Novel multi-objective, multi-item and four-dimensional transportation problem with vehicle speed in LR-type intuitionistic fuzzy environment

  • Sarbari Samanta
  • Dipak Kumar JanaEmail author
  • Goutam Panigrahi
  • Manoranjan Maiti
Original Article


In this paper, we present some novel multi-objective, multi-item and four-dimensional transportation problems in LR-type intuitionistic fuzzy environment. Here, for the first time, the speed of different vehicles and rate of disturbance of speed due to the road condition of different routes for the time minimization objective are introduced. Furthermore, three models are presented under three different conditions. The reduced deterministic models are obtained on implementation of a defuzzification approach by using the accuracy function. Moreover, a new method for converting multi-objective problem into single-objective one is proposed and also we use convex combination method. The models are illustrated by some numerical examples and optimal results are presented.


Four-dimensional transportation problem Intuitionistic fuzzy number LR-type intuitionistic fuzzy number Accuracy function 


Compliance with ethical standards


We declared that research work was done by self-finance. No institutional fund has been provided.

Conflict of interest

The authors have no conflict of interest for the publication of this paper.

Ethical approval

The authors declared that this article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2020

Authors and Affiliations

  • Sarbari Samanta
    • 1
    • 2
  • Dipak Kumar Jana
    • 1
    Email author
  • Goutam Panigrahi
    • 2
  • Manoranjan Maiti
    • 3
  1. 1.Department of Applied SciencesHaldia Institute of TechnologyHaldia, Purba MedinipurIndia
  2. 2.Department of MathematicsNational Institute of TechnologyDurgapurIndia
  3. 3.Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar UniversityMidnaporeIndia

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