Preference solutions of probability decision making with rim quantifiers

Abstract

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.

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

“…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]). …”

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

“…Some aggregation methods with importance or weights information have been proposed for OWA operators, quasi-arithmetic means, and other aggregation operators [6,[9][10][11]14,16,21,33,[35][36][37][38]47]. These weighted aggregation methods have been used for the fuzzy number estimation or defuzzification in recent years [14,22,23,[25][26][27][28]31,39,47,51]. If the membership function of a fuzzy set is replaced with the probability density function, these methods can also be used to estimate the random variables.…”

SUOWA operators: Constructing semi-uninorms and analyzing specific cases

“…Two of the best-known solutions are the operator proposed by Engemann et al [10], and the weighted OWA operator (WOWA) introduced by Torra [3]. The operator proposed by Engemann et al [10], which has been rediscovered as MO2P (Roy [6]), IP-OWA operator (Merigó [11]), and HWAA operator (Lin and Jiang [12]), has some interesting properties but also has an important shortcoming: it is not monotonic (see Liu [13], Llamazares [9], Wang [14] and Lin [15]). For its part, WOWA operators have good properties given that they are Choquet integral-based operators with respect to normalized capacities (see Torra [16]).…”