Knowledge Acquisition in Incomplete E-Commerce Information Systems

A three-way decision approach with a probability dominance relation based on prospect theory for incomplete information systems

The traditional rough set (RS) theory is a powerful tool to deal with complete information system, and its performance to process incomplete information system is weak, especially, its effect of combining the incomplete information system with fuzzy objective information system is weaker. The paper improves the tolerance relation proposed by M.Kryszkiewcz to obtain the γ− tolerance relation and γ− tolerance classes, presents the concept of the incomplete and fuzzy objective information system (IFOIS in short), and gives its rough set model based on the γ− tolerance relation, i.e., the rough set model in incomplete and fuzzy objective information system. Finally, the concept of precision reduction is defined, and the corresponding algorithm is provided.

Abstract: Machine learning can extract desired knowledge from training examples and ease the development bottleneck in building expert systems. Most learning approaches derive rules from complete and incomplete data sets. If attribute values are known as possibility distributions on the domain of the attributes, the system is called an incomplete fuzzy information system. Learning from incomplete fuzzy data sets is usually more difficult than learning from complete data sets and incomplete data sets. In this paper, we deal with the problem of producing a set of certain and possible rules from incomplete fuzzy data sets based on rough sets. The notions of lower and upper generalized fuzzy rough approximations are introduced. By using the fuzzy rough upper approximation operator, we transform each fuzzy subset of the domain of every attribute in an incomplete fuzzy information system into a fuzzy subset of the universe, from which fuzzy similarity neighbourhoods of objects in the system are derived. The fuzzy lower and upper approximations for any subset of the universe are then calculated and the knowledge hidden in the information system is unravelled and expressed in the form of decision rules.

A regret theory-based multi-granularity three-way decision model with incomplete T-spherical fuzzy information and its application in forest fire management

Further Investigation of Characteristic Relation in Incomplete Information System

Updating three-way decisions in incomplete multi-scale information systems

Generally, two ways are used to handle null value in incomplete information systems. One is transforming an incomplete system to a complete system. The other is process the incomplete information table based on toleration relation. In this paper we propose a method to process the incomplete information table based on granular computing directly. The incomplete information table is divided into granules only use the known value of instances. The rules are generated based on the granules.

An information system as a database that shows relationships between objects and attributes is a crucial mathematical model in the field of artificial intelligence. A real-valued information system is an information system where information function values of each attribute are real numbers. This paper explores information structures in an incomplete real-valued information system. Distances between two objects in a given subsystem of an incomplete real-valued information system is first constructed. Then, the fuzzy T cos -equivalence relation, induced by this subsystem by using Gaussian kernel method, is obtained, where Gaussian kernel is based on this distance. Next, information structure of this subsystem is proposed. Moreover, relationships between two information structures are studied from the two aspects of dependence and separation. Finally, the dependence between two information structures is studied by using inclusion degree. These results will be helpful for establishing a framework of granular computing.

With the view point of granular computing, there are different granules at different levels of scale in data sets having hierarchical scale structures. In this paper, the notion of incomplete multi-scale information systems is first introduced. Using tolerance relation, the lower and upper approximations in incomplete multi-scale information systems are then defined and their properties are examined.

Classical rough set theory (RST) can't process incomplete information system (IIS) because it is based on an indiscernibility relation which is a kind of equivalent relation. In the literature a non-symmetric similarity relation based rough set model (NS-RSM) has been introduced as an extended model under IIS with ``?" values directly. Unfortunately, in this model objects in the same similarity class are not necessarily similar to each other and may belong to different target classes. In this paper, a new inequivalent relation called Maximal Limited Consistent block relation (MLC) is proposed. The proposed MLC relation improves the lower approximation accuracy by finding the maximal limited blocks of indiscernible objects in IIS with ``?" values. Maximal Limited Similarity rough set model (MLS) is introduced as an integration between our proposed relation (MLC) and NS-RSM. The resulted MLS model works efficiently under IIS with ``?" values. Finally, an illustrative example is given to validate MLS model. Furthermore, approximation accuracy comparisons have been conducted among NS-RSM and MLS. The results of this work demonstrate that the MLS model outperform NS-RSM.

