SOME PROPERTIES OF CONTINUOUS UNCERTAIN MEASURE

2009 ◽  
Vol 17 (03) ◽  
pp. 419-426 ◽  
Author(s):  
XIN GAO
Keyword(s):  
Uncertainty Theory ◽  
Uncertain Variable ◽  
Expected Value ◽  
Critical Values ◽  
Uncertain Measure ◽  
Uncertainty Distribution ◽  
Convergence Theorems ◽  
Basic Properties

In this paper, we discuss some properties in uncertainty theory when uncertain measure is continuous. Firstly, the judgement conditions of continuous uncertain measure are proposed. Secondly, basic properties of uncertainty distribution and critical values of uncertain variable are proved. Finally, the convergence theorems for expected value are discussed.

scholarly journals Dependent-Chance Goal Programming for Water Resources Management under Uncertainty

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Haiying Guo ◽  
Honghua Shi ◽  
Xiaosheng Wang
Keyword(s):  
Water Resources ◽  
Water Resources Management ◽  
Goal Programming ◽  
Uncertain Variable ◽  
Uncertain Measure ◽  
Unknown Parameters ◽  
Uncertainty Distribution ◽  
Resources Management ◽  
Objective Event ◽  
Priority Structure

Without sufficient data, consulting experts is a good way to quantify unknown parameters in water resources management which will result in human uncertainty. The aim of this paper is to introduce a new tool-uncertainty theory to deal with such uncertainty which is treated as uncertain variable with uncertainty distribution. And a dependent-chance goal programming (DCGP) model is provided for water resources management under such circumstance. In the model uncertain measure is used to measure possibility that an event will occur which is maximized by minimizing the deviation (positive or negative deviation) from target of objective event under a given priority structure. In the end, the developed model is applied to a numerical example to illustrate the effectiveness of the model. The result obtained contributes to the desired water-allocation schemes for decision-markers.

A new measure of indeterminacy for uncertain variables with application to portfolio selection

2021 ◽  
pp. 1-5
Author(s):  
Jin Liu ◽  
Jinsheng Xie ◽  
Hamed Ahmadzade ◽  
Mehran Farahikia
Keyword(s):  
Probability Theory ◽  
Portfolio Selection ◽  
Uncertainty Theory ◽  
Random Variable ◽  
Uncertain Variable ◽  
Uncertainty Distribution ◽  
Uncertain Variables ◽  
Selection Problems ◽  
Exponential Entropy

Entropy is a measure for characterizing indeterminacy of a random variable or an uncertain variable with respect to probability theory and uncertainty theory, respectively. In order to characterize indeterminacy of uncertain variables, the concept of exponential entropy for uncertain variables is proposed. For computing the exponential entropy for uncertain variables, a formula is derived via inverse uncertainty distribution. As an application of exponential entropy, portfolio selection problems for uncertain returns are optimized via exponential entropy-mean models. For better understanding, several examples are provided.

scholarly journals A New Formula for Calculating Uncertainty Distribution of Function of Uncertain Variables

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2429
Author(s):  
Yuxing Jia ◽  
Yuer Lv ◽  
Zhigang Wang
Keyword(s):  
Uncertainty Theory ◽  
Monotone Function ◽  
Uncertain Variable ◽  
Mathematical Tool ◽  
Human Beings ◽  
Uncertainty Distribution ◽  
Uncertain Variables ◽  
New Ideas ◽  
New Formula ◽  
Theory Uncertainty

As a mathematical tool to rationally handle degrees of belief in human beings, uncertainty theory has been widely applied in the research and development of various domains, including science and engineering. As a fundamental part of uncertainty theory, uncertainty distribution is the key approach in the characterization of an uncertain variable. This paper shows a new formula to calculate the uncertainty distribution of strictly monotone function of uncertain variables, which breaks the habitual thinking that only the former formula can be used. In particular, the new formula is symmetrical to the former formula, which shows that when it is too intricate to deal with a problem using the former formula, the problem can be observed from another perspective by using the new formula. New ideas may be obtained from the combination of uncertainty theory and symmetry.

scholarly journals Uncertain Comprehensive Evaluation Method Based on Expected Value

2014 ◽  
Vol 2 (5) ◽  
pp. 461-472
Author(s):  
Fangfang Yang ◽  
Youhua Fu
Keyword(s):  
Urban Environment ◽  
Uncertainty Theory ◽  
Evaluation Method ◽  
Comprehensive Evaluation ◽  
Uncertain Variable ◽  
Expected Value ◽  
Comprehensive Evaluation Method ◽  
Environment Quality

AbstractThe author presents a new comprehensive evaluation method based on uncertainty theory in this paper. According to this kind of method, the evaluation quality of each evaluated index given by every expert is regarded as an uncertain variable. Then a comparison rule of uncertain comprehensive evaluation is proposed by means of expected value of uncertain variable. Some properties about the comparison rule are discussed. At last, an example about the comparison of urban environment quality is given to illustrate the uncertain comprehensive evaluation method.

