity in information systems. Covering-based rough set theory is proposed as a significant generalization of classical rough sets. Matroid theory is a vital structure with high applicability and borrows extensively from linear algebra and graph theory. In this paper, one type of covering-based approximations is studied from the viewpoint of Eulerian matroids. First, we explore the circuits of an Eulerian matroid from the perspective of coverings. Second, this type of covering-based approximations is represented by the circuits of Eulerian matroids. Moreover, the conditions under which the covering-based upper approximation operator is the closure operator of a matroid are presented. Finally, a matroidal structure of covering-based rough sets is constructed. These results show many potential connections between covering-based rough sets and matroids.
... The vagueness and incompleteness of knowledge are common phenomenons in information systems. In order to deal with these knowledge, many theories and methods have been proposed, including rough set theory [1], fuzzy set theory [2], linguistic dynamic systems [3], computing with words [4,5], and knowledge classifying [6][7][8]. ...
Rough set theory is a useful tool for dealing with the vagueness, granularity and uncertainty in information systems. This
paper connects generalized rough sets based on relations with matroid theory. We define the upper approximation number to
induce a matroid from a relation. Therefore, many matroidal approaches can be used to study generalized rough sets based on
relations. Specifically, with the rank function of the matroid induced by a relation, we construct a pair of approximation
operators, namely, matroid approximation operators. The matroid approximation operators present some unique properties which
do not exist in the existing approximation operators. On the other hand, we present an approach to induce a relation from
a matroid. Moreover, the relationship between two inductions is studied.
... However, many efforts have been taken toward this objective in past, for example, knowledge based systems, agent systems, linguistic structures and multi-valued logic and so on[4−8], but the theories of stability analysis, control design of CDS have not been built yet. In order to make the analysis and synthesis of complex huge systems formal, consistent, and systemize, Wang[9−11]presented the theory frame of CW and LDS by synthesize fuzzy sets, nonlinear analyse, number theory, optimal control theory and approach the fixed point of LDS preliminary[12]. In this paper, we analyze the dynamical orbits of LDS along the direction of papers[9,10]and apply CW in complex financial systems. ...
Linguistic dynamic systems (LDS) are the systems based on computing with words (CW) instead of computing with numbers or symbols.
In this paper, LDS are divided into two types: type-I LDS being converted from conventional dynamical systems (CDS) by using
extension principle and type-II LDS by using fuzzy logic rules. For type-I LDS, the method of endograph is provided to discuss
the stabilities of type-I LDS and two cases of stabilities of logistic mappings: one is the states being abstracted and the
other is parameters also being abstracted. For type-II LDS, the method of degree of match is used to discuss the dynamical
behavior of arbitrary initial words under fuzzy rule.
... There is much need for dealing with the incomplete and vague information in classification, concept formulation, and data analysis. In order to achieve this goal, researchers have proposed many methods other than classical logic, for example, fuzzy set theory [41], rough set theory [19], computing with words [32,42], granular computing [1,14,39,40], computational theory for linguistic dynamic systems [33]. ...
Uncertainty and incompleteness of knowledge are widespread phenomena in information systems. Rough set theory is a tool for dealing with granularity and vagueness in data analysis. Rough set method has already been applied to various fields such as process control, economics, medical diagnosis, biochemistry, environmental science, biology, chemistry, psychology, and conflict analysis. Covering-based rough set theory is an extension to classical rough sets. In covering-based rough sets, there exist several basic concepts such as reducible elements of a covering, minimal descriptions, unary coverings, and the property that the intersection of any two elements is the union of finite elements in this covering. These concepts appeared in the literature of covering-based rough sets separately. In this paper we study the relationships between them. In particular, we establish the equivalence of the unary covering and the covering with the property that the intersection of any two elements is the union of finite elements in this covering. We also investigate the relationship between the covering lower approximation operation and the interior operator. A characterization of the interior operator by the covering lower approximation operation is presented in this paper. Correspondingly, we study the relationship between the covering upper approximation operation and the closure operator. In addition, we explore the conditions under which the covering upper approximation operation is monotone. The study of the relationships between these concepts will help us have a better understanding of covering-based rough sets.
