Solving Knapsack Problem with Fuzzy Random Variable Coefficients

2020 ◽  
pp. 1037-1048
Author(s):  
Vishnu Pratap Singh ◽  
Debjani Chakraborty
Keyword(s):  
Knapsack Problem ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Variable Coefficients ◽  
Fuzzy Random

Multiobjective Programming Problems Involving Fuzzy Coefficients, Random Variable Coefficients and Fuzzy Random Variable Coefficients

2015 ◽  
Vol 23 (04) ◽  
pp. 483-504 ◽  
Author(s):  
Hitoshi Yano
Keyword(s):  
Multiobjective Programming ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Variable Coefficients ◽  
Pareto Optimal ◽  
Possibility Measure ◽  
Generalized Pareto ◽  
Interactive Algorithm ◽  
Fuzzy Goal ◽  
Fuzzy Random

In this paper, we propose an interactive method for multiobjective linear programming problems, in which fuzzy coefficients, random variable coefficients and fuzzy random variable coefficients are involved in the objective functions respectively. In the proposed method, it is assumed that the decision maker has a fuzzy goal for each objective function, and such a fuzzy goal can be quantified by eliciting the membership function. Through a possibility measure and a fractile optimization model, the original problem is transformed to the well-defined multiobjective programming problem. Then, a generalized Pareto optimal concept is defined, and an interactive algorithm is proposed to obtain a satisfactory solution from among a generalized Pareto optimal solution set.

scholarly journals On Distribution Characteristics of a Fuzzy Random Variable

2018 ◽  
Vol 47 (2) ◽  
pp. 53-67 ◽  
Author(s):  
Jalal Chachi
Keyword(s):  
Probability Theory ◽  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Distribution Characteristics ◽  
Fuzzy Random Variables ◽  
Fuzzy Random

In this paper, rst a new notion of fuzzy random variables is introduced. Then, usingclassical techniques in Probability Theory, some aspects and results associated to a randomvariable (including expectation, variance, covariance, correlation coecient, etc.) will beextended to this new environment. Furthermore, within this framework, we can use thetools of general Probability Theory to dene fuzzy cumulative distribution function of afuzzy random variable.

Sign in / Sign up

Export Citation Format

Share Document