Z-Numbers Based TOPSIS Similarity Methodology for Company Performance Assessment in Malaysia

  • Ku Muhammad Naim Ku KhalifEmail author
  • Ahmad Syafadhli Abu Bakar
  • Alexander Gegov
Part of the Fuzzy Management Methods book series (FMM)


The management of uncertainty in decision making problems is a very challenging research issues. The deterministic or probabilistic classical decision approaches quite often do not fit well to real world decision making problems. This proposal presents Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) using fuzzy similarity for z-numbers. The classical fuzzy TOPSIS techniques use closeness coefficient to determine the rank order by calculating Fuzzy Positive Ideal Solution (FPIS) and Fuzzy Negative Ideal Solution (FNIS) simultaneously. The authors propose fuzzy similarity to replace closeness coefficient by doing ranking evaluation. Fuzzy similarity is used to calculate the similarity between two fuzzy ratings (FPIS and FNIS). Fuzziness is not sufficient enough when dealing with real information and a degree of reliability of the information is very critical. Therefore, the implementation of z-numbers is taken into consideration, where it has more authority to describe the knowledge of human being and extensively used in the uncertain information development to deal with linguistic decision making problems. A case study on group of company in Malaysia is given to illustrate the feasibility of the proposed methodology in ranking the performance assessment.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ku Muhammad Naim Ku Khalif
    • 1
    Email author
  • Ahmad Syafadhli Abu Bakar
    • 2
    • 3
  • Alexander Gegov
    • 4
  1. 1.Department of Science Program (Mathematics), Faculty of Industrial Sciences and TechnologyUniversiti Malaysia PahangPahangMalaysia
  2. 2.Mathematics Division, Centre for Foundation Studies in ScienceUniversity of MalayaKuala LumpurMalaysia
  3. 3.Centre of Research for Computational Sciences and Informatics in Biology, Bioindustry, Environment, Agriculture and Healthcare (CRYSTAL)University of MalayaKuala LumpurMalaysia
  4. 4.School of ComputingUniversity of PortsmouthPortsmouthUK

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