Related Experiment Video
Updated: May 1, 2026

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods
Published on: September 19, 2012
Analytical properties of credibilistic expectation functions
Shuming Wang1, Bo Wang2, Junzo Watada2
1Department of Industrial & Systems Engineering, National University of Singapore, Block E1A No. 05-19, 1 Engineering Drive 2, Singapore 117576.
This study explores the analytical properties of credibilistic expectation functions for fuzzy variables. We prove continuity theorems, derive a differentiation formula, and establish a law of large numbers for fuzzy variables.
Area of Science:
- Fuzzy Mathematics
- Optimization Theory
- Probability and Statistics
Background:
- The expectation function is crucial for fuzzy optimization.
- Understanding its properties aids in analyzing fuzzy optimization models and algorithms.
Purpose of the Study:
- To investigate analytical properties of credibilistic expectation functions for fuzzy variables.
- To establish foundational theorems for fuzzy variable analysis.
Main Methods:
- Proving continuity and semicontinuity theorems for expectation functions.
- Deriving a differentiation formula for fuzzy expectation functions.
- Utilizing Chebyshev Inequality for fuzzy variables to obtain a law of large numbers.
Main Results:
- Established continuity theorems for fuzzy expectation functions.
- Derived a formula relating the derivative of the fuzzy expectation function to the expectation of the derivative.
- Obtained a law of large numbers for sequences of fuzzy variables.
Conclusions:
- The analytical properties derived enhance the understanding of fuzzy expectation functions.
- Results provide theoretical support for fuzzy optimization model development and analysis.
- The study verifies findings with illustrative examples.
More Related Videos
06:08Exploring the Role of Deontic Reasoning and World Knowledge in Wason´s Selection Task
Published on: July 22, 2025
05:22Dissociation of the Confounding Influences of Expectancy and Integrative Difficulty Residing in Anomalous Sentences in Event-related Potential Studies
Published on: May 9, 2019
Related Concept Videos
Unrealistic Optimism Bias
Expected Frequencies in Goodness-of-Fit Tests
Determination of Expected Frequency
Expected Value
Hindsight Biases
Magical Thinking