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Some Inequalities Combining Rough and Random Information.

Yujie Gu¹, Qianyu Zhang¹, Liying Yu¹

¹School of Management, Shanghai University, Shanghai 200444, China.

Entropy (Basel, Switzerland)

|December 3, 2020

Summary

This summary is machine-generated.

This study extends rough random theory by proving key probabilistic inequalities for rough random variables. It also investigates properties of critical values for rough random optimization problems.

Keywords:

critical values inequalities rough random variable

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Area of Science:

Mathematics
Statistics
Decision-Making

Background:

Rough random theory integrates rough set and probability theories.
Rough random variables are random variables with rough variable values.

Purpose of the Study:

To extend and enrich rough random theory.
To provide theoretical support for further development.
To offer novel analytical approaches for optimization problems.

Main Methods:

Proving probabilistic inequalities (Markov, Chebyshev, Holder's, Minkowski, Jensen's) for rough random variables.
Investigating continuity and monotonicity properties of critical values for rough random variables.

Main Results:

Established probabilistic inequalities for rough random variables.
Characterized critical values of rough random variables regarding continuity and monotonicity.

Conclusions:

The study provides a firm theoretical foundation for rough random theory.
Novel analytical methods are presented for rough random optimization problems.