Rule extraction based on granulation order in interval-valued fuzzy information system

2011 ◽  
Vol 38 (10) ◽  
pp. 12249-12261 ◽  
Author(s):  
Yi Cheng ◽  
Duoqian Miao
Keyword(s):  
Information System ◽  
Rule Extraction ◽  
Fuzzy Information ◽  
Interval Valued

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.

scholarly journals Comparative Analysis of Hybrid Fuzzy MCGDM Methodologies for Optimal Robot Selection Process

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 839
Author(s):  
Tabasam Rashid ◽  
Asif Ali ◽  
Juan Guirao ◽  
Adrián Valverde
Keyword(s):  
Selection Process ◽  
Industrial Robot ◽  
Vital Role ◽  
Decision Makers ◽  
Fuzzy Information ◽  
Criteria Weights ◽  
Topsis Technique ◽  
Fuzzy Weights ◽  
Robot Selection ◽  
Interval Valued

The generalized interval-valued trapezoidal fuzzy best-worst method (GITrF-BWM) provides more reliable and more consistent criteria weights for multiple criteria group decision making (MCGDM) problems. In this study, GITrF-BWM is integrated with the extended TOPSIS (technique for order preference by similarity to the ideal solution) and extended VIKOR (visekriterijumska optimizacija i kompromisno resenje) methods for the selection of the optimal industrial robot using fuzzy information. For a criteria-based selection process, assigning weights play a vital role and significantly affect the decision. Assigning weights based on direct opinions of decision makers can be biased, so weight deriving models, such as GITrF-BWM, overcome this discrepancy. In previous studies, generalized interval-valued trapezoidal fuzzy weights were not derived by using any MCGDM method for the robot selection process. For this study, both subjective and objective criteria are considered. The preferences of decision makers are provided with the help of linguistic terms that are then converted into fuzzy information. The stability and reliability of the methods were tested by performing sensitivity analysis, which showed that the ranking results of both the methodologies are not symmetrical, and the integration of GITrF-BWM with the extended TOPSIS method provides stable and reliable results as compared to the integration of GITrF-BWM with the extended VIKOR method. Hence, the proposed methodology provides robust optimal industrial robot selection.

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