Title: Generalised Fermatean fuzzy numbers-based exponentially weighted moving average control chart

Authors: Rajiv Kumar; Tanuj Kumar; Birjesh Kumar

Addresses: Janta Vedic College Baraut, Chaudhary Charan Singh University Meerut, Uttar Pradesh, 250611, India ' Department of Mathematics, SRM Institute of Science and Technology, NCR Campus, Ghaziabad, Delhi, Uttar Pradesh, 201204, India ' Department of Mathematics, Ramanujan College, University of Delhi, New Delhi, Delhi, 110019, India

Abstract: This work present a generalised Fermatean fuzzy numbers-based exponentially weighted moving average (EWMA) control chart. First, we introduce generalised Fermatean fuzzy numbers and their arithmetic operations. We also create novel defuzzification and ranking techniques to convert Fermatean fuzzy observations into crisp observations. Then, based on the generalised trapezoidal Fermatean fuzzy numbers, we suggested the Fermatean fuzzy EWMA (FFEWMA) statistic and the Fermatean fuzzy EWMA control chart limits. In order to confirm the effectiveness of the suggested Fermatean fuzzy EWMA control, a simulation study is performed. In comparison to the well-known EWMA charts, simulation studies demonstrate that the proposed Fermatean fuzzy chart detects very small shifts as early as possible in the process. In order to handle the uncertainty in the process observations, the proposed Fermatean fuzzy EWMA control chart is more reliable.

Keywords: intuitionistic fuzzy numbers; IFNs; Fermatean fuzzy numbers; fuzzy exponentially weighted average control charts; Fermatean fuzzy EWMA control chart; membership and non-membership functions.

DOI: 10.1504/IJPQM.2024.143222

International Journal of Productivity and Quality Management, 2024 Vol.43 No.4, pp.526 - 547

Received: 02 Oct 2022
Accepted: 18 Feb 2023
Published online: 10 Dec 2024 *

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