Three-way decision for incomplete real-valued data

2020 ◽  
Vol 39 (5) ◽  
pp. 7843-7862
Author(s):  
Haili Wen ◽  
Fei Xia ◽  
Hongxiang Tang
Keyword(s):  
Information System ◽  
Decision Rule ◽  
Rough Set ◽  
Equivalence Relation ◽  
Risk Preference ◽  
Decision Makers ◽  
Gaussian Kernel ◽  
Decision Attributes ◽  
Different Levels ◽  
Conditional Attribute

An information system (IS) is a database that expresses relationships between objects and attributes. An IS with decision attributes is said to be a decision information system (DIS). An incomplete real-valued decision information system (IRVDIS) is a DIS based on incomplete real-valued data. This paper studies three-way decision (3WD) for incomplete real-valued data and its application. In the first place, the distance between two objects on the basis of the conditional attribute set in an IRVDIS is constructed. In the next place, the fuzzy Tcos-equivalence relation on the object set of an IRVDIS is received by means of Gaussian kernel. After that, the decision-theoretic rough set model for an IRVDIS is presented. Furthermore, the 3WD method is proposed based on this model. Lastly, to illustrate the feasibility of the proposed method, an application of the proposed method is given. It is worth mentioning that levels of risk may be determined by thresholds that can be directly acquired according to risk preference of different decision-makers, as well as the decision rule for each decision class under different levels of risk is showed in tabular forms.

A three-way decision method based on hybrid data1

2021 ◽  
Vol 40 (5) ◽  
pp. 8639-8650
Author(s):  
Sheng Luo
Keyword(s):  
Artificial Intelligence ◽  
Mathematical Model ◽  
Information System ◽  
Data Analysis ◽  
Rough Set ◽  
Gaussian Kernel ◽  
Inclusion Degree ◽  
Decision Method ◽  
Hybrid Data ◽  
Conditional Attribute

An information system as a database that represents relationships between objects and attributes is an important mathematical model in the field of artificial intelligence. Hybrid data means boolean, categorical, real-valued, set-valued data and missing data in this paper. A hybrid information system is an information system where its attribute is hybrid data. This paper proposes a three-way decision method based on hybrid data. First, the distance between two objects based on the conditional attribute set in a given hybrid information system is developed and Gaussian kernel based on this distance is acquired. Then, the fuzzy Tcos-equivalence relation, induced by this information system, is obtained by using Gaussian kernel. Next, the decision-theoretic rough set model in this hybrid information system is presented. Moreover, a three-way decision method is given by means of this decision-theoretic rough set model and inclusion degree between two fuzzy sets. Finally, an example is employed to illustrate the feasibility of the proposed method, which may provide an effective method for hybrid data analysis in real applications.

scholarly journals Multiple Granulation Rough Set Approach to Interval-Valued Intuitionistic Fuzzy Ordered Information Systems

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 949
Author(s):  
Zhen Li ◽  
Xiaoyan Zhang
Keyword(s):  
Information Theory ◽  
Pattern Recognition ◽  
Information System ◽  
Information Systems ◽  
Rough Set ◽  
Fuzzy Set ◽  
Equivalence Relation ◽  
Target Concept ◽  
Actual Case ◽  
Interval Valued

As a further extension of the fuzzy set and the intuitive fuzzy set, the interval-valued intuitive fuzzy set (IIFS) is a more effective tool to deal with uncertain problems. However, the classical rough set is based on the equivalence relation, which do not apply to the IIFS. In this paper, we combine the IIFS with the ordered information system to obtain the interval-valued intuitive fuzzy ordered information system (IIFOIS). On this basis, three types of multiple granulation rough set models based on the dominance relation are established to effectively overcome the limitation mentioned above, which belongs to the interdisciplinary subject of information theory in mathematics and pattern recognition. First, for an IIFOIS, we put forward a multiple granulation rough set (MGRS) model from two completely symmetry positions, which are optimistic and pessimistic, respectively. Furthermore, we discuss the approximation representation and a few essential characteristics for the target concept, besides several significant rough measures about two kinds of MGRS symmetry models are discussed. Furthermore, a more general MGRS model named the generalized MGRS (GMGRS) model is proposed in an IIFOIS, and some important properties and rough measures are also investigated. Finally, the relationships and differences between the single granulation rough set and the three types of MGRS are discussed carefully by comparing the rough measures between them in an IIFOIS. In order to better utilize the theory to realistic problems, an actual case shows the methods of MGRS models in an IIFOIS is given in this paper.

