Consistent Solutions and Related Axiomatic Results under Multicriteria Management Systems

Liao, Yu-Hsien; Chung, Ling-Yun; Du, Wei-Shih; Ho, Shun-Chin

doi:10.1080/01966324.2017.1388201

Cited by 3 publications

(9 citation statements)

References 6 publications

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“…Liao et al [12] provided a multi-choice generalized EANSC under multiattribute situation as follows.…”

Section: Definitions and Notationsmentioning

confidence: 99%

“…If w : ∪ s∈U F + s → R + be a positive map, then w is said to be a weight map for levels. By these two kinds of weight maps, two weighted extensions of the MEANSC is considered by Liao et al [12] as follows.…”

Section: Definitions and Notationsmentioning

confidence: 99%

“…Stability has been always analyzed under many subjects by considering reduced games, such as bargaining issues, resource distribution issues, and so on. Based on notion the equal allocation of non-separable costs (EANSC, Ransmeier [11]), Liao et al [12] introduce two allocation rules by assigning weights to the operators and its activity levels (decisions) respectively under multiattribute multi-choice situations. Inspired by the axiomatic techniques due to Moulin [13], Liao et al [12] also proposed an extended complement-reduced game to manifest that these two allocation rules present fair mechanisms for allocating usability.…”

Section: Introductionmentioning

confidence: 99%

“…Three rules, the weighted lower-aggregate multiattribute index (WLAMI), the weighted regular multiattribute index (WRMI), and the weighted upper-aggregate multiattribute index (WUAMI), are introduced by assigning weights to the operators and its working levels (strategies) simultaneously in Section 2. These three rules are weighted generalizations of the maximal multiattribute index (MMI) due to Liao et al [12] under multiattribute multi-choice games.…”

Section: Introductionmentioning

confidence: 99%

“…Several axiomatic results of the MEANSC, the 1-MWANSC and the 2-MWANSC are proposed by Liao et al [12] as follows.…”

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confidence: 99%

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Axiomatic Results for Weighted Allocation Rules under Multiattribute Situations

Liao

2021

Mathematics

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In many interactive environments, operators may have to deal with different work objectives at the same time. In a realistic context, such as differences in the target type to be addressed, or changes in the behavior of other operators, operators may therefore have to cope with by adopting different work levels (strategies) at any given time. On the other hand, the importance or influence brought by operators may vary depending on many subjective and objective factors, such as the size of the constituency represented by a congressman, and the bargaining power of a business personnel which may vary. Therefore, it is reasonable that weights are apportioned to operators and arbitrary usability should be distributed according to these weights under various working levels and multiattribute situations. In pre-existing results for allocation rules, weights might be always apportioned to the “operators” or the “levels” to modify the differences among the operators or its working levels respectively. By applying weights to the operators and its working levels (strategies) simultaneously, we adopt the maximal marginal variations among working level (strategy) vectors to propose an allocation rule under multiattribute situations. Furthermore, we introduce some axiomatic outcomes to display the rationality for this weighted allocation rule. By replacing weights to be maximal marginal variations, a generalized index is also introduced.

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“…Liao et al [12] provided a multi-choice generalized EANSC under multiattribute situation as follows.…”

Section: Definitions and Notationsmentioning

confidence: 99%

Section: Definitions and Notationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Several axiomatic results of the MEANSC, the 1-MWANSC and the 2-MWANSC are proposed by Liao et al [12] as follows.…”

mentioning

confidence: 99%

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Axiomatic Results for Weighted Allocation Rules under Multiattribute Situations

Liao

2021

Mathematics

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A weighted power distribution mechanism under fuzzy behavior systems

Liao

2021

IFS

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In real situations, players might represent administrative areas of different scales; players might have different activity abilities. Thus, we propose an extension of the Banzhaf-Owen index in the framework of fuzzy transferable-utility games by considering supreme-utilities and weights simultaneously, which we name the weighted fuzzy Banzhaf-Owen index. Here we adopt three existing notions from traditional game theory and reinterpret them in the framework of fuzzy transferable-utility games. The first one is that this weighted index could be represented as an alternative formulation in terms of excess functions. The second is that, based on an reduced game and related consistency, we offer an axiomatic result to present the rationality of this weighted index. Finally, we introduce two dynamic processes to illustrate that this weighted index could be reached by players who start from an arbitrary efficient payoff vector and make successive adjustments.

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Evaluating Mechanism and Related Axiomatic Results under Multiple Considerations

Liao

2024

Mathematics

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Under many interactive environments in the real world, there is often a need to evaluate the minimization effects and subsequent allocation outcomes derived from these interactions under multiple considerations. For instance, in the context of product sales, it is necessary to evaluate how to minimize the manufacturing costs of various producing factors, and sometimes, from a holistic perspective, it may even be necessary to evaluate situations with minimal sales benefits. On the other hand, in order to evaluate related effects derived from interactions and subsequent allocation outcomes, many game-theoretical studies are based on interactive models to formulate evaluating mechanisms, and then they apply axiomatic processes to analyze the rationality of these mechanisms. Therefore, this study first proposes a mechanism for evaluating the minimization effects and subsequent allocation outcomes under multiple considerations. Additionally, considering that different environmental impacts result from varying participation factors, this study also presents several weighted derivatives based on participation factors and their behaviors. Concurrently, we utilize axiomatic results to demonstrate the mathematical correctness and practicality for these evaluating mechanisms.

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Consistent Solutions and Related Axiomatic Results under Multicriteria Management Systems

Cited by 3 publications

References 6 publications

Axiomatic Results for Weighted Allocation Rules under Multiattribute Situations

Axiomatic Results for Weighted Allocation Rules under Multiattribute Situations

A weighted power distribution mechanism under fuzzy behavior systems

Evaluating Mechanism and Related Axiomatic Results under Multiple Considerations

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