A fuzzy goal programming technique for multi-objective chance constrained programming with normally distributed fuzzy random variables and fuzzy numbers

2013 ◽  
Vol 5 (5) ◽  
pp. 551 ◽  
Author(s):  
Animesh Biswas ◽  
Nilkanta Modak
Keyword(s):  
Goal Programming ◽  
Fuzzy Numbers ◽  
Random Variables ◽  
Chance Constrained Programming ◽  
Fuzzy Random Variables ◽  
Programming Technique ◽  
Objective Chance ◽  
Fuzzy Goal ◽  
Constrained Programming ◽  
Fuzzy Random

On Development of a Fuzzy Stochastic Programming Model with Its Application to Business Management

2017 ◽  
pp. 353-378
Author(s):  
Animesh Biswas ◽  
Arnab Kumar De
Keyword(s):  
Production Planning ◽  
Goal Programming ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Random Variables ◽  
Fuzzy Goal Programming ◽  
Fuzzy Random Variables ◽  
Fuzzy Goal ◽  
Constrained Programming ◽  
Fuzzy Random

This chapter expresses efficiency of fuzzy goal programming for multiobjective aggregate production planning in fuzzy stochastic environment. The parameters of the objectives are taken as normally distributed fuzzy random variables and the chance constraints involve joint Cauchy distributed fuzzy random variables. In model formulation process the fuzzy chance constrained programming model is converted into its equivalent fuzzy programming using probabilistic technique, a-cut of fuzzy numbers and taking expectation of parameters of the objectives. Defuzzification technique of fuzzy numbers is used to find multiobjective linear programming model. Membership function of each objective is constructed depending on their optimal values. Afterwards a weighted fuzzy goal programming model is developed to achieve the highest degree of each of the membership goals to the extent possible by minimizing group regrets in a multiobjective decision making context. To explore the potentiality of the proposed approach, production planning of a health drinks manufacturing company has been considered.

On Solving Multiobjective Transportation Problems with Fuzzy Random Supply and Demand Using Fuzzy Goal Programming

2017 ◽  
Vol 8 (3) ◽  
pp. 54-81 ◽  
Author(s):  
Animesh Biswas ◽  
Nilkanta Modak
Keyword(s):  
Goal Programming ◽  
Fuzzy Numbers ◽  
Optimal Allocation ◽  
Programming Model ◽  
Fuzzy Goal Programming ◽  
Chance Constrained Programming ◽  
Transportation Problems ◽  
Goal Programming Model ◽  
Fuzzy Goal ◽  
Fuzzy Random

In this article a fuzzy goal programming model is developed to solve multiobjective unbalanced transportation problems with fuzzy random parameters. In model formulation process the cost coefficients of the objectives are considered as fuzzy numbers and the supplies and demands are considered as fuzzy random variables with known fuzzy probability distribution from the view point of probabilistic as well as possibilistic uncertainties involved with the model. A fuzzy programming model is first constructed by applying chance constrained programming methodology in fuzzy environment. Then, the model is decomposed on the basis of the tolerance ranges of the fuzzy numbers associated with it. The individual optimal solution of each decomposed objectives is found in isolation to construct the membership goals of the objectives. Finally, priority based fuzzy goal programming technique is used to achieve the highest degree of each of the defined membership goals to the extent possible by minimizing the under deviational variables and thereby obtaining optimal allocation of products by using distance function in a cost minimizing decision making environment. An illustrative example is solved and compared with existing technique to explore the potentiality of the proposed methodology.

Using Fuzzy Goal Programming Technique to Solve Multiobjective Chance Constrained Programming Problems in a Fuzzy Environment

2012 ◽  
Vol 2 (1) ◽  
pp. 71-80 ◽  
Author(s):  
Animesh Biswas ◽  
Nilkanta Modak
Keyword(s):  
Decision Making ◽  
Programming Problem ◽  
Goal Programming ◽  
Fuzzy Goal Programming ◽  
Chance Constrained Programming ◽  
Membership Functions ◽  
Programming Technique ◽  
Goal Programming Model ◽  
Fuzzy Goal ◽  
Constrained Programming