... In order to extract useful information hidden in voluminous data, many methods in addition to classical logic have been proposed. These include fuzzy set theory [27], rough set theory [13], computing with words [22,[28][29][30][31] and computational theory for linguistic dynamic systems [23]. ...
Rough sets, a tool for data mining, deal with the vagueness and granularity in information systems. This paper studies covering-based rough sets from the topological view. We explore the topological properties of this type of rough sets, study the interdependency between the lower and the upper approximation operations, and establish the conditions under which two coverings generate the same lower approximation operation and the same upper approximation operation. Lastly, axiomatic systems for the lower approximation operation and the upper approximation operation are constructed.
... Much useful information is hidden in the accumulated voluminous data, but it is very hard for us to obtain it. In order to mine knowledge from the rapidly growing volumes of digital data, researchers have proposed many methods other than classical logic, for example, fuzzy set theory [1], rough set theory [2], computing with words [3,4], granular computing [5], computational theory for linguistic dynamic systems [6], etc. ...
Rough set theory was proposed by Pawlak to deal with the vagueness and granularity in information systems that are characterized
by insufficient, inconsistent, and incomplete data. Its successful applications draw attentions from researchers in areas
such as artificial intelligence, computational intelligence, data mining and machine learning. The classical rough set model
is based on an equivalence relation on a set, but it is extended to generalized model based on binary relations and coverings.
This paper reviews and summarizes the axiomatic systems for classical rough sets, generalized rough sets based on binary relations,
and generalized rough sets based on coverings.
... Thus, how to solve this bottleneck problem becomes an important issue in computer science and industry. In order to cope with this issue, researchers have developed many techniques such as fuzzy set theory [56], rough set theory [22], computing with words [38,57,58,59,60], formal concept analysis [40,41], quotient space theory [63,64], computational theory for linguistic dynamic systems [39], and granular computing [1,14,15,51,53]. ...
Rough set theory has been proposed by Pawlak as a tool for dealing with the vagueness and granularity in information systems. The core concepts of classical rough sets are lower and upper approximations based on equivalence relations, or partitions. This paper studies covering-based generalized rough sets. In this setting, a covering can generate a lower approximation operation and an upper approximation operation, but some of common properties of classical lower and upper approximation operations are no longer satisfied. We investigate conditions for a covering under which these properties hold for the third type of covering-based lower and upper approximation operations.
... For data in an information system, the acquisition of knowledge and reasoning may involve vagueness, incompleteness, and granularity. In order to deal with the incomplete and vague information in classification, concept formulation, and data analysis, researchers have proposed many methods other than classical logic, for example, fuzzy set theory [53], rough set theory [21], [22], [23], [24], computing with words [26], [38], [54], [55], [56], [57], [58], granular computing [2], [7], [10], [16], [49], [50], formal concept analysis [40], quotient space theory [60], [61], and computational theory for linguistic dynamic systems [39]. The advantage of the rough set method is that it does not need any additional information about the data, like probability in statistics or membership in fuzzy set theory. ...
Rough set theory is a useful tool for data mining. It is based on equivalence relations and has been extended to covering-based generalized rough set. This paper studies three kinds of covering generalized rough sets for dealing with the vagueness and granularity in information systems. First, we examine the properties of approximation operations generated by a covering in comparison with those of the Pawlak's rough sets. Then, we propose concepts and conditions for two coverings to generate an identical lower approximation operation and an identical upper approximation operation. After the discussion on the interdependency of covering lower and upper approximation operations, we address the axiomization issue of covering lower and upper approximation operations. In addition, we study the relationships between the covering lower approximation and the interior operator and also the relationships between the covering upper approximation and the closure operator. Finally, this paper explores the relationships among these three types of covering rough sets.
