T-sum of sigmoid-shaped fuzzy intervals

  • Authors:

  • Dug Hun Hong;Changha Hwang;Kyung Tae Kim

  • Affiliations:

  • Department of Mathematics, Myongji University, Kyunggi 449-728, South Korea;Division of Information and Computer Sciences, Dankook University, Seoul 140-714, South Korea;Department of Electronics and Electrical Information Engineering, Kyungwon University, Sungnam Kyunggido, South Korea

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2007

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Abstract

The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. A t-norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation, if this arithmetic operation is closed for this class. It is important to know which t-norms are consistent with particular types of fuzzy intervals. Recently, Dombi and Gyorbiro [J. Dombi, N. Gyorbiro, Additions of sigmoid-shaped fuzzy intervals using the Dombi operator and infinite sum theorems, Fuzzy Sets and Systems 157 (2006) 952-963] proved that addition is closed if the Dombi t-norm is used with sigmoid-shaped fuzzy intervals. In this paper, we define a broader class of sigmoid-shaped fuzzy intervals. Then, we study t-norms that are consistent with these particular types of fuzzy intervals. Dombi and Gyorbiro's results are special cases of the results described in this paper.