scholarly journals Modified Uncertainty Measure of Rough Fuzzy Sets from the Perspective of Fuzzy Distance

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Jie Yang ◽  
Taihua Xu ◽  
Fan Zhao
Keyword(s):  
Fuzzy Sets ◽  
Rough Sets ◽  
Boundary Region ◽  
Uncertainty Measure ◽  
Approximation Spaces ◽  
Rough Sets Theory ◽  
Fuzzy Distance ◽  
Rough Approximation ◽  
Sets Theory

As an extension of Pawlak’s rough sets, rough fuzzy sets are proposed to deal with fuzzy target concept. As we know, the uncertainty of Pawlak’s rough sets is rooted in the objects contained in the boundary region, while the uncertainty of rough fuzzy sets comes from three regions (positive region, boundary region, and negative region). In addition, in the view of traditional uncertainty measures, the two rough approximation spaces with the same uncertainty are not necessarily equivalent, and they cannot be distinguished. In this paper, firstly, a fuzziness-based uncertainty measure is proposed. Meanwhile, the essence of the uncertainty for rough fuzzy sets and its three regions in a hierarchical granular structure is revealed. Then, from the perspective of fuzzy distance, we introduce a modified uncertainty measure based on the fuzziness-based uncertainty measure and present that our method not only is strictly monotonic with finer approximation spaces, but also can distinguish the two rough approximation spaces with the same uncertainty. Finally, a case study is introduced to demonstrate that the modified uncertainty measure is more suitable for evaluating the significance of attributes. These works are useful for further study on rough sets theory and promote the development of uncertain artificial intelligence.

Similarity measure for multi-granularity rough approximations of vague sets

2021 ◽  
Vol 40 (1) ◽  
pp. 1609-1621
Author(s):  
Jie Yang ◽  
Wei Zhou ◽  
Shuai Li
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Target Concept ◽  
Uncertainty Measure ◽  
Approximation Spaces ◽  
Vague Sets ◽  
Rough Approximation ◽  
Vague Concept

Vague sets are a further extension of fuzzy sets. In rough set theory, target concept can be characterized by different rough approximation spaces when it is a vague concept. The uncertainty measure of vague sets in rough approximation spaces is an important issue. If the uncertainty measure is not accurate enough, different rough approximation spaces of a vague concept may possess the same result, which makes it impossible to distinguish these approximation spaces for charactering a vague concept strictly. In this paper, this problem will be solved from the perspective of similarity. Firstly, based on the similarity between vague information granules(VIGs), we proposed an uncertainty measure with strong distinguishing ability called rough vague similarity (RVS). Furthermore, by studying the multi-granularity rough approximations of a vague concept, we reveal the change rules of RVS with the changing granularities and conclude that the RVS between any two rough approximation spaces can degenerate to granularity measure and information measure. Finally, a case study and related experiments are listed to verify that RVS possesses a better performance for reflecting differences among rough approximation spaces for describing a vague concept.

The Intuitionistic Fuzzy S-Rough Sets Model and Dynamic Transfer Degree

2014 ◽  
Vol 513-517 ◽  
pp. 4352-4356
Author(s):  
Jun Hong Hu ◽  
Guo Dong Gu ◽  
Fu Xian Liu
Keyword(s):  
Fuzzy Sets ◽  
Equivalence Relation ◽  
Fuzzy System ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Rough Sets Theory ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Characteristic ◽  
Sets Theory ◽  
System Movement

The Intuitionistic Fuzzy S-Rough Sets (IFS-RS) is the intuitionistic fuzzy extension of S-Rough sets theory. It has dynamic characteristic of S-Rough sets, as well as intuitionistic fuzzy characteristic of Intuitionistic Fuzzy sets. Based on S-Rough sets theory, this paper introduced the membership and non-membership concepts of Intuitionistic Fuzzy sets, builded the model of IFS-RS under general equivalence relation, put forward the rough property and transfer degree concepts of IFS-RS. By calculating the rough property and transfer degree of IFS-RS, Thus being able to describe the transformation degree of the elements in fuzzy system movement into or movement out more clearly and precisely.

The Rough Sets Theory and Evidence Theory

1990 ◽  
Vol 13 (3) ◽  
pp. 245-262
Author(s):  
Andrzej Skowron
Keyword(s):  
Rough Sets ◽  
Evidence Theory ◽  
Decision Table ◽  
Combination Rule ◽  
Approximation Space ◽  
Approximation Spaces ◽  
Rough Sets Theory ◽  
Decision Attributes ◽  
Lower And Upper Approximations ◽  
Sets Theory

The aim of the paper is to show some connections between the rough sets theory and the Dempser-Shafer approach. We prove that for every Pawlak’s approximation space there exists a Dempster-Shafer space with the qualities of the lower and upper approximations of sets in the approximation space equal to the credibility and plausibility of sets in the Dempster-Shafer space, respectively. Analogous connections hold between approximation spaces generated by the decision tables and Dempster-Shafer spaces, namely for every decision table space there exists a Dempster-Shafer space such that the qualities of the lower and upper approximations (with respect to the condition attributes) of sets definable in the decision table by condition and decision attributes coincide with the credibility and plausibility of sets in the Dempster-Shafer space, respectively. A combination rule in approximation spaces analogous to the combination rule used in the Dempster approach is derived.

Compound-Fault Diagnosis of Bearing Based on Order Tracking Wavelet Packet and Rough Sets

2011 ◽  
Vol 130-134 ◽  
pp. 1681-1685 ◽  
Author(s):  
Guang Tian ◽  
Hao Tian ◽  
Guang Sheng Liu ◽  
Jin Hui Zhao ◽  
Li Ping Luo
Keyword(s):  
Fault Diagnosis ◽  
Rough Sets ◽  
Wavelet Packet ◽  
Decision Rules ◽  
Vibration Signals ◽  
Rough Sets Theory ◽  
Equal Angle ◽  
Order Tracking ◽  
Start Up ◽  
Sets Theory

The diagnosis of compound-fault is always a difficult point, and there is not an effective method in equipment diagnosis field, then a new method of compound-fault diagnosis was presented. The vibration signals at start-up in the gearbox are non-stationary signals, and traditional ways of diagnosis have low precision. Order tracking and wavelet packet and rough sets theory are introduced in the compound-fault diagnosis of bearing. First, the vibration signals at start-up were resampled using computer order tracking arithmetic and equal angle distributed vibration signals were obtained, and wavelet packet has been used for equal angle distributed vibration signals decomposition and reconstruction. Then, energy distribution of every frequency band can be calculated according to normalization process. A new feature vector can be obtained, then clear and concise decision rules can be obtained by rough sets theory. Finally, the result of compound-fault example proves that the proposed method has high validity and more amplitude appliance foreground.

Next-day peak electricity price forecasting using NN based on rough sets theory

2008 ◽  
Author(s):  
Hirofumi Toyama ◽  
Tomonobu Senjyu ◽  
Shantanu Chakraborty ◽  
Atsushi Yona ◽  
Toshihisa Funabashi ◽  
...  
Keyword(s):  
Rough Sets ◽  
Electricity Price ◽  
Price Forecasting ◽  
Rough Sets Theory ◽  
Electricity Price Forecasting ◽  
Sets Theory
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