Integrating quality function deployment with fuzzy cognitive maps for resolving correlation issues in the roof matrix

Emel A. G., Petriçli G., Kayguluoğlu C.

Ege Academic Review, vol.22, no.2, pp.117-138, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.21121/eab.787075
  • Journal Name: Ege Academic Review
  • Journal Indexes: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
  • Page Numbers: pp.117-138
  • Keywords: Quality Function Deployment, Fuzzy Cognitive Maps, Asymmetric Square Roof Matrix, Independence Axiom, Fuzzy Analytic Hierarchy Process, Extent Analysis, ANALYTIC HIERARCHY PROCESS, PRODUCT DESIGN, QFD, REQUIREMENTS, INFORMATION, DECISION, SYSTEM, RISK
  • Bursa Uludag University Affiliated: Yes


The roof matrix represents correlations among engineering characteristics (EC) in the house of quality (HoQ) in Quality Functions Deployment (QFD). Correlations are usually measured qualitatively and omitted in the analysis. However, ignoring them may cause duplication of effort, decreased product performance, and unsatisfied customer requirements (CR). Hence, this paper intends to propose an approach to considering the correlations quantitatively. Fuzzy Cognitive Maps (FCM) were used for this purpose. Additionally, Axiomatic Design (AD), for examining relationships between CRs and ECs, and Fuzzy Analytic Hierarchy Process (FAHP) with the Extent Analysis (EA) were used for checking the consistency of the evaluations. The proposed approach was applied in a sheet metal die making company for ranking CRs and ECs. Results show that FCM enables analyzing the quantitative roof matrix practically. The square roof matrix that also supports FCM’s adjacency matrix structure successfully represents asymmetric relationships among ECs. Integrating the correlations into the analysis resulted in a change in the final ranking. It also helped to determine the most manageable ECs, better satisfiable CRs, and most critical/least manageable ECs.