Sufficient Conditions for Triangular Norms Preserving ⊗-Convexity
School of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
Shaanxi Key Laboratory of Network Data Analysis and Intelligent Processing, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
School of Statistics, Xi’an University of Finance and Economics, Xi’an 710100, China
Author to whom correspondence should be addressed.
Received: 5 November 2018 / Revised: 25 November 2018 / Accepted: 30 November 2018 / Published: 7 December 2018
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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
convexity on bounded lattices,
convexity in the real unite interval
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MDPI and ACS Style
Li, L.; Luo, Q. Sufficient Conditions for Triangular Norms Preserving ⊗-Convexity. Symmetry 2018, 10, 729.
Li L, Luo Q. Sufficient Conditions for Triangular Norms Preserving ⊗-Convexity. Symmetry. 2018; 10(12):729.
Li, Lifeng; Luo, Qinjun. 2018. "Sufficient Conditions for Triangular Norms Preserving ⊗-Convexity." Symmetry 10, no. 12: 729.
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