Neonatal pathological jaundice (NPJ) is easy to cause bilirubin encephalopathy, which has high mortality and sequelae rate. Therefore, accurate risk evaluation can help clinicians take appropriate measures to timely intervene in neonatal jaundice level and avoid complications. In this article, five indexes are extracted as the factor set for the risk evaluation of NPJ, and the diagnostic criteria are determined. Then, five index sets are described by interval type-2 fuzzy sets, and the corresponding membership functions and membership function figures are provided. The feasibility of interval type-2 fuzzy comprehensive evaluation in risk evaluation of NPJ is demonstrated through example, and the fuzzy rule bases of prevention and treatment for NPJ are constructed according to the results of risk evaluation. Finally, this article demonstrates that the proposed risk evaluation and treatment process of NPJ is actually a dynamic closed-loop control process, which is consistent with the clinical treatment process. This article provides a new solution for the aided diagnosis and decision-making treatment of NPJ, which is of great significance in reducing neonatal mortality and alleviating the pressure of medical staff.
For diabetes mellitus (DM), the technology of blood glucose monitoring provides detection information for patients and helps sufferers to ameliorate bad states. Management rules and intervention measures, which are consistent with blood glucose situation, help to control blood glucose stability, establish a healthy lifestyle, and prevent the occurrence of DM complications. Formulating effective rules and measures is the key to the blood sugar management. What is more, the analysis of blood glucose situation is beneficial to the formulation of management rules and intervention measures. In this paper, interval type-2 fuzzy sets (IT2 FSs) and fuzzy comprehension evaluation are applied in the analysis of blood sugar situation. Moreover, dynamic fuzzy rules are built to provide the corresponding blood glucose management rules. Linguistic dynamic systems (LDS) are used to describe and analyze the evolution process of blood glucose situation. Finally, the analysis results indicate the method is applicable and valuable for actual management.
New and revised definitions such as unit fuzzy sets, type-2 fuzzy sets (T2 FSs) and their restriction at a point are introduced by the method of set theory to make them easily understandable. All the definitions are uniform and formal, and able to represent type-2 fuzzy sets conveniently. An embedded unit fuzzy set is defined to describe general T2 FSs and the representations of discrete and partially connected T2 FSs are given as well. Based on the universes of discourse, primary membership grade, and membership function, type-2 fuzzy sets are divided into four classes: discrete, partially connected, connected, and compounded. Connected T2 FSs are further classified into two types: single connected and multi-connected. The partition method for closure of support (CoS) is used to represent the primary membership grades and interval type-2 fuzzy sets. A method of second/third partition for CoS is proposed to represent single connected/multiconnected T2 FS, respectively after CoS is divided twice and three times; the upper and lower membership functions, and the restriction of the secondary membership function have same analytic expressions, respectively. Finally, the connections among the restriction of T2 FS at a point, primary membership function, CoS, embedded type-1 fuzzy set are discussed.
In this paper, conventional dynamic systems are converted to type-I and type-II linguistic dynamic systems (LDS). The evolving laws of a type-I LDS are the same as those of its conventional counterpart while Its states are linguistic. Since the evolving laws of type-I LDS are In the numerical do. main, a type-I LDS can be directly constructed from its conventional counterpart by using extension principle. The evolving laws of a type-II LDS are modeled by linguistic rules while its states are linguistic. By using extension principle, a method of converting a conventional dynamic system into a type-II LDS is presented. Based on a-cuts, the existence of fixed points of type-I LDS is studied. Also based on a-cuts, an efficient numerical procedure called acute mapping is developed for studying LDS. Numerical examples using a conventional dynamic system, namely, logistic map, are presented.
