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Approximation set of the interval set in Pawlak's space
Qinghua Zhang1, Jin Wang2, Guoyin Wang2
1The Chongqing Key Laboratory of Computational Intelligence, Chongqing University of Posts and Telecommunications, Chongqing 400065, China ; School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China.
Thescientificworldjournal
|September 2, 2014
Summary
This study introduces a new method for approximating uncertain concepts using interval sets. It identifies an optimal approximation set, R0.5(Z), enhancing granular computing and interval set models.
Area of Science:
- Fuzzy Mathematics
- Granular Computing
- Set Theory
Background:
- Interval sets model uncertainty using upper and lower crisp boundaries.
- Existing approximation methods for interval sets have limitations.
Purpose of the Study:
- To define similarity degrees for interval sets and their approximations.
- To propose a novel method for finding a better approximation set for interval sets.
- To establish and prove the optimality of a new approximation set.
Main Methods:
- Defining similarity degrees between interval sets.
- Analyzing the properties of upper and lower approximation sets.
- Developing and validating a new optimal approximation set, R0.5(Z).
- Investigating the behavior of R0.5(Z) under different binary relations.
Main Results:
- Similarity degrees for interval sets and their approximations are presented.
- Disadvantages of traditional approximation sets are identified.
- The approximation set R0.5(Z) is proven to be an optimal approximation set for interval set Z.
- Change rules of R0.5(Z) with varying binary relations are analyzed.
Conclusions:
- The R0.5(Z) set serves as an optimal approximation for interval sets.
- This research contributes to the advancement of interval set models and granular computing theory.
- A crisp approximation set for interval sets has been successfully constructed.
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