On the specificity of a possibility distribution
Fuzzy Sets and Systems
Gaussian processes and Martingales for fuzzy valued random variables with continuous parameter
Information Sciences: an International Journal - Fuzzy random variables
Theory and Practice of Uncertain Programming
Theory and Practice of Uncertain Programming
On probabilistic methods in fuzzy theory
International Journal of Intelligent Systems - Intelligent Technologies
Fuzzy random chance-constrained programming
IEEE Transactions on Fuzzy Systems
Fuzzy random dependent-chance programming
IEEE Transactions on Fuzzy Systems
Expected value of fuzzy variable and fuzzy expected value models
IEEE Transactions on Fuzzy Systems
Chance-constrained programming models for capital budgeting with NPV as fuzzy parameters
Journal of Computational and Applied Mathematics
Portfolio selection with fuzzy returns
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Fuzzy Sets and Systems
Fractional Liu process with application to finance
Mathematical and Computer Modelling: An International Journal
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It is well-known that Hölder, Minkowski, Markov, Chebyshev and Jensen's inequalities are important and useful results in probability theory. This paper proposes to extend the usefulness of the above inequalities to the context of unccertainity analysis in intelligent systems. In order to further discuss the mathematical properties of fuzzy random variables, theanalogous inequalities for fuzzy random variables are first proved based on the chance measure and expected value operator. After that, monotonicity and continuity of critical values of fuzzy random variables are also investigated. Finally, a convergence theorem of critical values for fuzzy random sequence is obtained.