Data mining technology and its possible applications in city planning

Uncertainty about future developments constitutes the most important and most difficult challenge for mankind. Despite this fact, uncertainty is not a part of general science. General science assumes that the future development follows cause-effect relations which can be described by mathematical functions, where the argument represents the cause and the image represents the effect. Scientific theories have exactly this form and it is widely believed that these functions represent “truth”. Of course, this is nonsense as all the scientific theories are with certainty wrong and cannot describe the real evolution correctly. The inappropriate handling of uncertainty in science has produced a strange variety of “uncertainty theories” that causes confusion and helplessness. A friend of mine has expressed his confusion by the following words: ‘Crisp sets’, ‘fuzzy sets’, ‘rough sets’, ‘grey sets’, ‘fuzzy rough sets’, ‘rough fuzzy sets’, ‘fuzzy grey sets’, ‘grey fuzzy sets’, ‘rough grey sets’, ‘grey rough sets’, and now ‘affinity sets’. My goodness! Is there anybody around who can enlighten me, i.e., help me to see a clear pattern in this set of sets, allegedly providing powerful tools to model various kinds of uncertainty? This paper examines the role and the handling of uncertainty in quality control. How is uncertainty quantified in quality control for making decisions aiming at maintaining or improving quality of processes and products.KeywordsRandomnessIgnoranceKnowledgeFuzzynessQuantificationProbabilityCredibilityProbability spaceUncertainty spaceBernoulli space

Theories of fuzzy sets and rough sets are powerful mathematical tools for modelling various types of uncertainty. Molodtsov (Comput Math Appl 37:19–31, 1999 [6]) initiated a novel concept called soft sets, a new mathematical tool for dealing with uncertainties. It has been found that fuzzy sets, rough sets, and soft sets are closely related concepts (Aktas and Cagman in Inf Sci 1(77):2726–2735, 2007 [1]). Research works on soft sets are very active and progressing rapidly in these years. In 2001, Maji et al. (J Fuzzy Math 9(3):589–602, 2001 [5]) proposed the idea of intuitionistic fuzzy soft set theory and established some results on them. Based on an equivalence relation on the universe of discourse, Dubois and Prade (Int J Gen Syst 17:191–209, 1990 [3]) introduced the lower and upper approximation of fuzzy sets in a Pawlak approximation space and obtained a new notion called rough fuzzy sets. Feng et al. (Soft Compt 14:899–911, 2009 [4]) introduced lower and upper soft rough approximation of fuzzy sets in a soft approximation space and obtained a new hybrid model called soft rough fuzzy sets which is the extension of Dubois and Prade’s rough fuzzy sets. The aim of this chapter is to consider lower and upper soft rough intuitionistic fuzzy approximation of intuitionistic fuzzy sets in intuitionistic fuzzy soft approximation space (IF soft approximation space) and obtain a new hybrid model called soft rough intuitionistic fuzzy sets which can be seen as extension of both the previous work by Dubois and Prade and Feng et al.

Rough set theory for the interval-valued fuzzy information systems

This paper researched and constructed residuation implication operator of intuitionistic fuzzy T-norms.Based on this,the paper deducted the intuitionistic fuzzy rough sets model,and proved that the Pawlak rough sets,intuitionistic fuzzy sets,fuzzy rough sets,rough fuzzy sets and fuzzy T-norms rough sets were special cases of intuitionistic fuzzy rough sets.At last,some properties of intuitionistic fuzzy sets were presented and proved.

Theories of fuzzy sets and rough sets are powerful mathematical tools for modelling various types of uncertainty. Dubois and Prade investigated the problem of combining fuzzy sets with rough sets. Soft set theory was proposed by Molodtsov as a general framework for reasoning about vague concepts. The present paper is devoted to a possible fusion of these distinct but closely related soft computing approaches. Based on a Pawlak approximation space, the approximation of a soft set is proposed to obtain a hybrid model called rough soft sets. Alternatively, a soft set instead of an equivalence relation can be used to granulate the universe. This leads to a deviation of Pawlak approximation space called a soft approximation space, in which soft rough approximations and soft rough sets can be introduced accordingly. Furthermore, we also consider approximation of a fuzzy set in a soft approximation space, and initiate a concept called soft---rough fuzzy sets, which extends Dubois and Prade's rough fuzzy sets. Further research will be needed to establish whether the notions put forth in this paper may lead to a fruitful theory.

Rough sets and fuzzy sets are both theories for handling uncertain problems, and the viewpoints between them are different. They are complementary than competitive. Much seminal research has been carried out into combining them both; the results are rough fuzzy sets and fuzzy rough sets. In this paper, we introduce the idea of fuzzy rough sets in research of decision tables with quantitative data. Thus, we can handle the decision table directly without discretization. Combining the idea of variable precision rough sets, we make the form of the upper and lower approximation uniform.

