Aggregation functions on bounded partially ordered sets and their classification

Komorníková, Magda; Mesiar, Radko

doi:10.1016/j.fss.2011.01.015

Cited by 132 publications

(38 citation statements)

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“…Hence, the aggregation clone C L can be generated by the set of functions consisting of the lattice operations and by the functions defined by (10) and (6). It is worth noticing that the formulae (9) and (13) remain valid also if L is infinite. In contrast to a finite case, there are infinite suprema in (9), and infinite infima in (13) respectively, which can be understood as a kind of limit process.…”

Section: Aggregation Functions On Latticesmentioning

confidence: 99%

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On the clone of aggregation functions on bounded lattices

Halaš

Pócs

2016

Information Sciences

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The main aim of this paper is to study aggregation functions on lattices via clone theory approach. Observing that the aggregation functions on lattices just correspond to 0, 1-monotone clones, as the main result we show that for any finite n-element lattice L there is a set of at most 2n + 2 aggregation functions on L from which the respective clone is generated. Namely, the set of generating aggregation functions consists only of at most n unary functions, at most n binary functions, and lattice operations ∧, ∨, and all aggregation functions of L are composed of them by usual term composition. Moreover, our approach works also for infinite lattices (such as mostly considered bounded real intervals [a, b]), where in contrast to finite case infinite suprema and (or, equivalently, a kind of limit process) have to be considered.

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Section: Aggregation Functions On Latticesmentioning

confidence: 99%

“…It is worth noticing that the formulae (9) and (13) remain valid also if L is infinite. In contrast to a finite case, there are infinite suprema in (9), and infinite infima in (13) respectively, which can be understood as a kind of limit process. This fact is especially important when considering a classical case, i.e.…”

Section: Aggregation Functions On Latticesmentioning

confidence: 99%

On the clone of aggregation functions on bounded lattices

Halaš

Pócs

2016

Information Sciences

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“…DFNs can be monotonic with respect to the predefined partial orders [45][46]63]. The rankings of six approaches are listed in Table 11.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Total orders of extended hesitant fuzzy linguistic term sets: Definitions, generations and applications

Wang

Zhang

2016

Knowledge-Based Systems

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“…Let (L, ≤, 0, 1) be a bounded lattice and n ∈ N, n > 1. In the sequel, the following partial ordering of L n is considered (see [2], p. 8): [10,20].) Let n ∈ N, n > 1.…”

Section: Aggregation Functions and Semicopulas On Latticesmentioning

confidence: 99%

“…Aggregation functions appear in many areas of mathematics and applications (see [1,3,4,7,10,[18][19][20]). The class of ∨-distributive n-ary aggregation functions on bounded lattices and the class of infinitely ∨-distributive n-ary aggregation functions on complete lattices are important classes of n-ary aggregation functions on lattices.…”

Section: Introductionmentioning

confidence: 99%