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Modified Ordinal Sums of Triangular Norms and Triangular Conorms on Bounded Lattices
Author(s) -
Ertuğrul Ümit,
Karaçal Funda,
Mesiar Radko
Publication year - 2015
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21713
Subject(s) - mathematics , bounded function , lattice (music) , discrete mathematics , fuzzy set , norm (philosophy) , t norm , hexagonal lattice , fuzzy logic , combinatorics , pure mathematics , fuzzy number , computer science , mathematical analysis , artificial intelligence , law , physics , condensed matter physics , antiferromagnetism , acoustics , political science
Having in mind that ordinal sum construction of triangular norms (triangular conorms) may not work on bounded lattices, in general, we propose a modification of ordinal sums of t‐norms (t‐conorms) resulting to a t‐norm (t‐conorm) on an arbitrary bounded lattice. In particular, our method can be applied to define connectives for fuzzy sets type 2, interval‐valued fuzzy sets, intuitionistic fuzzy sets, etc. Some illustrative examples are added, considering the interval lattice L ([0, 1]), the intuitionistic lattice LI, and the diamond lattice.