Compromise principle based methods of identifying capacities in the framework of multicriteria decision analysis

Wu, Jian‐Zhang; Zhang, Qiang; Du, Qinjun; Dong, Zhiliang

doi:10.1016/j.fss.2013.12.016

Cited by 39 publications

(35 citation statements)

References 28 publications

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“…As mentioned in the introduction, the input information required for the interaction index oriented capacity identification methods is the decision maker's explicit preference information about decision criteria. In the literatures about the capacity identification methods (see, e.g., Angilella et al., , ; Beliakov, ; Grabisch et al., ; Grabisch and Labreuche, ; Kojadinovic, ; Marichal and Roubens, ; Roubens, ; Wu et al., ), those explicit preference information are usually formulated by a weak partial order

{\underset{̲}{≻}}_{N}

on the criteria set N as well as a weak partial order

{\underset{̲}{≻}}_{P}

on the set of pairs of criteria (Grabisch et al., ). These two weak partial orders can be translated into the formulations of the Shapley importance and interaction indices (Wu et al., ).…”

Section: The Empty Set Interaction Index Oriented Identification Prinmentioning

confidence: 99%

“…In the literatures about the capacity identification methods (see, e.g., Angilella et al., , ; Beliakov, ; Grabisch et al., ; Grabisch and Labreuche, ; Kojadinovic, ; Marichal and Roubens, ; Roubens, ; Wu et al., ), those explicit preference information are usually formulated by a weak partial order

{\underset{̲}{≻}}_{N}

on the criteria set N as well as a weak partial order

{\underset{̲}{≻}}_{P}

on the set of pairs of criteria (Grabisch et al., ). These two weak partial orders can be translated into the formulations of the Shapley importance and interaction indices (Wu et al., ). For

i, j, k, l \in N

, we have (Angilella et al., ; Beliakov, ; Grabisch et al., ; Kojadinovic, ; Marichal and Roubens, ; Wu et al., ): The criterion i is more important than the criterion j ,

i ≻_{N} j \Leftrightarrow I_{Sh}^{μ} false({i} false) - I_{Sh}^{μ} false({j} false) \geq δ_{Sh};

The criteria i and j have the same importance,

i \sim_{N} j \Leftrightarrow - δ_{Sh} \leq I_{Sh}^{μ} false({i} false) - I_{Sh}^{μ} false({j} false) \leq δ_{Sh};

The interaction between the criteria i and j is greater than that between the criteria k and l ,

I_{Sh}^{μ} false({i, j} false) ≻_{P} I_{Sh}

…”

Section: The Empty Set Interaction Index Oriented Identification Prinmentioning

confidence: 99%

“…In the framework of the capacity based multicriteria decision analysis, the capacity identification method is one of the research focuses and its major aim is to deal with the exponential complexity inherent in the construction process (Grabisch, ). The capacity identification methods usually begin with the decision maker's explicit preference information about the multiple decision criteria (Angilella et al., , ; Grabisch et al., ; Grabisch and Labreuche, ; Kojadinovic, ; Marichal and Roubens, ; Roubens, ; Wu et al., ), which is provided from the comparison perspective, e.g., criterion i is more important than criterion j , the interaction between criteria i and j is greater than that between criteria k and l , and so on. Generally, these explicit preference information about decision criteria can only constitute a region of the feasible capacities and some additional selection principle should be applied to identify the most satisfactory one(s) (Wu et al., ).…”

Section: Introductionmentioning

confidence: 99%

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Two kinds of explicit preference information oriented capacity identification methods in the context of multicriteria decision analysis

Pap

Szakál

2017

Int Trans Operational Res

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The decision maker's preference information on the importance and interaction of decision criteria can be explicitly described by the probabilistic interaction indices in the framework of the capacity based multicriteria decision analysis. In this paper, we first investigate some properties of the probabilistic interaction indices of the empty set, and propose the maximum and minimum empty set interaction principles based capacity identification methods, which can be considered as the comprehensive interaction trend preference information oriented capacity identification methods. Then, by introducing the deviation variables, the goal constraints, as well as the goal objective function, we give a new and more flexible approach to representing the decision maker's explicit preference information on the kind and degree of the interaction of any given combination of decision criteria as well as on the degree of the importance of any decision criterion, and construct the nonempty set interaction indices based capacity identification method, which can be considered as the detailed explicit preference information oriented identification method. Finally, two illustrative examples are respectively given to show the feasibility and applicability of the two kinds of methods. In addition, the comparison analysis between these two kinds of methods and some existing capacity identification methods are also mentioned.

