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 ] .
Highlights
Fuzzy set theory introduced by Zadeh in 1965, as an mathematical tool to deal with uncertainty in information system and knowledge base, has been widely used in various fields of science and technology
The above condition is called intersection preserving quasiconvexity. This property is true for lattice valued fuzzy sets
Which are the properties of a lattice L and an aggregation A, such that A preserves quasiconvexity
Summary
Fuzzy set theory introduced by Zadeh in 1965, as an mathematical tool to deal with uncertainty in information system and knowledge base, has been widely used in various fields of science and technology. The above condition is called intersection preserving quasiconvexity. This property is true for lattice valued fuzzy sets. Suppose ⊗ : [0, 1]2 → [0, 1] is a triangular norm, Nourouzi [10] given the concept of ⊗−convex set which generalized Zadeh’s quasiconvex fuzzy set. Following [7,10], in the present paper, we continue to study sufficient conditions for aggregation operators and triangular norms that preserve ⊗−convexity on a bounded lattice.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
