scholarly journals Geometric Mean Method to Solve Multi-Objective Transportation Problem Under Fuzzy Environment

2020 ◽  
Vol 9 (5) ◽  
pp. 1739-1744
Keyword(s):  
Transportation Problem ◽  
Geometric Mean ◽  
Method Comparison ◽  
Optimal Solution ◽  
Pareto Optimal Solution ◽  
Pareto Optimal ◽  
Numerical Examples ◽  
Multi Objective ◽  
Fuzzy Environment ◽  
Single Objective

Transportation problem is a very common problem for a businessman. Every businessman wants to reduce cost, time and distance of transportation. There are several methods available to solve the transportation problem with single objective but transportation problems are not always with single objective. To solve transportation problem with more than one objective is a typical task. In this paper we explored a new method to solve multi criteria transportation problem named as Geometric mean method to Solve Multi-objective Transportation Problem Under Fuzzy Environment. We took a problem of transportation with three objectives cost, time and distance. We converted objectives into membership values by using a membership function and then geometric mean of membership values is taken. We also used a procedure to find a pareto optimal solution. Our method gives the better values of objectives than other methods. Two numerical examples are given to illustrate the method comparison with some existing methods is also made.

scholarly journals Matrix Maxima Method to Solve Multi-objective Transportation Problem with a Pareto Optimality Criteria

2019 ◽  
Vol 8 (11) ◽  
pp. 1929-1932
Keyword(s):  
Pareto Optimality ◽  
Transportation Problem ◽  
Geometric Mean ◽  
Optimal Solution ◽  
Optimality Criteria ◽  
Pareto Optimal Solution ◽  
Fuzzy Membership ◽  
Fuzzy Membership Function ◽  
Pareto Optimal ◽  
Fast Method

In this paper we proposed a new method (Matrix Maxima Method) using Geometric mean approach to solve multiobjective transportation problem with a Pareto Optimality Criteria. Fuzzy membership function is used to convert objectives into membership values and then we take Geomertic mean of membership values. We used a different criteria to find Pareto Optimal Solution. This is an easy and fast method to find the Pareto Optimal solution. The method is illustrated by numerical examples. The result is compared with some other available methods in the literature.

A two-sided matching decision-making approach based on regret theory under intuitionistic fuzzy environment

2021 ◽  
pp. 1-18
Author(s):  
Xiang Jia ◽  
Xinfan Wang ◽  
Yuanfang Zhu ◽  
Lang Zhou ◽  
Huan Zhou
Keyword(s):  
Decision Making ◽  
Hamming Distance ◽  
Optimal Solution ◽  
Intuitionistic Fuzzy Sets ◽  
Regret Theory ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Objective Model ◽  
Single Objective

This study proposes a two-sided matching decision-making (TSMDM) approach by combining the regret theory under the intuitionistic fuzzy environment. At first, according to the Hamming distance of intuitionistic fuzzy sets and regret theory, superior and inferior flows are defined to describe the comparative preference of subjects. Hereafter, the satisfaction degrees are obtained by integrating the superior and inferior flows of the subjects. The comprehensive satisfaction degrees are calculated by aggregating the satisfaction degrees, based on which, a multi-objective TSMDM model is built. Furthermore, the multi-objective TSMDM model is converted to a single-objective model, the optimal solution of the latter is derived. Finally, an illustrative example and several analyses are provided to verify the feasibility and the effectiveness of the proposed approach.

Multi-Objective Optimization Algorithm Design and Implementation of Mobile Base Station Site Selection

2010 ◽  
Vol 29-32 ◽  
pp. 2496-2502
Author(s):  
Min Wang ◽  
Jun Tang
Keyword(s):  
Site Selection ◽  
Engineering Application ◽  
Optimal Solution ◽  
Base Station ◽  
Pareto Optimal Solution ◽  
Antibody Concentration ◽  
Pareto Optimal ◽  
Memory Cells ◽  
Multi Objective Optimization ◽  
Multi Objective

The number of base station location impact the network quality of service. A new method is proposed based on immune genetic algorithm for site selection. The mathematical model of multi-objective optimization problem for base station selection and the realization of the process were given. The use of antibody concentration selection ensures the diversity of the antibody and avoiding the premature convergence, and the use of memory cells to store Pareto optimal solution of each generation. A exclusion algorithm of neighboring memory cells on the updating and deleting to ensure that the Pareto optimal solution set of the distribution. The experiments results show that the algorithm can effectively find a number of possible base station and provide a solution for the practical engineering application.

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