On variable-precision-based rough set approach to incomplete interval-valued fuzzy information systems and its applications

2021 ◽  
Vol 40 (1) ◽  
pp. 463-475
Author(s):  
Juan Li ◽  
Yabin Shao ◽  
Xiaoding Qi
Keyword(s):  
Information System ◽  
Information Systems ◽  
Attribute Reduction ◽  
Misclassification Rate ◽  
Fuzzy Information ◽  
Attribute Weights ◽  
Variable Precision ◽  
Multiple Attribute ◽  
Rough Approximation ◽  
Interval Valued

 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.

Attribute significance based on inclusion degree for incomplete information systems and their applications to MADM problems

2021 ◽  
pp. 1-17
Author(s):  
Zhanhong Shi ◽  
Dinghai Zhang
Keyword(s):  
Information System ◽  
Information Systems ◽  
Incomplete Information ◽  
Dominance Relation ◽  
General Description ◽  
Fuzzy Information ◽  
Inclusion Degree ◽  
Attribute Weights ◽  
Incomplete Information Systems ◽  
Interval Valued

Attribute significance is very important in multiple-attribute decision-making (MADM) problems. In a MADM problem, the significance of attributes is often different. In order to overcome the shortcoming that attribute significance is usually given artificially. The purpose of this paper is to give attribute significance computation formulas based on inclusion degree. We note that in the real-world application, there is a lot of incomplete information due to the error of data measurement, the limitation of data understanding and data acquisition, etc. Firstly, we give a general description and the definition of incomplete information systems. We then establish the tolerance relation for incomplete linguistic information system, with the tolerance classes and inclusion degree, significance of attribute is proposed and the corresponding computation formula is obtained. Subsequently, for incomplete fuzzy information system and incomplete interval-valued fuzzy information system, the dominance relation and interval dominance relation is established, respectively. And the dominance class and interval dominance class of an element are got as well. With the help of inclusion degree, the computation formulas of attribute significance for incomplete fuzzy information system and incomplete interval-valued fuzzy information system are also obtained. At the same time, results show that the reduction of attribute set can be obtained by computing the significance of attributes in these incomplete information systems. Finally, as the applications of attribute significance, the attribute significance is viewed as attribute weights to solve MADM problems and the corresponding TOPSIS methods for three incomplete information systems are proposed. The numerical examples are also employed to illustrate the feasibility and effectiveness of the proposed approaches.

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.

Rough set theory for the interval-valued fuzzy information systems

2008 ◽  
Vol 178 (8) ◽  
pp. 1968-1985 ◽  
Author(s):  
Zengtai Gong ◽  
Bingzhen Sun ◽  
Degang Chen
Keyword(s):  
Information Systems ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Fuzzy Information ◽  
Interval Valued

Some Interval-Valued Pythagorean Fuzzy Einstein Weighted Averaging Aggregation Operators and Their Application to Group Decision Making

2018 ◽  
Vol 29 (1) ◽  
pp. 393-408 ◽  
Author(s):  
Khaista Rahman ◽  
Saleem Abdullah ◽  
Muhammad Sajjad Ali Khan
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Multiple Attribute ◽  
Interval Valued

Abstract In this paper, we introduce the notion of Einstein aggregation operators, such as the interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operator and the interval-valued Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. We also discuss some desirable properties, such as idempotency, boundedness, commutativity, and monotonicity. The main advantage of using the proposed operators is that these operators give a more complete view of the problem to the decision makers. These operators provide more accurate and precise results as compared the existing method. Finally, we apply these operators to deal with multiple-attribute group decision making under interval-valued Pythagorean fuzzy information. For this, we construct an algorithm for multiple-attribute group decision making. Lastly, we also construct a numerical example for multiple-attribute group decision making.

scholarly journals Attribute reduction in interval-valued information systems based on information entropies

2016 ◽  
Vol 17 (9) ◽  
pp. 919-928 ◽  
Author(s):  
Jian-hua Dai ◽  
Hu Hu ◽  
Guo-jie Zheng ◽  
Qing-hua Hu ◽  
Hui-feng Han ◽  
...  
Keyword(s):  
Information Systems ◽  
Attribute Reduction ◽  
Interval Valued
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