SAR

2011 ◽  
Vol 1 (4) ◽  
pp. 38-52
Author(s):  
Rabiei Mamat ◽  
Tutut Herawan ◽  
Mustafa Mat Deris
Keyword(s):  
Decision Making ◽  
Information System ◽  
Set Theory ◽  
Rough Set ◽  
Soft Set ◽  
Decision Makers ◽  
Benchmark Datasets

Soft-set theory proposed by Molodstov is a general mathematic tool for dealing with uncertainty. Recently, several algorithms have been proposed for decision making using soft-set theory. However, these algorithms still concern on Boolean-valued information system. In this paper, Support Attribute Representative (SAR), a soft-set based technique for decision making in categorical-valued information system is proposed. The proposed technique has been tested on three datasets to select the best partitioning attribute. Furthermore, two UCI benchmark datasets are used to elaborate the performance of the proposed technique in term of executing time. On these two datasets, it is shown that SAR outperforms three rough set-based techniques TR, MMR, and MDA up to 95% and 50%, respectively. The results of this research will provide useful information for decision makers to handle categorical datasets.

Algebraic Properties of Rough Set on Two Universal Sets based on Multigranulation

2014 ◽  
Vol 1 (2) ◽  
pp. 49-61 ◽  
Author(s):  
Mary A. Geetha ◽  
D. P. Acharjya ◽  
N. Ch. S. N. Iyengar
Keyword(s):  
Information System ◽  
Rough Set ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Granular Computing ◽  
Real Life ◽  
Equivalence Relations ◽  
Life Problems ◽  
Algebraic Properties ◽  
The Universe

The rough set philosophy is based on the concept that there is some information associated with each object of the universe. The set of all objects of the universe under consideration for particular discussion is considered as a universal set. So, there is a need to classify objects of the universe based on the indiscernibility relation (equivalence relation) among them. In the view of granular computing, rough set model is researched by single granulation. The granulation in general is carried out based on the equivalence relation defined over a universal set. It has been extended to multi-granular rough set model in which the set approximations are defined by using multiple equivalence relations on the universe simultaneously. But, in many real life scenarios, an information system establishes the relation with different universes. This gave the extension of multi-granulation rough set on single universal set to multi-granulation rough set on two universal sets. In this paper, we define multi-granulation rough set for two universal sets U and V. We study the algebraic properties that are interesting in the theory of multi-granular rough sets. This helps in describing and solving real life problems more accurately.

scholarly journals Rough Set Approach to Incomplete Multiscale Information System

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Xibei Yang ◽  
Yong Qi ◽  
Dongjun Yu ◽  
Hualong Yu ◽  
Xiaoning Song ◽  
...  
Keyword(s):  
Information System ◽  
Rough Set ◽  
Rough Sets ◽  
Decision Rules ◽  
Structured Data ◽  
Representation System ◽  
New Knowledge ◽  
Real World Applications ◽  
Knowledge Representation System ◽  
Different Levels

Multiscale information system is a new knowledge representation system for expressing the knowledge with different levels of granulations. In this paper, by considering the unknown values, which can be seen everywhere in real world applications, the incomplete multiscale information system is firstly investigated. The descriptor technique is employed to construct rough sets at different scales for analyzing the hierarchically structured data. The problem of unravelling decision rules at different scales is also addressed. Finally, the reduct descriptors are formulated to simplify decision rules, which can be derived from different scales. Some numerical examples are employed to substantiate the conceptual arguments.

