Rule Extraction Based on Interval-Valued Rough Fuzzy Sets

2014 ◽  
Vol 665 ◽  
pp. 668-673
Author(s):  
Hua Ni Qin ◽  
Da Rong Luo
Keyword(s):  
Knowledge Discovery ◽  
Rough Set ◽  
Fuzzy Set ◽  
Fuzzy Numbers ◽  
Fuzzy Information ◽  
Modified Model ◽  
Sorting Method ◽  
Rough Fuzzy Set ◽  
General Sorting ◽  
Interval Valued

A model of interval-valued rough fuzzy set combining interval-valued fuzzy set and rough set is investigated in this paper. Firstly, considering the deficiency of general sorting method between any interval-valued fuzzy numbers, an improved sorting method and a pair of new approximation operators about minimum and maximum are presented. Based on the improved operators, a model of interval-valued rough fuzzy set is established. At last, by using the modified model of interval-valued rough fuzzy set, a method of knowledge discovery in interval-valued fuzzy information systems is investigated.

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

scholarly journals Some Novel Geometric Aggregation Operators of Spherical Cubic Fuzzy Information with Application

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zafar Ullah ◽  
Huma Bashir ◽  
Rukhshanda Anjum ◽  
Mabrook Al-Rakhami ◽  
Suheer Al-Hadhrami ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Score Function ◽  
Membership Degree ◽  
Fuzzy Information ◽  
Numerical Illustration ◽  
Decision Making Processes ◽  
Risks Factors ◽  
Excellent Tool ◽  
Interval Valued

Technology is quickly evolving and becoming part of our lives. Life has become better and easier due to the technologies. Although it has lots of benefits, it also brings serious risks and threats, known as cyberattacks, which are neutralized by cybersecurities. Since spherical fuzzy sets (SFSs) and interval-valued SFS (IVSFS) are an excellent tool in coping with uncertainty and fuzziness, the current study discusses the idea of spherical cubic FSs (SCFSs). These sets are characterized by three mappings known as membership degree, neutral degree, and nonmembership degree. Each of these degrees is spherical cubic fuzzy numbers (SCFNs) such that the summation of their squares does not exceed one. The score function and accuracy function are presented for the comparison of SCFNs. Moreover, the spherical cubic fuzzy weighted geometric (SCFWG) operators and SCF ordered weighted geometric (SCFOWG) operators are established for determining the distance between two SCFNs. Furthermore, some operational rules of the proposed operators are analyzed and multiattribute decision-making (MADM) approach based on these operators is presented. These methods are applied to make the best decision on the basis of risks factors as a numerical illustration. Additionally, the comparison of the proposed method with the existing methods is carried out; since the proposed methods and operators are the generalizations of existing methods, they provide more general, exact, and accurate results. Finally, for the legitimacy, practicality, and usefulness of the decision-making processes, a detailed illustration is given.

Interval-Valued Dual Hesitant Fuzzy Heronian Mean Aggregation Operators and their Application to Multi-Attribute Decision Making

2018 ◽  
Vol 17 (01) ◽  
pp. 1850005 ◽  
Author(s):  
Yuqi Zang ◽  
Xiaodong Zhao ◽  
Shiyong Li
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Aggregation Operators ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Information ◽  
New Approach ◽  
Dual Hesitant Fuzzy Set ◽  
Multi Attribute Decision Making ◽  
Interval Valued ◽  
Heronian Mean

The interval-valued dual hesitant fuzzy set (IVDHFS) can depict the imprecise, vague and indeterminate information and Heronian mean (HM) has the prominent characteristic of capturing the correlation of the aggregated arguments. In this paper, we investigate multi-attribute decision making (MADM) problems based on HM, in which the attribute values are assumed in the form of interval-valued dual hesitant fuzzy information. Firstly, we briefly present some concepts of IVDHFS and HM. Then, we propose the interval-valued dual hesitant fuzzy Heronian mean (IVDHFHM) operator and the interval-valued dual hesitant fuzzy geometric Heronian mean (IVDHFGHM) operator. We also prove that they satisfy some desirable properties. Further, we consider the importance of the input arguments and derive the interval-valued dual hesitant fuzzy weighted Heronian mean (IVDHFWHM) operator and the interval-valued dual hesitant fuzzy weighted geometric Heronian mean (IVDHFWGHM) operator, and then develop the procedure of MADM. Finally, an illustrate example is given to demonstrate the practicality and effectiveness of the new approach.

A Kind of Fuzzy Set for Rough Fuzzy Sorting Method

2015 ◽  
Vol 740 ◽  
pp. 786-789
Author(s):  
Jia Tai Gang ◽  
Kun Liang ◽  
Ming Ming Niu ◽  
Xue Sheng Liu
Keyword(s):  
Partial Order ◽  
Rough Set ◽  
Fuzzy Set ◽  
Fuzzy Number ◽  
Approximate Expression ◽  
Sorting Method ◽  
Whole Process ◽  
Order Structures

Fuzzy set sorting method is studied in this prepare. Firstly, a sorting method of Fuzzy number is proposed under the condition of rough fuzzy number. Use rough fuzzy number to approach fuzzy set by rough set and fuzzy set; it is an approximate expression of fuzzy set. Secondly, prove partial order structures above method and give an example for fuzzy set sorting method, showing the whole process for the sorting method. Lastly, summarize the sorting method that is convenient, concise and easy to apply. It is enrich and supplement for fuzzy sorting method.

Modeling Uncertainty with Interval Valued Fuzzy Numbers

2018 ◽  
Vol 11 (2) ◽  
pp. 1-17 ◽  
Author(s):  
Palash Dutta
Keyword(s):  
Risk Assessment ◽  
Fuzzy Set ◽  
Fuzzy Numbers ◽  
Small Sample Size ◽  
Small Sample ◽  
Model Parameters ◽  
Type I ◽  
Mathematical Tool ◽  
Risk Assessment Models ◽  
Interval Valued

This article describes how risk assessment is a significant aid in decision-making process. It is usually performed using models and a ‘model' is a function of some parameters which are usually affected by uncertainty due to lack of data, imprecision, vagueness, and a small sample size.. Fuzzy set is a well-established mathematical tool to handle this type of uncertainty. Normally, triangular fuzzy numbers (TFNs) or trapezoidal fuzzy numbers (TrFNs) are extensively deliberated to embody this type of uncertainty. However, in real world situations, bell-shaped fuzzy numbers may occur to characterize uncertainty. It is pragmatic that type-I fuzzy set may not always dispense single value from [0,1] and on the other hand, assigning a precise value to expert's judgment is excessively restrictive, therefore, the assignment of an interval value is more practical. Thus, interval valued fuzzy set (IVFS) comes into picture. It can be observed that representation of some model parameters of the risk assessment models are triangular interval valued fuzzy numbers (TIVFNs) while representation of some other parameters are bell-shaped IVFNs. In such circumstances, it is most important to devise a technique to combine TIVFNs and bell shaped IVFNs, as they are non-comparable. For this purpose, this article presents a technique to combine both types of incomparable IVFNs within the same framework and finally, a case study is carried out in risk assessment under this setting.

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