Framework for firm-level performance evaluations using multivariate linear correlation with MCDM methods: application to Japanese firms

Abstract

Selection of the appropriate firms [industries] for investment or resource allocation has implications for high returns, productivity and overall economic growth. However, numerous evaluation criteria, especially financial performance criteria, that must be examined before reaching this decision sometimes present challenges for decision-makers. This research proposes a framework for firm-level performance evaluations based on two multi-criteria decision-making (MCDM) methods: fuzzy analytical hierarchical process (FAHP) and the technique of order preferences by similarity to ideal solutions (TOPSIS). The proposed framework evaluates the overall performance of individual firms by simultaneously utilizing all available financial performance criteria. Unlike previous research with Fuzzy AHP and TOPSIS methods, the proposed framework does not rely on expert judgements to create a pairwise comparison or to assign criteria weight but relies on the normalized multivariate linear correlation between performance criteria. Using the proposed framework, a sample of Japanese firms was evaluated and ranked based on their overall financial performance. The practical implication is that decision-makers can simultaneously utilize all established financial performance criteria for firm-level performance evaluation without giving priority to any criteria or requiring initial expert judgement to weight performance criteria. Moreover, the proposed framework simplifies the evaluation procedures, making it easy for benchmarking analyses.

Appendices

Appendix A

Arithmetic properties of triangular fuzzy numbers

Two triangular fuzzy numbers $\tilde{A }({\mathrm{a}}_{1},{\mathrm{a}}_{2},{\mathrm{a}}_{3})$ and $\tilde{B }({\mathrm{b}}_{1},{b}_{2},{\mathrm{b}}_{3})$ represented in Fig. 6 have the following properties:

• 1. Addition of two TFNs

  $$\tilde{A }\oplus \tilde{B }=\left({\mathrm{a}}_{1}+{b}_{1},{\mathrm{a}}_{2}+{\mathrm{b}}_{2},{\mathrm{a}}_{3}+{\mathrm{b}}_{3}\right), {\mathrm{a}}_{1}\ge 0, {\mathrm{b}}_{1}\ge 0.$$

• 2. Multiplication of two TFNs

  $$\tilde{A }\otimes \tilde{B }=\left({\mathrm{a}}_{1}\times {b}_{1},{\mathrm{a}}_{2}\times {\mathrm{b}}_{2},{\mathrm{a}}_{3}\times {\mathrm{b}}_{3}\right), {\mathrm{a}}_{1}\ge 0, {\mathrm{b}}_{1}\ge 0.$$

• 3. Subtraction of two TFNs

  $$\tilde{A }\ominus \tilde{B }=\left({\mathrm{a}}_{1}-{b}_{1},{\mathrm{a}}_{2}-{\mathrm{b}}_{2},{\mathrm{a}}_{3}-{\mathrm{b}}_{3}\right), {\mathrm{a}}_{1}\ge 0, {\mathrm{b}}_{1}\ge 0.$$

• 4. Division of two TFNs

  $$\tilde{A }\oslash \tilde{B }=\left({\mathrm{a}}_{1}/{b}_{1},{\mathrm{a}}_{2}/{\mathrm{b}}_{2},{\mathrm{a}}_{3}/{\mathrm{b}}_{3}\right), {\mathrm{a}}_{1}\ge 0, {\mathrm{b}}_{1}\ge 0.$$

• 5. Inverse and symmetry of a TFN

  $${\tilde{A }}^{-1}=\left(1/{\mathrm{a}}_{1},1/{\mathrm{a}}_{2},1/{\mathrm{a}}_{3}\right), {\mathrm{a}}_{1}\ge 0$$
  $$-\tilde{A }=\left({-\mathrm{a}}_{1.}-{a}_{2},-{\mathrm{a}}_{3}\right).$$

• 6. Distance between two TFNs

  $$d\left(\tilde{A },\tilde{B }\right)=\sqrt{\frac{1}{3}\left[{({\mathrm{a}}_{1}-{b}_{1})}^{2}+{({\mathrm{a}}_{2}-{b}_{2})}^{2}+{({\mathrm{a}}_{3}-{b}_{3})}^{2}\right].}$$

Fig. 6

The intersection of two triangular fuzzy numbers