Malcolm Baldrige National Quality Award (MBNQA) is a broadly used performance excellence framework to recognize organizations that have outstanding customer-focused processes. MBNQA system is based on an assessment system using a 0-1000 points scale. However, experts prefer making linguistic assessments rather than exact numerical assignments. Fuzzy set theory presents excellent tools and techniques to capture the vagueness and impreciseness in these assessments. This paper develops a new analytic hierarchy process (AHP)-based fuzzy multi-criteria decision-making approach to measure the performance excellence of firms applying for MBNQA. The proposed approach enables experts to use seven different fuzzy scales to evaluate firms using the MBNQA criteria. These fuzzy scales involve both positive fuzzy numbers and negative fuzzy numbers, and present an easier and efficient alternative to the calculations made in pairwise comparison matrices. In this way, the experts filling in a questionnaire can easily understand the reciprocal scale and establish comparison matrices. Using negative fuzzy numbers in AHP scale is the crucial point of this paper. To show the applicability of the method, a numerical example composed of a four-level hierarchy including seven main criteria, 18 sub-criteria, and three alternatives is also given. We use Buckley's Fuzzy AHP approach for comparative analysis. Our application reveals that the proposed fuzzy AHP approach efficiently measures the quality performance of the firms applying to MBNQA.