The modes of convergence in the approximation of fuzzy random optimization problems

Abstract We consider the median solution of the Newsvendor Problem. Some properties of such a solution are shown through a theoretical analysis and a numerical experiment. Sometimes, though not often, median solution may be better than solutions maximizing expected profit, or maximizing minimum possible, over distribution with the same average and standard deviation, expected profit, according to some criteria. We discuss the practical suitability of the objective function set and the solution derived, for the Newsvendor Problem, and other such random optimization problems.

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Hybrid Uncertainty-Goal Programming Model with Scaled Index for Production Planning Assessment

FinTech ◽

10.3390/fintech1010001 ◽

2021 ◽

Vol 1 (1) ◽

pp. 1-24

Author(s):

Junzo Watada ◽

Nureize Binti Arbaiy ◽

Qiuhong Chen

Keyword(s):

Production Planning ◽

Goal Programming ◽

Optimization Problems ◽

Programming Model ◽

Business Goals ◽

Target Values ◽

Goal Programming Model ◽

Quantitative Results ◽

Hybrid Uncertainty ◽

Fuzzy Random

Goal programming (GP) can be thought of as an extension or generalization of linear programming to handle multiple, normally conflicting objective measures. Each of these measures is given a goal or target value to be achieved. Unwanted deviations from this set of target values are then minimized in an achievement function. Production planning is an important process that aims to leverage the resources available in industry to achieve one or more business goals. However, the production planning that typically uses mathematical models has its own challenges where parameter models are sometimes difficult to find easily and accurately. Data collected with various data collection methods and human experts’ judgments are often prone to uncertainties that can affect the information presented by quantitative results. This study focuses on resolving data uncertainties as well as multi-objective optimization using fuzzy random methods and GP in production planning problems. GP was enhanced with fuzzy random features. Scalable approaches and maximum minimum operators were then used to solve multi-object optimization problems. Scaled indices were also introduced to resolve fuzzy symbols containing unspecified relationships. The application results indicate that the proposed approach can mitigate the characteristics of uncertainty in the analysis and achieve a satisfactory optimized solution.

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THE INDEPENDENCE OF FUZZY VARIABLES WITH APPLICATIONS TO FUZZY RANDOM OPTIMIZATION

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s021848850700456x ◽

2007 ◽

Vol 15 (supp02) ◽

pp. 1-20 ◽

Cited By ~ 119

Author(s):

YIAN-KUI LIU ◽

JINWU GAO

Keyword(s):

Distribution Function ◽

Sufficient Conditions ◽

Possibility Distribution ◽

Fuzzy Variables ◽

Fundamental Properties ◽

Random Optimization ◽

Fuzzy Random Programming ◽

Necessary And Sufficient ◽

The Relationship ◽

Fuzzy Random

This paper presents the independence of fuzzy variables as well as its applications in fuzzy random optimization. First, the independence of fuzzy variables is defined based on the concept of marginal possibility distribution function, and a discussion about the relationship between the independent fuzzy variables and the noninteractive (unrelated) fuzzy variables is included. Second, we discuss some properties of the independent fuzzy variables, and establish the necessary and sufficient conditions for the independent fuzzy variables. Third, we propose the independence of fuzzy events, and deal with its fundamental properties. Finally, we apply the properties of the independent fuzzy variables to a class of fuzzy random programming problems to study their convexity.

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