The study of psychological health state is helpful to build appropriate models and take effective intervention strategies, and the results benefit the intervened released from psychological distress within the shortest possible time. In this paper, interval type-2 fuzzy sets and fuzzy comprehension evaluation are applied in the analysis of mental health status and crisis intervention. A closed-loop linguistic dynamic intervention model for psychological health state is built. Linguistic dynamic systems based on interval type-2 fuzzy sets are used to describe and analyze the evolutionary process of psychological health status.
In China, traffic police's micro-bo provides instant information for travelers and can help drivers to avoid congested roads. Management rules and laws help to maintain the road traffic order, improve traffic flow, and prevent traffic accidents. How to build reasonable rules and laws is very important. The analysis of traffic flow is good for building traffic laws and rules. In this paper, the congestion time, congested place, and congestion reason are analyzed on the traffic police's micro-bo, and the theories of linguistic dynamic systems based on multifactor time-varying universe and fuzzy comprehension evaluation are used to analyze traffic flow and dynamic fuzzy rules on time-varying universe are built to provide the corresponding traffic management rules. As an example, Shenzhen's traffic police micro-bo is used to study the information of traffic congestion, including jam session, congestion location and reasons, and disposal methods, and their results are presented in language form, i.e., keywords walls; then, the traffic flow of Labor Day is discussed.
As a covering approximation space, its connectivity directly reflects a relationship, which plays an important role in data mining, among elements on the universe. In this paper, we study the connectivity of a covering approximation space and give its connected component. Especially, we give three methods to judge whether a covering approximation space is connected or not. Firstly, the conception of the maximization of a family of sets is given. Particularly, we find that a covering and its maximization have the same connectivity. Second, we investigate the connectivity of special covering approximation spaces. Finally, we give three methods of judging the connectivity of a covering approximation space from the viewpoint of matrix, graph and a new covering.
Rough set theory has been proposed by Pawlak as a useful tool for dealing with the vagueness and granularity in information systems. Classical rough set theory is based on equivalence relation. The covering rough sets is an improvement of Pawlak rough set to deal with complex practical problems which the latter one can not handle. This paper studies covering-based generalized rough sets. In this setting, a covering can also generate a lower approximation operation and an upper approximation operation, but some of common properties of classical lower and upper approximation operations are no longer satisfied. We investigate conditions for a covering under which these properties hold for the covering-based lower and upper approximation operations.
The results of traditional traffic status analysis are mostly single values, whose accuracy can't be determined; fuzzy c-means clustering (FCM) algorithm based on fuzzy theory can calculate the clustering center of plenty data quickly and easily; linguistic dynamic systems could describe the dynamic rules of complex systems in the language level. In this paper, membership functions are decided by FCM; result of a specific time period taken as one example is obtained; it's discussed that linguistic dynamic analysis of traffic status in different period within a day by the same method.
Computing with words (CWW) proposed by Zadeh is an useful paradigm to mimic the human decision-making ability in a wide variety of physical and mental tasks. To realize CWW, Mendel proposed a specific architecture called perceptual computer, in which interval type-2 (IT2) fuzzy sets (FSs) and perceptual reasoning (PR) method are adopted. The PR method has been proved to have good properties (e.g. it can output intuitive IT2 FSs) and has found several applications in decision making. In this study, we focus on simplifying this method by avoiding its a-cuts based inference process. We first present a novel property for the inference of the PR method. We observe from the property that, if the IT2 FSs in the consequents of the IF-THEN rules are trapezoidal and have consistent slopes, then the output IT2 FS will be strictly trapezoidal and can be determined easily. In this case, the computation of the PR method can be simplified. To achieve such simplification, the trapezoidal IT2 FSs without consistent slopes should be approximated by the slope-consistent trapezoidal IT2 FSs. This issue is also studied in this paper by solving the constrained linear-quadratic optimization problem. At last, examples are given. The simplified PR method will be useful when the CWW models are utilized in the modeling and/or control problems of complex systems or multivariable dynamic systems.
