Expected value of fuzzy variable and fuzzy expected value models

By Baoding Liu, Yian-Kui Liu. IEEE transactions on fuzzy systems, 2002

1,909 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/86c46e818a902a9b596a10313861c30112cc94f9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Yankui Liu
2. Baoding Liu
3. Fang-Fang Hao
4. Samarjit Kar
5. Wei-guo Zhang
6. Kai Yang
7. Xiang Li
8. Yunxia Chen

In Management Science and Operations Research

1. Baoding Liu
2. Yuanguo Zhu
3. Yankui Liu
4. Xiaowei Chen
5. Fang-Fang Hao
6. Samarjit Kar
7. Jiajun Sun
8. Xiang Li

In Statistics and Probability

1. Baoding Liu
2. Yuanguo Zhu
3. Yankui Liu
4. Fang-Fang Hao
5. Xiaowei Chen
6. Jiajun Sun
7. Samarjit Kar
8. Xiang Li

Citations in the corpus

• Some Research Problems in Uncertainty Theory (2009, background): “In order to ensure that the number M{Λ} has certain mathematical properties, Liu [9] proposed the following four axioms: Axiom 1.”
• Asian Option Pricing Formula for Uncertain Financial Market (2015, background): “From then on many researchers studied such as possibility measure [21], credibility measure [7].”
• OPTIMISTIC VALUE MODEL OF UNCERTAIN OPTIMAL CONTROL (2013, background): “Taking the supremum with respect to u|[t+∆t,T ] in (4), we get J(t,x) ≥ J̃(t,x).”
• Mean-variance-skewness model for portfolio selection with fuzzy returns (2010, methodology): “Then its variance was defined by Liu and Liu [15] as In what follows, we write n ¼ ð a ; b ; c Þ (see Fig.”
• Expected Value of Function of Uncertain Variables (2010, background): “2 Preliminary Different from probability measure, capacity [1], fuzzy measure [13], possibility measure [15] and credibility measure [5], Liu [6] proposed a concept of uncertain measure as follows.”
• Optimizing fuzzy p-hub center problem with generalized value-at-risk criterion (2014, methodology): “Therefore, motivated by the idea of Choquet integral, Liu and Liu [23] presented the following definition about the expected value of fuzzy variable.”
• A survey of credibility theory (2006, methodology): “Fuzzy simulation, developed by Liu and Iwamura (1998), Liu (1998, 1999) and Liu and Liu (2002) , was defined as a technique for conducting sampling experiments on models of fuzzy systems.”
• Mean-variance models for portfolio selection with fuzzy random returns (2009, methodology): “Let ξ be a fuzzy variable with finite expected value e. The variance of ξ is defined by [ 33 ]”
• Fuzzy Process, Hybrid Process and Uncertain Process (2008, background): “Definition 3 (Liu and Liu [8]) The set function Cr is called a credibility measure if it satisfies the normality, monotonicity, self-duality and maximality axioms.”
• Portfolio adjusting optimization with added assets and transaction costs based on credibility measures (2011, positive): “In fuzzy portfolio optimization, credibility theory is developed by Liu and Liu (2002) in which credibility measure is self-dual.”
• Fuzzy Random Variables: A Scalar Expected Value Operator (2003, background): “First, we recall the expected value of f.v.s defined by Liu and Liu (2002) .”
• Uncertain Entailment and Modus Ponens in the Framework of Uncertain Logic (2009, background): “However, fortunately, some “mathematical scales” have been invented to measure the truth degree of an event, for example, probability measure, capacity [3], fuzzy measure [13], possibility measure [15], credibility measure [7] as well as uncertain measure [8].”