A Numerical Method for Integration of a Fuzzy Function over a Fuzzy Interval


Temelcan G., Kocken H. G. , Albayrak I.

International Conference on Intelligent and Fuzzy Systems, INFUS 2021, İstanbul, Turkey, 24 - 26 August 2021, vol.307, pp.281-288 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 307
  • Doi Number: 10.1007/978-3-030-85626-7_34
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.281-288
  • Keywords: Extension principle, Fuzzy function, Fuzzy integral, Triangular fuzzy number

Abstract

© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.A numerical method is presented for evaluating the integration of a fuzzy function (FF) over a fuzzy interval (FI) by combining the integration methods proposed by Zimmerman, which is known as the fuzzy Riemann integral (FRI) of type-II. In this study, monotonic increasing (or nondecreasing) nonnegative continuous FFs are considered for integration. In the proposed method, first, a fuzzy-valued function (FvF) is induced by a real-valued function (RvF) via extension principle and then each component of the triangular fuzzy valued-function, which is a RvF, is determined as a triangular fuzzy number (TFN) by integrating over the FI. The left and right components of fuzzy integral value are determined from the TFNs obtained by taking the minimum of the left components and the maximum of right components, and the middle component is provided using a ranking function. Some numerical examples are given to explain the methodology.