An Improved Value Reduction Algorithm Based on Core Value

2011 ◽  
Vol 187 ◽  
pp. 216-220
Author(s):  
Wei Du ◽  
Wei Wang
Keyword(s):  
Information System ◽  
Decision Rule ◽  
Reduction Algorithm ◽  
Core Value ◽  
Conditional Attribute ◽  
Improved Algorithm ◽  
Attribute Value

Value reduction algorithm can filter and delete redundant conditional attribute value, so as to obtain decision rule of information system with least conditional attribute values. Based on the introduction of basic value reduction algorithm, the paper supplemented functions. Aiming at the circumstance of there is no repeated record and no conflict after deleting some attributes of a record, the algorithm supplement it. The example of value reduction based on the improved algorithm illustrated that it is an effective value reduction algorithm and an important supplement of basic value reduction algorithm.

SAR

2013 ◽  
pp. 266-280
Author(s):  
Rabiei Mamat ◽  
Tutut Herawan ◽  
Mustafa Mat Deris
Keyword(s):  
Decision Making ◽  
Information System ◽  
Set Theory ◽  
Rough Set ◽  
Soft Set ◽  
Decision Makers ◽  
Benchmark Datasets

Soft-set theory proposed by Molodstov is a general mathematic tool for dealing with uncertainty. Recently, several algorithms have been proposed for decision making using soft-set theory. However, these algorithms still concern on Boolean-valued information system. In this paper, Support Attribute Representative (SAR), a soft-set based technique for decision making in categorical-valued information system is proposed. The proposed technique has been tested on three datasets to select the best partitioning attribute. Furthermore, two UCI benchmark datasets are used to elaborate the performance of the proposed technique in term of executing time. On these two datasets, it is shown that SAR outperforms three rough set-based techniques TR, MMR, and MDA up to 95% and 50%, respectively. The results of this research will provide useful information for decision makers to handle categorical datasets.

On Correctness of Decision Algorithms in Information Systems

1988 ◽  
Vol 11 (3) ◽  
pp. 219-239
Author(s):  
Anita Wasilewska
Keyword(s):  
Information System ◽  
Information Systems ◽  
Decision Rule ◽  
Direct Product ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Decision Algorithm ◽  
Decision Algorithms

The concept of an information system, with manipulation based on the rough set theory, was introduced by Pawlak in 1982. The information system is defined by its set of objects, set of attributes, set of values of attributes, and a function, which maps the direct product of the first two sets onto the set of values of attributes. We introduce here, after [Pawlak 1985(1)], concepts of the decision rule, decision algorithm, static learning and describe the automatic procedures of deciding whether a given decision rule or decision algorithm is correct.

scholarly journals Uncertainty Measurement for a Set-Valued Information System: Gaussian Kernel Method

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 199 ◽  
Author(s):  
Jiali He ◽  
Pei Wang ◽  
Zhaowen Li
Keyword(s):  
Information System ◽  
Equivalence Relation ◽  
Kernel Method ◽  
Gaussian Kernel ◽  
Intrinsic Properties ◽  
Information Structures ◽  
Effectiveness Analysis ◽  
Uncertainty Measurement ◽  
Properties Of Information

A set-valued information system (SIS) is the generalization of a single-valued informationsystem. This article explores uncertainty measurement for a SIS by using Gaussian kernel. The fuzzyTcos-equivalence relation lead by a SIS is first obtained by using Gaussian kernel. Then, informationstructures in this SIS are described by set vectors. Next, dependence between information structuresis presented and properties of information structures are investigated. Lastly, uncertainty measuresof a SIS are presented by using its information structures. Moreover, effectiveness analysis is doneto assess the feasibility of our presented measures. The consequence of this article will help usunderstand the intrinsic properties of uncertainty in a SIS.

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