Aggregation operators preserving quasiconvexity

Janiš, Vladimír; Kráľ, Pavol; Renčová, Magdaléna

doi:10.1016/j.ins.2012.12.003

Cited by 12 publications

(10 citation statements)

References 5 publications

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“…In this Section, we generalize Propositions 2 and 3 (in [7]), and give some sufficient conditions for an aggregation operator which preserves ⊗−convexity.…”

Section: Sufficient Conditions For An Aggregation Operator Preservingmentioning

confidence: 92%

“…The arithmetic mean, the ordered weighted averaging operator and the probabilistic aggregation are widely used examples. In reference [7] Janiš, Král and Renčová pointed that the intersection of fuzzy sets is not the only operator preserving quasiconvexity in general, and they gave someconditions in order that an aggregation operator preserves quasiconvexity.…”

Section: Introductionmentioning

confidence: 99%

“…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. In Section 3, we give some sufficient conditions for aggregation operator preserving ⊗−convexity, those results are generalizations of Propositions 2 and 3 (in [7]). Triangular norm is a kind of important aggregation operator, we give some sufficient conditions for triangular norm preserving ⊗−convexity in Section 4.…”

Section: Introductionmentioning

confidence: 99%

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Sufficient Conditions for Triangular Norms Preserving ⊗-Convexity

Luo

2018

Symmetry

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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 ⊗ D − convexity and ⊗ a − convexity on bounded lattices, ⊗ M preserves ⊗ H − convexity in the real unite interval [ 0 , 1 ] .

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“…In this Section, we generalize Propositions 2 and 3 (in [7]), and give some sufficient conditions for an aggregation operator which preserves ⊗−convexity.…”

Section: Sufficient Conditions For An Aggregation Operator Preservingmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sufficient Conditions for Triangular Norms Preserving ⊗-Convexity

Luo

2018

Symmetry

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“…We can observe the following condition for Tconcavity (S-convexity) of interval-valued fuzzy relations (more generally than in [16]). …”

Section: De Inition 36 ( [24]) An Interval-valued Fuzzy Relation On mentioning

confidence: 95%

Group Decision Making Problem by General Convexity or Concavity and Aggregation Process

Pękala

2016

JAMRIS

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“…The idea of the proof is based on similar consideration used in [10]. 2 → [0, 1] be a mapping, let A be an arbitrary binary aggregation function on the unit interval.…”

Section: Convexity With Respect To Triangular Norms and Aggregation Omentioning

confidence: 99%