During the recent years the smart cities knows a great extension as a modern shape of sustainable expansion. It's a urban area that utilize various devices connected with internet and integrates them with ICTs to promote goodness and execution of services for the best interaction among citizens and city's government. The basic for smart cities is distributed and independent information infrastructure. Using information effectively is going to be a main factor for success in the smart cities. The sources of information's (models, experts, and sensors) must be reason, perfect and complete. The generated information from independent and distributed sources can be imprecise, uncertain, and/or incomplete in real life. Any deficiency in gathered information will have a negative effect on the performance of services and decision making process within smart cities. So, we need a general framework to represent all types of imperfect and incomplete information. Since the classical methods fails to deal with vague, inconsistent and incomplete information, the fuzzy set was introduced to solve this drawback. The fuzzy set was not the perfect method for dealing with these drawbacks because it considers only truthiness and fails to deal with indeterminacy. The efficient mathematical tool for dealing with uncertain, vague and inconsistent objects is rough sets theory which introduced by Pawlak. The theory of neutrosophic rough sets is powerful for dealing with incompleteness and neutrosophic set deals with indeterminate and inconsistent data efficiently through considering truthiness, indeterminacy and falsity degrees. So, in this research we will propose a general framework for dealing with imperfect and incomplete information through using single valued neutrosophic and rough set theories. The combination of two sets will deal with all aspects of vagueness, inconsistency and incompleteness of data and information, and then will enhance the quality of introduced services and decisions from smart cities to their citizens. As experimentation, we applied the proposed framework for modeling imperfect and incomplete data in healthcare field.

With respect to multiple attribute group decision making problems in which the attribute weights and the expert weights take the form of real numbers and the attribute values take the form of interval-valued uncertain linguistic variable. In this paper, we introduce the idea of variable precision into the incomplete interval-valued fuzzy information system and propose the theory of variable precision rough sets over incomplete interval-valued fuzzy information systems. Then, we give the properties of rough approximation operators and study the knowledge discovery and attribute reduction in the incomplete interval-valued fuzzy information system under the condition that a certain degree of misclassification rate is allowed to exist. Furthermore, a decision rule and decision model are given. Finally, an illustrative example is given and compared with the existing methods, the practicability and effectiveness of this method are further verified.

Based on an intuitionistic knowledge content nature of information gain, the concept of combination entropy CE(A) in incomplete information systems is first introduced, and some of its important properties are given. Then, the conditional combination entropy CE(Q | P) and the mutual information CE(P;Q) are defined. Unlike all existing measures for the uncertainty in incomplete information systems, the relationships among these three concepts can be established, which are formally expressed as CE(Q | P) = CE(P ⋃ Q)-CE(P) and CE(P;Q) = CE(P)-CE(P | Q). Furthermore, a variant CE(CA) of the combination entropy with maximal consistent block nature is introduced to measure the uncertainty of an incomplete information system in the view of maximal consistent block technique. Its monotonicity is the same as that of the combination entropy. Finally, the combination granulation CG(A) and its variant CG(CA) with maximal consistent block nature are defined to measure discernibility ability of an incomplete information system, and the relationship between the combination entropy and the combination granulation is established as well. These results will be very helpful for understanding the essence of knowledge content and uncertainty measurement in incomplete information systems. Note that the combination entropy also can be further extended to measure the uncertainty in non-equivalence-based information systems.

With the development of big data, incomplete fuzzy information systems (IFISs) exist in many applications. The processing of incomplete information (missing values) is an essential issue in the study of IFIS. Existing studies either increase the uncertainty of missing values, e.g., the neighborhood tolerance relation, or discard the uncertainty of missing values completely, e.g., the imputation approaches based on attribute relevancy. They may lead to unreasonable classification results. In this paper, we propose an interval-value replacement-based neighborhood rough set model (IVR-NRSM) from the perspective of preserving uncertainty to some extent rather than two extremes. According to two semantics of missing values, we first replace lost values in IFIS with interval values. Then the IFIS can be transformed into a replaced IFIS with only one semantic (i.e., the do not care). In the replaced IFIS, we define a distance function for numerical data and interval-value data. Furthermore, we construct the improved neighborhood tolerance relation and the corresponding neighborhood tolerance classes in the replaced IFIS. Finally, we design two experiments on 4 UCI data sets by introducing three performance metrics. Experimental results illustrate that the proposed IVR-NRSM has higher classification performance than the two representative models.

Knowledge reduction is one of the main problems in the study of rough set theory. This paper deals with knowledge reduction in incomplete information systems based on Dempster-Shafer theory of evidence. The concepts of plausibility and belief consistent sets as well as plausibility and belief reducts in incomplete information systems are introduced. It is proved that a plausibility consistent set in an incomplete information system must be a consistent set and an attribute set in an incomplete information system is a belief reduct if and only if it is a classical reduct.