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Today, the editor will bring you the bipolar capacity concept interpretation of the journal paper "Biopolar capacity multi-attribute decision-making VIKOR method for attribute association".
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Today, the editor brings you the theoretical part of the journal paper "Bipolar Tolerance Multi-attribute Decision-Making VIKOR Method for Attribute Correlation"Bipolar Tolerance Concept Interpretation,
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Multi-attribute evaluation As one of the branches of multi-criteria decision-making, it has a wide range of applications in real life. However, in real problems, there are often associations between evaluation attributes, such as complementary associations, redundant associations, etc., and it is difficult to build a completely independent attribute system. Therefore, ignoring the association between attributes may cause misevaluation. The prerequisite for the use of existing evaluation methods is to assume that attributes are independent of each other and cannot be directly used in cases where there is correlation between attributes. The capacity theory is an effective theory to solve the correlation between attributes. In recent years, researchers have expanded the capacity theory to bipolar capacity theory . Bipolar capacity theory is more general and can effectively deal with situations where the evaluation value is negative.
As one of the branches of multi-criteria decision-making, multi-attribute evaluation has a wide range of applications in real life. However, in real problems, there are often associations between evaluation attributes, such as comprehensive associations, redundant associations, etc., and it is difficult to build a completely independent attribute system. Therefore, ignoring associations between attributes can result in false evaluations. Premise of the existing evaluation method is to assume that the attributes are independent of each other and cannot be directly used in the case of correlation between the attributes. Tolerance theory is an effective theory to solve the correlation between attributes, and in recent years, researchers have expanded the tolerance theory to bipolar tolerance theory. Bipolar tolerance theory is more general and can effectively deal with cases where the evaluation value is negative.
Bipolar capacity can model the index weight and correlation between indicators whose index values are in the bipolar interval. The most commonly used is that the bipolar interval is [-1,1].The following is the definition of bipolar capacity:
Bipolar tolerance can model the index weight and the association between indicators whose index values are in the bipolar range, and the most commonly used bipolar range is [-1,1]. The following is the definition of bipolar capacity:
In this kind of multi-attribute decision with attribute association, it is necessary to comprehensively examine the role of a single attribute on all attribute sets. Therefore, according to the definition of Shapley value, the Shapley value that defines bipolar capacity is as follows:
For the multi-attribute Decision problem of attribute association, the degree to which the attribute contributions to the decision result must be comprehensively examined by the role of all attribute sets, referring to the definition of Shapley values in game theory, and defining the Shapley value of the bipolar tolerance of the limited discrete attribute (set).
Next, the author uses the Choquet integral operator to aggregate information on multi-attribute decision problems. According to the different importance of the attribute, the bipolar tolerance is used to model and measure it. The definition of the bipolar tolerance Choquet integral operator is as follows:
When the criticality of the attribute set is to be modeled and measured using bipolar tolerance, the information of the multi-attribute decision problem can be aggregated by the Choquet integral operator, and the definition of the bipolar tolerance Choquet integration operator is given:
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References: Google Translation, Baidu Encyclopedia
References:
[1] Lin Pingping, Li Dengfeng, Jiang Binqian, Yu Gaofeng, Wei Anpeng. VIKOR method of bipolar capacity multi-attribute decision-making with attribute association [J]. System Engineering Theory and Practice, 2021, 41(08): 2147-2156.
[2] Zhang Lei. Evaluation of urban land use efficiency and its allocation in Jiangsu Province considering the correlation between indicators [D]. Nanjing University of Aeronautics and Astronautics, 2019.
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