Uncertain Measure

2014 ◽  
pp. 9-28 ◽  
Author(s):  
Baoding Liu
Keyword(s):  
Uncertain Measure

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.

scholarly journals Redundancy Optimization of an Uncertain Parallel-Series System with Warm Standby Elements

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Linmin Hu ◽  
Wei Huang ◽  
Guofang Wang ◽  
Ruiling Tian
Keyword(s):  
Optimization Algorithm ◽  
Optimization Model ◽  
Cost Minimization ◽  
Cost Optimization ◽  
Series System ◽  
Uncertain Measure ◽  
Uncertain Variables ◽  
Warm Standby ◽  
Parallel Series ◽  
Redundancy Optimization

The redundancy optimization problem is formulated for an uncertain parallel-series system with warm standby elements. The lifetimes and costs of elements are considered uncertain variables, and the weights and volumes of elements are random variables. The uncertain measure optimization model (UMOM), the uncertain optimistic value optimization model (UOVOM), and the uncertain cost optimization model (UCOM) are developed through reliability maximization, lifetime maximization, and cost minimization, respectively. An efficient simulation optimization algorithm is provided to calculate the objective values and optimal solutions of the UMOM, UOVOM, and UCOM. A numerical example is presented to illustrate the rationality of the models and the feasibility of the optimization algorithm.

Project selection and adjustment based on uncertain measure

2016 ◽  
Vol 352-353 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaoxia Huang ◽  
Tianyi Zhao
Keyword(s):  
Project Selection ◽  
Uncertain Measure

Advanced reliability analysis method for mechanisms based on uncertain measure

2020 ◽  
Vol 39 (1) ◽  
pp. 1045-1059
Author(s):  
Shuang Zhou ◽  
Jianguo Zhang ◽  
Lei Zhang ◽  
Lingfei You
Keyword(s):  
Reliability Analysis ◽  
Analysis Method ◽  
Uncertain Measure

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.

Vehicle Scheduling Model for Fresh Agriculture Products Pickup with Uncertain Demands

2014 ◽  
Vol 974 ◽  
pp. 282-287
Author(s):  
Li Xia Rong ◽  
Huan Bin Sha
Keyword(s):  
Genetic Algorithm ◽  
Hybrid Genetic Algorithm ◽  
Optimal Solution ◽  
Vehicle Scheduling ◽  
Uncertain Measure ◽  
Uncertainty Distribution ◽  
Uncertain Variables ◽  
Scheduling Model ◽  
Agriculture Products ◽  
The Impact

A chance-constrained vehicle scheduling model for fresh agriculture products pickup with uncertain demands is proposed in this paper. The uncertain measure that vehicle loading will not exceed capacity constraint is presented in the model because of the uncertainty of demands. Based on uncertainty theory, when the demands are some special uncertain variables with uncertainty distribution such as linear, zigzag and normal uncertain distribution etc., the model can be transformed to a deterministic form and solved by genetic algorithm. When the demands are general uncertain variables, a hybrid genetic algorithm with uncertain simulation is presented to obtain the optimal solution. At last, to illustrate the effective of the model and algorithm, and to analyze the impact of parameters on model solution, an experiment is provided.

scholarly journals Data Envelopment Analysis with Uncertain Inputs and Outputs

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Meilin Wen ◽  
Linhan Guo ◽  
Rui Kang ◽  
Yi Yang
Keyword(s):  
Data Envelopment Analysis ◽  
Deterministic Model ◽  
The Other ◽  
Data Envelopment ◽  
Decision Tool ◽  
Uncertain Measure ◽  
Dea Model ◽  
Dea Models ◽  
The One ◽  
Inputs And Outputs

Data envelopment analysis (DEA), as a useful management and decision tool, has been widely used since it was first invented by Charnes et al. in 1978. On the one hand, the DEA models need accurate inputs and outputs data. On the other hand, in many situations, inputs and outputs are volatile and complex so that they are difficult to measure in an accurate way. The conflict leads to the researches of uncertain DEA models. This paper will consider DEA in uncertain environment, thus producing a new model based on uncertain measure. Due to the complexity of the new uncertain DEA model, an equivalent deterministic model is presented. Finally, a numerical example is presented to illustrate the effectiveness of the uncertain DEA model.

UNCERTAINTY EXTENSION THEOREM AND PRODUCT UNCERTAIN MEASURE

2010 ◽  
Vol 18 (02) ◽  
pp. 197-208
Author(s):  
CUILIAN YOU
Keyword(s):  
Uncertainty Principle ◽  
Uncertainty Theory ◽  
Measure Theory ◽  
Extension Theorem ◽  
Uncertain Measure ◽  
Self Duality

The additivity axiom of classical measure theory has been challenged by many mathematicians. Different replacements of the additivity correspond with different theory. In uncertainty theory, the additivity is replaced with self-duality and countable subadditivity. Similar to classical measure theory, there are some properties studied in uncertainty theory. Given the measure of each singleton set, the measure can be fully and uniquely determined in the sense of the maximum uncertainty principle. Generally speaking, a product uncertain measure may be defined in many ways, in this paper, a kind of definition is proposed.

Criteria for the a Priori Shortest Path Generation in Uncertain Time-Varying Transportation Networks

2015 ◽  
Vol 23 (06) ◽  
pp. 807-827 ◽  
Author(s):  
Li Wang ◽  
Ziyou Gao ◽  
Lixing Yang
Keyword(s):  
A Priori ◽  
Time Interval ◽  
Time Varying ◽  
Uncertain Measure ◽  
First Order ◽  
Dominance Rule ◽  
Time Period ◽  
Comparison Criteria ◽  
Definition Of ◽  
Uncertain Time

This paper proposes a new definition of uncertain time-varying network to capture the uncertain and dynamic characteristics of the network with discrete uncertain link travel times. To find the a priori non-dominated paths in this type of network, three comparison criteria based on the uncertain measure, namely, deterministic dominance rule, first-order uncertain dominance rule and uncertain expected value dominance rule, are proposed to generate non-dominated paths in a single time interval and a time period, as more than one path may exist between an origin and destination for a given departure time. The proposed comparison methods are then applied to solving a simple uncertain time-varying network. The computational results verify the efficiency of three dominance rules for finding non-dominated paths.

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