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{\underset{̲}{≻}}_{N}

on the criteria set N as well as a weak partial order

{\underset{̲}{≻}}_{P}

on the set of pairs of criteria (Grabisch et al., ). These two weak partial orders can be translated into the formulations of the Shapley importance and interaction indices (Wu et al., ).…”

Section: The Empty Set Interaction Index Oriented Identification Prinmentioning

confidence: 99%

{\underset{̲}{≻}}_{N}

on the criteria set N as well as a weak partial order

{\underset{̲}{≻}}_{P}

on the set of pairs of criteria (Grabisch et al., ). These two weak partial orders can be translated into the formulations of the Shapley importance and interaction indices (Wu et al., ). For

i, j, k, l \in N

, we have (Angilella et al., ; Beliakov, ; Grabisch et al., ; Kojadinovic, ; Marichal and Roubens, ; Wu et al., ): The criterion i is more important than the criterion j ,

i ≻_{N} j \Leftrightarrow I_{Sh}^{μ} false({i} false) - I_{Sh}^{μ} false({j} false) \geq δ_{Sh};

The criteria i and j have the same importance,

i \sim_{N} j \Leftrightarrow - δ_{Sh} \leq I_{Sh}^{μ} false({i} false) - I_{Sh}^{μ} false({j} false) \leq δ_{Sh};

The interaction between the criteria i and j is greater than that between the criteria k and l ,

I_{Sh}^{μ} false({i, j} false) ≻_{P} I_{Sh}

…”

Section: The Empty Set Interaction Index Oriented Identification Prinmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Two kinds of explicit preference information oriented capacity identification methods in the context of multicriteria decision analysis

Pap

Szakál

2017

Int Trans Operational Res

View full text Add to dashboard Cite

show abstract

“…For some given alternatives, the decision makers can also provide his/her preference about them, generally a ranking order for some alternatives, or dominance among some pairs of alternatives; in some situations, even be able to give the desired overall evaluation values of the alternatives. This preference information on the alternatives actually reflects the decision maker's preference on the decision criteria too, hence can be considered as implicit preference information …”

Section: Introductionmentioning

confidence: 99%

“…With the explicit and implicit preference information, as well as the boundary and monotonicity conditions on the capacity, we usually only get a feasible region of capacities from which the complete ranking order on the decision alternatives cannot be obtained directly. To find this ranking order, some selection principle should be adopted to obtain the most desired capacity, like the maximum entropy principle, the compromise principle, the interaction index oriented principle, the Multiple Criteria Correlation Preference Information based least square and absolute deviation principles, and learning set based principles . It is quite possible that different principles lead to different ranking orders of decision alternatives even using the same feasible capacity region.…”

Section: Introductionmentioning

confidence: 99%

Nonadditive robust ordinal regression with nonadditivity index and multiple goal linear programming

Beliakov

2019

Int J Intell Syst

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Nonadditive robust ordinal regression (NAROR) is a widely adopted approach to analyze and reveal the dominance relationships among all decision alternatives based on nonadditive measures, called capacities. In this paper, we first investigate some advantages of the nonadditivity index as an explicit interaction index, as compared with the traditional probabilistic simultaneous interaction indices, and show that nonadditivity index can serve as an equivalent representation of a capacity. Then we enhance the NAROR method by using nonadditivity index as well as multiple‐goal linear programming, where the former is used to replace the traditional interaction index to more naturally represent the decision maker's preferences, and the latter aims to replace the 0 to 1 mixed integer programming to enhance the ability to detect and adjust contradictory and redundant preference information. The updated NAROR's steps are constructed and discussed in detail and illustrated with a practical example.

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Probabilistic bipartition interaction index of multiple decision criteria associated with the nonadditivity of fuzzy measures

Beliakov

2018

Int J Intell Syst

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The probabilistic simultaneous interaction index has been widely adopted to measure the interaction among the decision criteria. However, this type of indices sometimes fails to reflect the kind of interaction associated with the nonadditivity of a fuzzy measure (capacity). For example, any simultaneous interaction index of the universal set of criteria w.r.t. a strictly superadditive capacity is not always positive. The main reason is that the simultaneous interaction index generalizes the notion of value by replacing the marginal contribution of a single criterion with the marginal simultaneous interaction of criteria subset. In this paper, we reform the generalization process and replace the marginal contribution with the marginal bipartition interaction, which can better reflect the kind of interaction associated with the nonadditivity, for example, superadditivity, subadditivity, strict‐superadditivity, or strict‐subadditivity. We construct a family of probabilistic bipartition interaction indices of subsets of criteria and study its properties. We discuss the issue of capacity identification based on the bipartition interaction index and demonstrate that the new type of interaction index can be adopted as a feasible alternative to describing the interaction phenomenon among the decision criteria.

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Compromise principle based methods of identifying capacities in the framework of multicriteria decision analysis

Cited by 39 publications

References 28 publications

Two kinds of explicit preference information oriented capacity identification methods in the context of multicriteria decision analysis

Two kinds of explicit preference information oriented capacity identification methods in the context of multicriteria decision analysis

Nonadditive robust ordinal regression with nonadditivity index and multiple goal linear programming

Probabilistic bipartition interaction index of multiple decision criteria associated with the nonadditivity of fuzzy measures

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