Dealing with Nonmonotonic Criteria in Decision-Making Problems Using Fuzzy Normalization

Kizielewicz B., Wieckowski J., Paradowski B., Salabun W.

4th International Conference on Intelligent and Fuzzy Systems (INFUS), Bornova, Turkey, 19 - 21 July 2022, vol.504, pp.27-35 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 504
  • Doi Number: 10.1007/978-3-031-09173-5_5
  • City: Bornova
  • Country: Turkey
  • Page Numbers: pp.27-35
  • Keywords: TOPSIS, Fuzzy normalization, Fuzzy logic
  • Yıldız Technical University Affiliated: No


The modeling of the decision-making process frequently has many simplifications. One of such typical actions is the assumption that we have in the decisional problem only monotonic criteria. However, in many cases, it is contradictory to reality. Therefore, the proper normalization of nonmonotonic (and strongly nonlinear) criteria should be applied more and more often. We, therefore, take up the challenge of showing an easy way to normalize strongly nonlinear criteria that have a nonmonotonic character. The proposed normalization must be well fitted with expert knowledge. As the main contribution, we propose to use fuzzy normalization based on Triangular Fuzzy Numbers (TFNs) and the TOPSIS technique. First, we present the idea of our proposed approach. Then we show short study cases that demonstrate the differences between results obtained using our approach and the assumption about monotonic criteria. Finally, we analyze our ranking result using similarity coefficients and present future research directions.