On averaging operators for Atanassov's intuitionistic fuzzy sets

  • Authors:

  • G. Beliakov;H. Bustince;D. P. Goswami;U. K. Mukherjee;N. R. Pal

  • Affiliations:

  • The School of Information Technology, Deakin University, 221 Burwood Hwy, Burwood 3125, Australia;The Department of Automation and Computing, Public University of Navarra, Pamplona, Spain;School of BioScience and Engineering, Jadavpur University, Kolkata, India;Sarat Centenary College, Dhaniakhali, Hooghly, India;The Indian Statistical Institute, Calcutta, India

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

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Abstract

Atanassov's intuitionistic fuzzy set (AIFS) is a generalization of a fuzzy set. There are various averaging operators defined for AIFSs. These operators are not consistent with the limiting case of ordinary fuzzy sets, which is undesirable. We show how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. We provide two generalizations of the existing methods for other averaging operators. We relate operations on AIFS with operations on interval-valued fuzzy sets. Finally, we propose a new construction method based on the Lukasiewicz triangular norm, which is consistent with operations on ordinary fuzzy sets, and therefore is a true generalization of such operations.