The interval type-2 fuzzy extension principle is presented and the conventional one-to-one mapping is abstracted as its interval type-2 fuzzy counterpart. Then, the computing with words procedure based on the interval type-2 fuzzy extension principle is introduced. Finally, the linguistic dynamic trajectories of interval type-2 fuzzy sets are analyzed.
In order to describe the fuzzy set whose intention varies with time interval, we present the theory of time-varying universe of discourse and dynamic fuzzy rules by synthesizing fuzzy set, linguistic dynamic systems (LDS), and dynamic programming. The time-varying universe discourse is divided into two types: discrete type and continuous type, and each type is sorted into incremental, decremental, and mixed classes. Then, how to build dynamic fuzzy rules and how to compute with words on time-varying universe of discourse are discussed. Finally, the linguistic dynamic orbits on the time-varying universe of discourse are given.
The multigranulation rough set (MGRS) is becoming a rising theory in rough set area, which offers a desirable theoretical method for problem solving under multigranulation environment. However, it is worth noticing that how to effectively extract decision rules in terms of multigranulation rough sets has not been more concerned. In order to address this issue, we firstly give a general rule-extraction framework through including granulation selection and granule selection in the context of MGRS. Then, two methods in the framework (i.e. a granulation selection method that employs a heuristic strategy for searching a minimal set of granular structures and a granule selection method constructed by an optimistic strategy for getting a set of granules with maximal covering property) are both presented. Finally, an experimental analysis shows the validity of the proposed rule-extraction framework in this paper.
The linguistic dynamic systems (LDSs) based on type-1 fuzzy sets can provide a powerful tool for modeling, analysis, evaluation and control of complex systems. However, as pointed out in earlier studies, it is much more reasonable to take type-2 fuzzy sets to model the existing uncertainties of linguistic words. In this paper, the LDS based on type-2 fuzzy sets is studied, and its reasoning process is realized through the perceptual reasoning method. The properties of the perceptual reasoning method based LDS (PR-LDS) are explored. These properties demonstrated that the output of PR-LDS is intuitive and the computation complexity can be reduced when the consequent type-2 fuzzy numbers in the rule base satisfy some conditions. Further, a data driven method for the design of the PR-LDS is provided. At last, the effectiveness and rationality of the proposed data-driven method are verified by an example.
The rough set theory, proposed by Pawlak is termed as basic (traditional) rough set theory and it has been extended in many directions. Covering based rough set is one of the extensions of the basic rough set theory. A covering is a generalisation of notion of partitioned rough set (Pawalk rough set) introduced by W. Zakowski. In this article it is introduced a new type of covering-based rough set in which both lower and upper approximation operators are improved.
In this paper, principles of management systems are being converted to the corresponding fuzzy logic rule, and the behavior of employees can be predicted in the parallel systems, at the same time, the principles of management systems are modified and improved continuously and then form dynamic fuzzy rule base bank, at last the linguistic dynamic orbits of employee behavior are achieved.
In order to describe the fuzzy sets whose intension varies with different time interval,the paper presents a new defi- nition of time-varying universe of discourse,then discuss how to build dynamic fuzzy rules and how to compute with words on time-varying universe of discourse, finally gives the linguistic dynamic orbits on the time-varying universe of discourse.
Rough sets, a tool for data mining, deal with the vagueness and granularity in information systems. This paper studies a type of covering generalized rough sets. After presenting their basic properties, this paper explores the inter dependency between the lower and the upper approximation operations, conditions under which two coverings generate a same upper approximation operation, and the axiomatic systems for these operations. In the end, this paper establishes the relationships between this type of covering rough sets and the other covering rough sets in literature
Rough sets, a tool for data mining, deal with the vagueness and granularity in information systems. For further studies on privacy protection, we study a new type of covering-based rough sets. After presenting their basic properties, this paper explores the interdependency between the lower and upper approximation operations, and condition under which two coverings generate an identical upper approximation operation. Meanwhile this paper explores the relationships among the five types of covering-based rough sets and our new type of covering-based rough sets.
