Modelling Decision Making Using Immediate Probabilities

Engemann, Kurt J.; Filev, Dimitar; Yager, Ronald R.

doi:10.1080/03081079608945123

Cited by 88 publications

(61 citation statements)

References 5 publications

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“…Notice that, as pointed out by Wang [13], the IP-OWA operator and the HWAA operator are the same type of aggregation functions, although the interpretation of their weighting vectors are different. In fact, these functions coincide with the operator proposed by Engemann et al [9], which has been analyzed by Llamazares [14] (on the monotonicity of this operator, see also Liu [15], Wang [13] and Lin [16]). …”

Section: Introductionmentioning

confidence: 81%

“…Some families of functions suggested in the literature generalize weighted means and OWA operators in the sense that one of these functions is obtained when the other one has a "neutral" behavior; that is, its weighting vector is that of the arithmetic mean. This is the case of the operator proposed by Engemann et al [9], the weighted OWA (WOWA) operator (Torra [2]), the hybrid weighted averaging (HWA) operator (Xu and Da [10]), the IP-OWA operator (Merigó [11]) and the hybrid weighted arithmetical averaging (HWAA) operator (Lin and Jiang [12]). Notice that, as pointed out by Wang [13], the IP-OWA operator and the HWAA operator are the same type of aggregation functions, although the interpretation of their weighting vectors are different.…”

Section: Introductionmentioning

confidence: 99%

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Constructing Choquet integral-based operators that generalize weighted means and OWA operators

Llamazares

2015

Information Fusion

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In this paper we introduce the semi-uninorm based ordered weighted averaging (SUOWA) operators, a new class of aggregation functions that, as WOWA operators, simultaneously generalize weighted means and OWA operators. To do this we take into account that weighted means and OWA operators are particular cases of Choquet integral. So, SUOWA operators are Choquet integral-based operators where their capacities are constructed by using semi-uninorms and the values of the capacities associated to the weighted means and the OWA operators. We also show some interesting properties of these new operators and provide examples showing that SUOWA and WOWA operators are different classes of aggregation operators.

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Section: Introductionmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Constructing Choquet integral-based operators that generalize weighted means and OWA operators

Llamazares

2015

Information Fusion

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show abstract

Section: Introductionmentioning

confidence: 99%

“…Moreover, since, in some cases, the results provided by these operators may be questionable, we propose to use functions that maintain the relationship among the weights of a weighting vector when the non-zero components of the other weighting vector are equal. In this way, we obtain a class of functions that have been previously introduced by Engemann et al [2] in a framework of decision making under risk and uncertainty.The paper is organized as follows. In Section 2 we introduce weighted means, OWA operators and the two classes of functions proposed in the literature to simultaneously generalize weighted means and OWA operators: WOWA operators and HWA operators.…”

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confidence: 99%

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On generalizations of weighted means and OWA operators

Llamazares¹

2011

Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011)

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In this paper we analyze two classes of functions proposed in the literature to simultaneously generalize weighted means and OWA operators: WOWA operators and HWA operators. Since, in some cases, the results provided by these operators may be questionable, we introduce functions that also generalize both operators and characterize those that satisfy a condition imposed to maintain the relationship among the weights. Keywords:Weighted means, OWA operators, WOWA operators, HWA operators. IntroducciónWeighted means and ordered weighted averaging (OWA) operators (Yager [12]) are well-known functions widely used in the aggregation processes. Although both are defined through a weighting vector, their behavior is quite different: The weighted means allow to weight each information source in relation to their reliability while OWA operators allow to weight the values according to their ordering.The need to combine both functions has been reported by several authors (see, among others, Torra [6] and Torra and Narukawa [9]). For this reason, two classes of functions have appeared in the literature with the intent of simultaneously generalizing weighted means and OWA operators: the weighted OWA (WOWA) operator (Torra [6]) and the hybrid weighted averaging (HWA) operator (Xu and Da [11]).The aim of this paper is to analyze WOWA operators and HWA operators. Moreover, since, in some cases, the results provided by these operators may be questionable, we propose to use functions that maintain the relationship among the weights of a weighting vector when the non-zero components of the other weighting vector are equal. In this way, we obtain a class of functions that have been previously introduced by Engemann et al. [2] in a framework of decision making under risk and uncertainty.The paper is organized as follows. In Section 2 we introduce weighted means, OWA operators and the two classes of functions proposed in the literature to simultaneously generalize weighted means and OWA operators: WOWA operators and HWA operators. Section 3 shows some drawbacks of both generalizations. In Section 4 we propose a condition to maintain the relationship among the weights and characterize the functions that satisfy this condition. The paper concludes in Section 5.

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Preference solutions of probability decision making with rim quantifiers

Liu

2005

Int. J. Intell. Syst.

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This article extends the quantifier-guided aggregation method to include probabilistic information. A general framework for the preference solution of decision making under an uncertainty problem is proposed, which can include decision making under ignorance and decision making under risk methods as special cases with some specific preference parameters. Almost all the properties, especially the monotonicity property, are kept in this general form. With the generating function representation of the Regular Increasing Monotone~RIM! quantifier, some properties of the RIM quantifier are discussed. A parameterized RIM quantifier to represent the valuation preference for probabilistic decision making is proposed. Then the risk attitude representation method is integrated in this quantifier-guided probabilistic decision making model to make it a general form of decision making under uncertainty.

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Modelling Decision Making Using Immediate Probabilities

Cited by 88 publications

References 5 publications

Constructing Choquet integral-based operators that generalize weighted means and OWA operators

Constructing Choquet integral-based operators that generalize weighted means and OWA operators

On generalizations of weighted means and OWA operators

Preference solutions of probability decision making with rim quantifiers

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