Arithmetic operations on normal semi elliptic intuitionistic fuzzy numbers and their application in decision-making

Abstract

Decision-making problems are more often tainted with uncertainty. Fuzzy numbers play utmost important role to band uncertainty, more especially intuitionistic fuzzy number (IFN) which is the extension of fuzzy number (FN). Different types of IFNs such as normal and generalized trapezoidal, triangular and symmetric hexagonal IFNs are explored. However, based on nature of the data, semi-elliptic type of IFN may exists in real world decision-making problems. In this paper, a maiden attempt has been made to study normal semi elliptic intuitionistic fuzzy number (NSEIFN). Our emphasis has been on arithmetic operations of NSEIFNs and comparing with the other existing IFNs. Also rank of NSEIFNs has been proposed based on mean and value. Apart from that inverse, exponential, logarithm, square root and nth root of NSEIFNs are derived. Finally, the proposed ranking method is applied to the decision making problem where criteria and rating of alternatives are represented in terms of NSEIFN. It is observed that the proposed model produces better results and overcome the drawbacks of existing approaches.

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Correspondence to Palash Dutta.

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Dutta, P., Saikia, B. Arithmetic operations on normal semi elliptic intuitionistic fuzzy numbers and their application in decision-making. Granul. Comput. 6, 163–179 (2021). https://doi.org/10.1007/s41066-019-00175-5

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Keywords

  • Intuitionistic fuzzy number
  • Trapezoidal intuitionistic fuzzy number
  • Triangular intuitionistic fuzzy number
  • Normal semi elliptic intuitionistic fuzzy number
  • Ranking
  • Decision making