In this paper a fuzzy goal programming technique is presented to solve multiobjective decision making problems in a probabilistic decision making environment where the right sided parameters associated with the system constraints are exponentially distributed fuzzy random variables. In model formulation of the problem, the fuzzy chance constrained programming problem is converted into a fuzzy programming problem by using general chance constrained methodology. Then by realizing the fuzzy nature of the parameters associated with the system constraints, the problem is decomposed by considering the tolerance ranges of the parameters. The tolerance membership functions of each of the individual objectives are defined in isolation to measure the degree of achievements of the goal levels of the objectives. Then a fuzzy goal programming model is developed to achieve the highest degree of each of the defined membership functions to the extent possible. In the solution process the minsum fuzzy goal programming technique is used to find the most satisfactory decision in the decision making environment. An example is solved to illustrate the proposed methodology and the achieved solution is compared with the solution of another existing technique.

On Solving Multiobjective Transportation Problems With Fuzzy Random Supply and Demand Using Fuzzy Goal Programming

2018 ◽  
pp. 791-821
Author(s):  
Animesh Biswas ◽  
Nilkanta Modak
Keyword(s):  
Goal Programming ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Optimal Solution ◽  
Fuzzy Goal Programming ◽  
Transportation Problems ◽  
Fuzzy Goal ◽  
Constrained Programming ◽  
The Individual ◽  
Fuzzy Random

In this article a fuzzy goal programming model is developed to solve multiobjective unbalanced transportation problems with fuzzy random parameters. In model formulation process the cost coefficients of the objectives are considered as fuzzy numbers and the supplies and demands are considered as fuzzy random variables with known fuzzy probability distribution from the view point of probabilistic as well as possibilistic uncertainties involved with the model. A fuzzy programming model is first constructed by applying chance constrained programming methodology in fuzzy environment. Then, the model is decomposed on the basis of the tolerance ranges of the fuzzy numbers associated with it. The individual optimal solution of each decomposed objectives is found in isolation to construct the membership goals of the objectives. Finally, priority based fuzzy goal programming technique is used to achieve the highest degree of each of the defined membership goals to the extent possible by minimizing the under deviational variables and thereby obtaining optimal allocation of products by using distance function in a cost minimizing decision making environment. An illustrative example is solved and compared with existing technique to explore the potentiality of the proposed methodology.

Some inequalities and limit theorems for fuzzy random variables adopted with $$\alpha $$-values of fuzzy numbers

2019 ◽  
Vol 24 (5) ◽  
pp. 3797-3807
Author(s):  
Gholamreza Hesamian ◽  
Mohammad Ghasem Akbari ◽  
Vahid Ranjbar
Keyword(s):  
Limit Theorems ◽  
Fuzzy Numbers ◽  
Random Variables ◽  
Fuzzy Random Variables ◽  
Fuzzy Random

scholarly journals Flexible Route Planning for Sightseeing with Fuzzy Random and Fatigue-Dependent Satisfactions

2014 ◽  
Vol 18 (2) ◽  
pp. 190-196 ◽  
Author(s):  
Takashi Hasuike ◽  
◽  
Hideki Katagiri ◽  
Hiroe Tsubaki ◽  
Hiroshi Tsuda ◽  
...  
Keyword(s):  
Fuzzy Numbers ◽  
Random Variables ◽  
Route Planning ◽  
Planning Problem ◽  
Optimal Route ◽  
Travel Times ◽  
Fuzzy Random Variables ◽  
Order Relations ◽  
Proposed Model ◽  
Fuzzy Random

This paper proposes a flexible route planning problem for sightseeing with fuzzy random variables for travel times and satisfaction with activities under general sightseeing constraints. Travel time between sightseeing sites and satisfactions with activities depend on weather and climate conditions, and on traveler fatigue, so both fuzzy random variables for travel times and satisfactions and traveler fatigue-dependence are introduced. Tourists are likely to plan favored without drastically changing from the optimal route under usual conditions such as fine weather that suddenly changes for the worse. A route planning problem is proposed to obtain a favorite route similar to the optimal route under usual conditions. Trapezoidal fuzzy numbers and order relations are introduced as a basic case of fuzzy numbers. From order relations, the proposed model is transformed into an extended model of network optimization problems. A numerical example is used to compare the proposed model to standard route planning problems in sightseeing.

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