Soft Set Based Intelligent Assistive Model for Multiobjective and Multimodal Transportation Problem

Gaurav Sharma,Vaibhav Sharma,Mohammed Alshehri,Kamal Raj Pardasani

doi:10.1109/access.2020.2997302

Abstract

The real world conditions of transportation pose new challenges for development of intelligent assistive systems for effective decision making. The ignorance of relationships among various attributes and parameters is one of the major causes of uncertainty in existing models of transportation problems. Fuzzy sets have been explored by various investigators to address the uncertainty issues due to relationships among various attributes. However fuzzy sets are not fully capable of dealing all kinds of uncertainty to provide intelligent solutions of transportation problems. A soft set is explored in this paper to model the uncertainty arising from the relationships of attributes with the parameters in a multimodal and multi objective transportation problem. The three modes of transportation incorporated in this model are road, rail and air. The real data set is prepared using the tariff, distance and time duration of transport available on websites of transport service agencies. The objectives are to minimize the cost and time duration of transportation. The proposed model evaluates multiple criteria using various combinations of different modes of transport to optimize the objectives of the problem. The model has been illustrated using the real data set using existing methods of solution. The soft set approach is found to be quite effective in dealing with the relationships of attributes with the parameters arising due to multi criteria decision making and leads to intelligent optimal solutions. The proposed model can be used as intelligent assistive system for decision making of multi objective and multimodal transportation problems.

Highlights

Anumber of decisions are made by professionals in their daily work in an uncertain environment
Elumalai et al [15] and others proposed a new algorithm by applying zero simplex method to obtain the optimal solution for a fuzzy transportation problem based on hexagonal fuzzy numbers using robust ranking method
A soft set based approach is developed and successfully illustrated for a numerical example based on real data set for multi-objective and multi-model transportation problem

Summary

INTRODUCTION

Anumber of decisions are made by professionals in their daily work in an uncertain environment. Fuzzy Logic based optimization models facilitate the decision making under the conditions of incomplete information and are able to deal with interdependence between variables and conflicts of interest. A new algorithm based on a ranking function to obtain an optimal solution for the fuzzy transportation problem was introduced by Hussein and Dheyab [10]. Elumalai et al [15] and others proposed a new algorithm by applying zero simplex method to obtain the optimal solution for a fuzzy transportation problem based on hexagonal fuzzy numbers using robust ranking method. In the past soft set approach has not been reported for multi objective and multi modal transportation problems. The soft sets are potential tools for such conditions and can be useful to develop models which can form the basis for intelligent assistive systems for decision making

MATHEMATICAL FORMULATION

NUMERICAL EXAMPLE Problem

SOLUTION

DISCUSSION

CONCLUSION