NUMERICAL APPROACH TO AN OPTIMAL MULTI-ITEM IMPERFECT PRODUCTION CONTROL PROBLEM IN UNCERTAIN ENVIRONMENT

2014 ◽  
Vol 22 (01) ◽  
pp. 125-144
Author(s):  
DIPAK KUMAR JANA ◽  
K. MAITY ◽  
M. MAITI
Keyword(s):  
General Model ◽  
Production Control ◽  
Measure Theory ◽  
Control Variable ◽  
Uncertain Variable ◽  
Production Costs ◽  
Uncertain Measure ◽  
Fuzzy Variables ◽  
Imperfect Production ◽  
Production Inventory

In this paper, some multi-item imperfect production-inventory models without shortages for defective and deteriorating items with uncertain/imprecise holding and production costs and resource constraint have been formulated and solved for optimal production. Here, the rate of production is assumed to be a function of time and considered as a control variable. Also the demand is time dependent and known. Uncertain or imprecise space constraint is also considered. The uncertain and imprecise holding and production costs are represented by uncertain and fuzzy variables respectively. These are converted to crisp constraint/numbers using uncertain measure theory for uncertain variable and possibility/necessity measure for fuzzy variable. The multi-item production inventory model is formulated as a constrained single objective cost minimization problem with the help of global criteria method. The reduced problem is then solved using Kuhn-Tucker conditions and generalized reduced gradient(GRG-LINGO 10.0) technique. Form the general model, models for particular cases with different production and demand functions are derived. Models for a single item are also presented. The optimum results for different models are presented in both tabular and graphical forms. Sensitivity analysis of average cost for the general model with respect to the changes in holding and production costs are presented.

SINE ENTROPY FOR UNCERTAIN VARIABLES

2013 ◽  
Vol 21 (05) ◽  
pp. 743-753 ◽  
Author(s):  
KAI YAO ◽  
JINWU GAO ◽  
WEI DAI
Keyword(s):  
Maximum Entropy ◽  
Uncertainty Theory ◽  
Maximum Entropy Principle ◽  
Expected Value ◽  
Uncertain Variables ◽  
Entropy Principle

Entropy is a measure of the uncertainty associated with a variable whose value cannot be exactly predicated. In uncertainty theory, it has been quantified so far by logarithmic entropy. However, logarithmic entropy sometimes fails to measure the uncertainty. This paper will propose another type of entropy named sine entropy as a supplement, and explore its properties. After that, the maximum entropy principle will be introduced, and the arc-cosine distributed variables will be proved to have the maximum sine entropy with given expected value and variance.

Analysis of Fault Tree Base on Uncertain Optimistic Value

2011 ◽  
Vol 50-51 ◽  
pp. 140-144
Author(s):  
Jian Jun Liu ◽  
Yu Fu Ning
Keyword(s):  
Internal Combustion Engine ◽  
Empirical Data ◽  
Uncertainty Theory ◽  
Statistical Data ◽  
Combustion Engine ◽  
Fault Tree ◽  
Internal Combustion ◽  
Uncertain Variable ◽  
Simulation Technology ◽  
Optimistic Value

Based on uncertainty theory, this paper proposes a method that constructs and analyzes fault tree. In this paper, it would be characterized as crisp number if fault rate of bottom event is obtained from reliable handbook, empirical data and so on; it would be characterized as uncertain variable if fault rate of bottom event has no statistical data but is obtained from expert's subjective judgment. The optimistic value of overall system’s top event is calculated by using uncertain simulation technology. Finally feasibility and validity of this method is confirmed by taking fault tree of internal combustion engine as example.

Uncertain production risk process with breakdowns and its shortage index and shortage time

2020 ◽  
Vol 39 (5) ◽  
pp. 7151-7160
Author(s):  
Waichon Lio ◽  
Lifen Jia
Keyword(s):  
Uncertainty Theory ◽  
Risk Process ◽  
Uncertainty Distribution ◽  
Production Risk ◽  
Numerical Examples ◽  
Cycle Times ◽  
Production Problem

Since the practical production is not continuously available and sometimes suffers unexpected breakdowns, this paper applies uncertainty theory to introducing an uncertain production risk process with breakdowns to handle the production problem with uncertain cycle times (consisting of uncertain on-times and uncertain off-times) and uncertain production amounts. The concept of shortage index of the uncertain production risk process with breakdowns is provided and some formulas for the calculation are given. Furthermore, the shortage time of the uncertain production risk process with breakdowns is proposed and its uncertainty distribution is obtained. Finally, some numerical examples are revealed.

Portfolio Investment with Options Based on Uncertainty Theory

2019 ◽  
Vol 18 (03) ◽  
pp. 929-952 ◽  
Author(s):  
Xiaoxia Huang ◽  
Xuting Wang
Keyword(s):  
Financial Markets ◽  
Stock Prices ◽  
Uncertainty Theory ◽  
Equivalent Form ◽  
Uncertain Variable ◽  
Stock Index ◽  
Portfolio Investment ◽  
Expected Return ◽  
Important Conclusion ◽  
Exercise Price

In financial markets, there are situations where investors have the future stock prices according to the experts’ evaluations rather than historical data. Thus, the estimations of the stock prices contain much subjective imprecision instead of randomness. This paper discusses a portfolio investment with options in such a kind of situation. Treating the stock index price as an uncertain variable, we build an uncertain mean-chance portfolio model based on uncertainty theory and provide the equivalent form of the model. Furthermore, we make a comparison of the optimal expected return between portfolio investment with options and without options. An important conclusion is reached: The portfolio investment with options produces a no less expected return than that without options. In addition, we make sensitivity analysis and get two vital corresponding results. As an illustration, a numerical example is presented as well. The numerical results reveal that the options should be considered in portfolio investment. And the call option with maximum exercise price is most valuable per premium cost with the same exercise date.

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