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Open AccessArticle

Sufficient Conditions for Triangular Norms Preserving ⊗-Convexity

1,2,* and 3
1
School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
2
Shaanxi Key Laboratory of Network Data Analysis and Intelligent Processing, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
3
School of Statistics, Xi’an University of Finance and Economics, Xi’an 710100, China
*
Author to whom correspondence should be addressed.
Symmetry 2018, 10(12), 729; https://doi.org/10.3390/sym10120729
Received: 5 November 2018 / Revised: 25 November 2018 / Accepted: 30 November 2018 / Published: 7 December 2018
(This article belongs to the Special Issue Discrete Mathematics and Symmetry)
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PDF [236 KB, uploaded 7 December 2018]
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Abstract

The convexity in triangular norm (for short, ⊗−convexity) is a generalization of Zadeh’s quasiconvexity. The aggregation of two ⊗−convex sets is under the aggregation operator ⊗ is also ⊗−convex, but the aggregation operator ⊗ is not unique. To solve it in complexity, in the present paper, we give some sufficient conditions for aggregation operators preserve ⊗−convexity. In particular, when aggregation operators are triangular norms, we have that several results such as arbitrary triangular norm preserve D convexity and a convexity on bounded lattices, M preserves H convexity in the real unite interval [ 0 , 1 ] . View Full-Text
Keywords: aggregation operator; triangular norm; ⊗-convex set aggregation operator; triangular norm; ⊗-convex set
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Li, L.; Luo, Q. Sufficient Conditions for Triangular Norms Preserving ⊗-Convexity. Symmetry 2018, 10, 729.

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