Parameterized defuzzification with continuous weighted quasi-arithmetic means – An extension☆

Liu, Xinwang

doi:10.1016/j.ins.2008.12.005

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Cited by 12 publications

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“…68-69], [2, pp. 272-273] and the references therein, [6] (generalization for fuzzy sets and orness measure). Proposition 3.…”

Section: Applicationsmentioning

confidence: 99%

Scales of quasi-arithmetic means determined by an invariance property

Pasteczka

2015

Journal of Difference Equations and Applications

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Abstract. It is well known that if P t denotes a set of power means then the mapping R ∋ t → P t (v) ∈ (min v, max v) is both 1-1 and onto for any non-constant sequence v = (v 1 , . . . , v n ) of positive numbers. Shortly: the family of power means is a scale.If I is an interval and f : I → R is a continuous, strictly monotone) is a natural generalization of power means, so called quasi-arithmetic mean generated by f .A famous folk theorem says that the only homogeneous, quasi-arithmetic means are power means. We prove that, upon replacing the homogeneity requirement by an invariant-type axiom, one gets a family of quasi-arithmetic means building up a scale, too.

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“…68-69], [2, pp. 272-273] and the references therein, [6] (generalization for fuzzy sets and orness measure). Proposition 3.…”

Section: Applicationsmentioning

confidence: 99%

Scales of quasi-arithmetic means determined by an invariance property

Pasteczka

2015

Journal of Difference Equations and Applications

View full text Add to dashboard Cite

show abstract

“…[6], [29], [4], [15], [5], [52], [51], [50], [54], [17]. Yager introduced the ordered weighted averaging (OWA) operator, providing the parameterized aggregation operators of min, max and average [35].…”

Section: Introductionmentioning

confidence: 99%