Journal
FUZZY SETS AND SYSTEMS
Volume 202, Issue -, Pages 75-88Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.fss.2012.03.002
Keywords
Triangular norm; Ordinal sum; Bounded lattice
Funding
- Junta de Andaluci a [P09-FQM-5233]
- EU (FEDER)
- Spanish Science and Education Ministry (MEC) [TIN2009-14562-C05-03]
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One of the most important operators in soft computing are the triangular norms (t-norms), as well as the combination among them. The ordinal sum of triangular norms on [0, 1] has been used to construct other triangular norms. However, on a bounded lattice, an ordinal sum of t-norms may not be a t-norm. Several necessary and sufficient conditions are presented in this paper for ensuring whether an ordinal sum on a bounded lattice of arbitrary t-norms is, in fact, a t-norm. Moreover, we show that a large set of ordinal sums verify these conditions. Hence, they are very interesting in order to verify whether an ordinal sum on a bounded lattice is a t-norm for a particular family of t-norms. (C) 2012 Elsevier B.V. All rights reserved.
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