The definition of basic rough sets [3] depends upon either a single equivalence relation defined on a universe or several equivalence relations defined over the universe, taken one each taken at a time. In the view of granular computing, classical rough set theory is based upon single granulation. Extending this notion, a rough set model based on multi-granulations (MGRS) was introduced in [5]. In this approach, approximations of sets were defined through multiple equivalence relations on the universe and their properties were investigated. Using hybridization of fuzzy set [13] with rough set the concept of rough fuzzy set was introduced by Dubois and Prade [1]. Recently, a Rough Fuzzy Set Model was introduced and studied by Wu and Kou [12], which is based on Multiple Granulation. Topological properties of rough sets introduced by Pawlak in terms of their types were recently studied by Tripathy and Mitra [10]. These were extended to the context of incomplete multi granulation by Tripathy and Raghavan [11]. In this paper we introduce incomplete multigranulation on rough fuzzy sets, study their basic properties and extend the topological properties in [11] to this context. Our findings are true for both complete and incomplete fuzzy rough set models based upon multi granulation.KeywordsRough SetsFuzzy rough setsequivalence relationstolerance relationstype of rough setsmulti granular fuzzy rough sets

Fuzzy concepts are represented by fuzzy sets, so a fuzzy knowledge is defined to be a collection of fuzzy sets (concepts) which includes two constants, 1 (true) and 0 (false). Abstractly, a logical derivation is a finite series of logical operations acting on a given knowledge. In fuzzy world, logical operations are defined by mathematical operations. So fuzzy logical derivations are mathematical derivations, and vice versa In this paper, the closure of fuzzy reasoning is characterized by fuzzy rough sets, and by topologies (neighborhood systems). A new fuzzy concept F N is derivable from the old knowledge K iff the membership function of F N is continuous in K-topology, or equivalently, iff F N is a rough fuzzy set (concept) of I N D(K),or plainly, iff the membership function of F N is a “step” function in the sense that it takes a constant value in each equivalence class of I N D(K).A fuzzy set L partitions the universe into equivalence classes; each equivalence class consists of those elements which have the same degree of membership. The indiscernibility relation I N D(K)over K is the “intersection” of all the equivalence relations induced by the fuzzy sets in K. The membership function of a fuzzy set is a real valued function, so U can be given the minimal topology such that the membership function of each fuzzy set in K is a continuous function. Such topology is called K-topology.

In order to effectively handle the real-valued data sets in practice, it is valuable from theoretical and practical aspects to combine fuzzy rough set and variable precision rough set so that a powerful tool can be developed. That is, the model of fuzzy variable precision rough set, which not only can handle numerical data but also is less sensitive to misclassification and perturbation,In this paper, we propose a new variable precision rough fuzzy set by introducing the variable precision parameter to generalized rough fuzzy set, i.e., the variable precision rough fuzzy set based on general relation. We, respectively, define the variable precision rough lower and upper approximations of any fuzzy set and it level set with variable precision parameter by constructive approach. Also, we present the properties of the proposed model in detail. Meanwhile, we establish the relationship between the variable precision rough approximation of a fuzzy set and the rough approximation of the level set for a fuzzy set. Furthermore, we give a new approach to uncertainty measure for variable precision rough fuzzy set established in this paper in order to overcome the limitations of the traditional methods. Finally, some numerical example are used to illuminate the validity of the conclusions given in this paper.

Extracting useful patterns is an important theme in data mining. Fuzzy logic and Rough sets are the most common techniques applied in data mining problems where rule sets are used to classify new cases. In order to extract minimum rules with high data coverage and fast processing time based on rule induction. This paper presents a hybrid method called, Updating Induction of Decision Rules based on Fuzzy Rough Set (UIDR-FRS). The UIDR-FRS method is based on the integration of fuzzy logic and rough sets and hence constructs a novel rule extraction model. The attribute reduction algorithm using fuzzy logic and rules extraction method based on rough sets are proposed. The attributes of decision table are analyzed using fuzzy logic and subsequently a rule extraction model based on these attributes is built through integration of rough sets and fuzzy logic model. Experiments on real-life data sets are conducted to test and verify the validity of the proposed measure. Applications of the proposed rule induction in rule extraction and accuracy are also studied with experiments. Extensive experimental results verify the effectiveness and efficiency of the attribute reduction algorithms for a compacted decision table.

Soft rough fuzzy sets and soft fuzzy rough sets

Intelligent computing system based on pattern recognition and data mining algorithms

In this study, we establish a connection between rough soft set (Shabir et al., Knowl Base Syst 40:72–80, 2013) and fuzzy set. Based on the novel granulation structure called modified soft rough approximation space, fuzzy rough soft set is introduced. The important basic properties of fuzzy rough soft set are studied and supported by illustrative examples. Moreover lattice theory is studied on fuzzy rough soft set. The definitions and propositions presented in this paper enrich the soft set theory, rough set theory and fuzzy set theory, and also extend their application scopes. The paper ends with conclusions having future investigations of the study.

Granular computing is a title of methodologies, techniques, and devices that make use of granules in the process of problem solving. The idea of granular computing has shown in a lot of areas, and it is likely playing a more and more important position in data mining. Rough set theory and fuzzy set theory, as two very important patterns of granular computing, are frequently used to process vague information in data mining. Combining rough set theory and fuzzy set theory, a flexible method is for processing imperfect information systems.

With the continuous development of business intelligence technology, the application research of decision support systems (DSSs) is deepening. In China, the work in this area started relatively late, and there are few DSS research cases to assist in marketing decision-making. Currently, marketing decision support systems have shortcomings in data integration, historical data, query functions, and data analysis. This article analyzes the characteristics of marketing decision-making, discusses the application of data warehouse, OLAP, and data mining technology in marketing decision support systems, and designs a marketing decision support system based on data mining technology. The system uses a BP neural network to conduct data mining marketing forecasting. A three-layer network model for marketing prediction is established, with sales time, product price, and customer purchasing power as network inputs and output as the sales volume of a certain type of product in different locations. The test results show that the average absolute percentage error of this method is 15.13%, and the prediction accuracy is high. Research shows that with the continuous development of data mining technology, the system cannot only help users conduct scientific and reasonable marketing decision-making analyses, making the marketing decision-making process more scientific and reasonable, but also can bring new ideas to enterprise decision-makers, promoting the continuous improvement and progress of the system.