Rough sets theory has been considered as a useful method to model the uncertainty and has been applied successfully in many fields. And every rough set is associated with some amount of fuzziness. On the other hand, rough sets theory has been generalized with coverings instead of classical partition. So it is necessary to consider the amount of fuzziness in generalized rough sets induced by a covering. In this paper, a measure of fuzziness in generalized rough sets induced by a covering is proposed. Moreover, some characterizations and properties of this measure are shown by examples, which is every useful in future research works of generalized rough sets induced by a covering.
Rough set theory has been proposed by Pawlak as a tool for dealing with the vagueness and granularity in information systems. The core concepts of classical rough sets are lower and upper approximations based on equivalence relations. This paper studies arbitrary binary relation based generalized rough sets. In this setting, a binary relation can generate a lower approximation operation and an upper approximation operation, but some of common properties of classical lower and upper approximation operations are no longer satisfied. We investigate conditions for a relation under which these properties hold for the relation based lower and upper approximation operations.This paper also explores the relationships between the lower or the upper approximation operation generated by the intersection of two binary relations and those generated by these two binary relations, respectively. Through these relationships, we prove that two different binary relations will certainly generate two different lower approximation operations and two different upper approximation operations.
Rough set theory is a technique of granular computing. As a generalization of classical rough set theory, covering-based rough set has been used for attribute reduction in data mining. Linguistic dynamic systems are dynamic processes involving mainly computing with words instead of numbers for modeling and analysis of complex systems and human-machine interfaces. They are all potential methods for granular computing. This paper proposes an outline to combine these two techniques into a better and unified granular computing methodology. We present research issues and challenges for this exploration.
Rough set theory has been proposed by Pawlak as a tool for dealing with the vagueness and granularity in information systems.
The core concepts of classical rough sets are lower and upper approximations based on equivalence relations. This paper studies
arbitrary binary relation based generalized rough sets. In this setting, a binary relation can generate a lower approximation
operation and an upper approximation operation. We prove that such a binary relation is unique, since two different binary
relations will generate two different lower approximation operations and two different upper approximation operations. This
paper also explores the relationships between the lower or upper approximation operation generated by the intersection of
two binary relations and those generated by these two binary relations, respectively.
In covering setting, there are five types of rough set models in literature, but only one type of them has been studied from the point of topological view. In this paper, we address the topological properties in the other four types of covering-based rough sets; especially we present the conditions under which lower approximation operations become interior operators and the conditions under which the upper approximation operations become closure operators.
With the rapid development of the internet, copying a digital document is so easy and economically affordable that digital piracy is rampant. As a result, software protection has become a vital issue in current computer industry and a hot research topic. Software watermarking and obfuscation are techniques to protect software from unauthorized access, modification, and tampering. While software watermarking tries to insert a secret message called software watermark into the software program as evidence of ownership, software obfuscation translates software into a semantically- equivalent one that is hard for attackers to analyze. In this thesis, firstly, we present a survey of software watermarking and obfuscation. Then we formalize two impor- tant concepts in software watermarking: extraction and recognition and we use a concrete software watermarking algorithm to illustrate issues in these two concepts. We develop a technique called the homomorphic functions through residue numbers to obfuscate variables and data structures in software programs. Lastly, we explore the complexity issues in software watermarking and obfuscation.
Linguistic dynamic systems (LDS) are man-machine interfaces for bridging between the machine world in numbers and the human world in words. The evolving laws of a type-I LDS are constructed by applying the fuzzy extension principle to those of its conventional counterpart while its states are linguistic. The evolving laws of a type-II LDS are modeled by linguistic rules while its states are also linguistic. In this paper, the existence of fixed points of type-II LDS is studied based on point-to-fuzzy-set mappings. Linguistic controllers are designed to control type-II LDS to goal states specified in words.
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