An Improved Intuitionistic Fuzzy Choquet Integral Operator for Multi-criteria Decision-making Problems

  • Bhagawati Prasad Joshi Department of Applied Sciences, Seemant Institute of Technology, Pithoragarh-262501 Uttarakhand (India)
  • Sanjay Kumar Department of Mathematics, Statistics and Computer Science, G. B. Pant University of Ag. and Technology, Pantnagar-263145 Uttarakhand (India)
Keywords: Fuzzy measure, Intuitionistic fuzzy sets (IFSs), Choquet integral operator, Multi-criteria decision making (MCDM), Portfolio analysis.


Aggregation operators based additive measures are not considered appropriate tools to aggregate the inter-dependent or interactive characteristics of criteria in multi-criteria decision-making problem. It would be more suitable to apply fuzzy measures to approximate human subjective decision-making process when the additivity and independence among the decision-making criteria are not necessary. In this paper, we propose a new intuitionistic fuzzy Choquet integral operator for multi-criteria decisionmaking problem with interaction phenomena among the decision making criteria. We introduce two operational laws on intuitionistic fuzzy values. Based on these operational laws and fuzzy measure, an intuitionistic fuzzy Choquet integral operator is proposed. Algorithm of multi-criteria decision making based on the proposed intuitionistic fuzzy Choquet integral operator is presented. A real-life example of ranking is also provided to illustrate the developed approach in multi-criteria decision making. To show the superiority of the proposed intuitionistic fuzzy Choquet integral operator, it is implemented in portfolio selection problem and portfolios are analyzed for their return and risk.