Linear Programming-Based TOPSIS Method for Solving MADM Problems with Three Parameter IVIFNs

  • Samir Kumar
  • Animesh Biswas
Part of the Studies in Computational Intelligence book series (SCI, volume 687)


The aim of this paper is to develop a TOPSIS approach using fractional programming techniques for effective modelling of real-life multiattribute decision-making (MADM) problems in interval-valued intuitionistic fuzzy (IVIF) settings by considering hesitancy degree as a dimension together with membership and non-membership degrees. In three-parameter characterizations of intuitionistic fuzzy (IF) sets, a weighted absolute distance between two IF sets with respect to IF weights is defined and employed in TOPSIS to formulate intervals of relative closeness coefficients (RCCs). The lower and upper bounds of the intervals of RCCs are given by a pair of nonlinear fractional programming models which are further transformed into two auxiliary linear programming models using mathematical methods and fractional programming technique. A simpler technique is also proposed for estimating the optimal degrees as performance values of alternatives from the possibility degree matrix generated by pairwise comparisons of RCC intervals. The validity and effectiveness of the proposed approach are demonstrated through two numerical examples.


Intuitionistic fuzzy sets Interval-valued intuitionistic fuzzy numbers TOPSIS Mathematical programming Possibility degree matrix 



The authors remain grateful to the anonymous reviewers for their valuable comments and suggestions in improving the quality of the manuscript.


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of MathematicsAcharya Jagadish Chandra Bose CollegeKolkataIndia
  2. 2.Department of MathematicsUniversity of KalyaniKalyani, NadiaIndia

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