scholarly journals Object-first Incremental Algorithms for Updating Approximations in Multi-granulation Fuzzy Probabilistic Rough Sets over Two Universes

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Zhan-Ao Xue ◽  
Haodong Hou ◽  
Bingxin Sun ◽  
Yongxiang Li ◽  
Yanna Zhang
Keyword(s):  
Rough Sets ◽  
Incremental Algorithms ◽  
Two Universes

scholarly journals Parametric Rough Sets with Application to Granular Association Rule Mining

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Xu He ◽  
Fan Min ◽  
William Zhu
Keyword(s):  
Recommender Systems ◽  
Association Rule ◽  
Rough Sets ◽  
Relational Databases ◽  
Data Sets ◽  
Rule Mining ◽  
Real World Data ◽  
New Model ◽  
New Type ◽  
Two Universes

Granular association rules reveal patterns hidden in many-to-many relationships which are common in relational databases. In recommender systems, these rules are appropriate for cold-start recommendation, where a customer or a product has just entered the system. An example of such rules might be “40% men like at least 30% kinds of alcohol; 45% customers are men and 6% products are alcohol.” Mining such rules is a challenging problem due to pattern explosion. In this paper, we build a new type of parametric rough sets on two universes and propose an efficient rule mining algorithm based on the new model. Specifically, the model is deliberately defined such that the parameter corresponds to one threshold of rules. The algorithm benefits from the lower approximation operator in the new model. Experiments on two real-world data sets show that the new algorithm is significantly faster than an existing algorithm, and the performance of recommender systems is stable.

On Simplified Axiomatic Characterizations of (υ σ)-Fuzzy Rough Approximation Operators

2017 ◽  
Vol 25 (03) ◽  
pp. 457-476 ◽  
Author(s):  
Hongying Zhang ◽  
Haijuan Song
Keyword(s):  
Rough Sets ◽  
Axiomatic Approach ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Constructive Approach ◽  
Axiomatic Characterizations ◽  
Approximation Operators ◽  
Rough Approximation ◽  
Potential Applications ◽  
Two Universes

The axiomatic approach is more appropriate than constructive approach for studying the algebraic structure of rough sets. In this paper, the more simple axiomatic characterizations of (υ σ)-fuzzy rough approximation operators are explored where υ is a residuated implicator and σis its dual implicator. Firstly, we review the existing independent axiomatic sets to characterize various types of υ-lower and σ-upper fuzzy rough approximation operators. Secondly, we present one-axiom characterizations of (υ σ)-fuzzy rough approximation operators constructed by a serial fuzzy relation on two universes. Furthermore, we show that (υ σ)-fuzzy rough approximation operators, corresponding to reexive, symmetric and T-transitive fuzzy relations, can be presented by only two axioms respectively. We conclude the paper by introducing some potential applications and future works.

scholarly journals Merger and Acquisition Target Selection Based on Interval Neutrosophic Multigranulation Rough Sets over Two Universes

Symmetry ◽  
2017 ◽  
Vol 9 (7) ◽  
pp. 126 ◽  
Author(s):  
Chao Zhang ◽  
Deyu Li ◽  
Arun Sangaiah ◽  
Said Broumi
Keyword(s):  
Rough Sets ◽  
Target Selection ◽  
Merger And Acquisition ◽  
Two Universes

scholarly journals Multi-Granulation Picture Hesitant Fuzzy Rough Sets

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 362 ◽  
Author(s):  
Bibin Mathew ◽  
Sunil Jacob John ◽  
José Carlos R. Alcantud
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Fuzzy Relations ◽  
Fuzzy Rough Sets ◽  
Fuzzy Rough Set ◽  
Standard Format ◽  
Two Universes ◽  
Novel Model ◽  
Theoretical Foundations

We lay the theoretical foundations of a novel model, termed picture hesitant fuzzy rough sets, based on picture hesitant fuzzy relations. We also combine this notion with the ideas of multi-granulation rough sets. As a consequence, a new multi-granulation rough set model on two universes, termed a multi-granulation picture hesitant fuzzy rough set, is developed. When the universes coincide or play a symmetric role, the concept assumes the standard format. In this context, we put forward two new classes of multi-granulation picture hesitant fuzzy rough sets, namely, the optimistic and pessimistic multi-granulation picture hesitant fuzzy rough sets. Further, we also investigate the relationships among these two concepts and picture hesitant fuzzy rough sets.

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