Multicriteria Decision Making with Cognitive Limitations: A DS/AHP-Based Approach

Ma, Wenjun; Luo, Xudong; Jiang, Yuncheng

doi:10.1002/int.21872

Cited by 17 publications

(38 citation statements)

References 64 publications

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“…Also, Ma et al . employ the ambiguity aversion principle of minimax regret to deal with the multicriteria decision‐making problem.…”

Section: Preliminariesmentioning

confidence: 99%

“…In these two studies, based on the method of DS/AHP, they consider the effect of incomplete information and gives two ranking rules for two situations for the relative ranking of the groups of strategies. Ma et al . first present the formal definition for distinguishing two situations of the relative ranking of the group of alternatives as follows: Definition Let

Θ = {a_{1}, \dots, a_{n}}

be a frame of discernment for all alternatives, and

A_{1}, \dots, A_{m}

(

S_{i} \cap S_{j} = \emptyset

i \neq j

) be the groups of strategies with respect to a given criterion that we can assign a preference scale value.…”

Section: Preliminariesmentioning

confidence: 99%

“…Hence, Ma et al . show that the preference ordering of each group of alternatives with respect to the given criterion can be obtained by pairwise comparing a group of alternatives with a frame of discernment Θ.…”

Section: Preliminariesmentioning

confidence: 99%

“…Then, by Definitions and , and Theorem , Ma et al . give two ranking rules as follows: Definition For a given criterion, let

a_{i}

be one of d focal elements of a criterion with scale values

x_{i}

, and Θ be the frame of discernment.…”

Section: Preliminariesmentioning

confidence: 99%

“…These sets of pure strategy profiles and the frame of discernment constitute a specific matrix. Through comparing a set of strategy with a frame of discernment Θ, the player can express his/her preference ordering of the sets of pure strategy profiles in the game by extending the ranking rules (i.e., Definitions and ) in the work of Ma et al . to the situation of matrix game as follows: Definition For a given game with incomplete payoff, let

(S_{i}^{P}, S_{- i}^{P})

be one of n focal elements such that

d_{i} false(S_{i}^{P}, S_{- i}^{P} false) \neq 0

with relative payoff

x_{k}

, and Θ be the frame of discernment.…”

Section: Ambiguous Nash Equilibriummentioning

confidence: 99%

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Matrix games with missing, interval, and ambiguous lottery payoffs of pure strategy profiles and compound strategy profiles

Luo

Jiang

2017

Int. J. Intell. Syst.

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In a matrix game, the interactions among players are based on the assumption that each player has accurate information about the payoffs of their interactions and the other players are rationally self‐interested. As a result, the players should definitely take Nash equilibrium strategies. However, in real‐life, when choosing their optimal strategies, sometimes the players have to face missing, imprecise (i.e., interval), ambiguous lottery payoffs of pure strategy profiles and even compound strategy profile, which means that it is hard to determine a Nash equilibrium. To address this issue, in this paper we introduce a new solution concept, called ambiguous Nash equilibrium, which extends the concept of Nash equilibrium to the one that can handle these types of ambiguous payoff. Moreover, we will reveal some properties of matrix games of this kind. In particular, we show that a Nash equilibrium is a special case of ambiguous Nash equilibrium if the players have accurate information of each player's payoff sets. Finally, we give an example to illustrate how our approach deals with real‐life game theory problems.

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“…Also, Ma et al . employ the ambiguity aversion principle of minimax regret to deal with the multicriteria decision‐making problem.…”

Section: Preliminariesmentioning

confidence: 99%