1) where ???? ???????? (????) is the PCI of the j-th sub-goal upon the i-th goal within the k-th group of
3.6. The Method of Goal Dynamic Evaluation of Alternatives
The Method of Goal Dynamic Evaluation of Alternatives (MGDEA) was developed for the evaluation of decision alternatives based on a goal-oriented hierarchical model (Totsenko, 2001). And to improve and provide the opportunity of evaluating alternatives (projects, measures, decision variants) when building strategic plans (Tsyganok, 2013b). MGDEA is primarily intended for the evaluation of alternatives (decision variants, projects, measures) on a time interval in DSSs. Evaluation is carried out based on an expert-constructed subject domain model. The method makes it possible to use the most general models of weakly structured subject domains, which fully and adequately reflect the peculiarities of one or another subject domain.
In contrast to other existing methods, for example, multi-criteria ones (Figueira, Salvatore, & Ehrgott, 2005), where appropriate optimization methods are used (Steuer, 1992), MGDEA allows for the evaluation of heterogeneous projects, for which it is difficult or impossible to formulate a single set of criteria.
In addition, MGDEA does not require an expert to master the entire problem as a whole, but instead allows decision-makers to involve expert groups. During the model construction, each expert only has full knowledge of some part of
164 / Vitaliy Tsyganok
the subject domain. Due to the aforementioned properties, MGDEA can be considered one of the fundamental methods in the field of expert decision-making support. The method makes it possible to calculate ratings (estimates) of decision variants (actions, measures, projects) based on KB.
The basis of MGDEA is a generalized procedure for determining the achievement degree of any goal in a hierarchy at a given moment in time t.
As stated in Totsenko (2001), when determining the degree of achievement of a goal, it is necessary to analyze the degree of achievement of its immediate sub-goals (for each alternative subset of compatible sub-goals). So,
3.6. The Method of Goal Dynamic Evaluation of Alternatives
The Method of Goal Dynamic Evaluation of Alternatives (MGDEA) was developed for the evaluation of decision alternatives based on a goal-oriented hierarchical model (Totsenko, 2001).
And to improve and provide the opportunity of evaluating alternatives (projects, measures, decision variants) when building strategic plans (Tsyganok, 2013b). MGDEA is primarily intended for the evaluation of alternatives (decision variants, projects, measures) on a time interval in DSSs. Evaluation is carried out based on an expert-constructed subject domain model.
The method makes it possible to use the most general models of weakly structured subject domains, which fully and adequately reflect the peculiarities of one or another subject domain.
In contrast to other existing methods, for example, multi-criteria ones (Figueira, Salvatore,
& Ehrgott, 2005), where appropriate optimization methods are used (Steuer, 1992), MGDEA allows for the evaluation of heterogeneous projects, for which it is difficult or impossible to formulate a single set of criteria. In addition, MGDEA does not require an expert to master the entire problem as a whole, but instead allows decision-makers to involve expert groups. During the model construction, each expert only has full knowledge of some part of the subject domain.
Due to the aforementioned properties, MGDEA can be considered one of the fundamental methods in the field of expert decision-making support. The method makes it possible to calculate ratings (estimates) of decision variants (actions, measures, projects) based on KB.
The basis of MGDEA is a generalized procedure for determining the achievement degree of any goal in a hierarchy at a given moment in time t. As stated in Totsenko (2001), when determining the degree of achievement of a goal, it is necessary to analyze the degree of achievement of its immediate sub-goals (for each alternative subset of compatible sub-goals). So, 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡), that is the degree of achievement of the i-th goal at the moment of time t, is determined by the following expression:
𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) =
⎩⎪
⎪⎨
⎪⎪
⎧ 0, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖
𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)�, if 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖< 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
1, if 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
≤ 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) ≤ 1
, (2)
where 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝑘𝑘𝑘𝑘 ∑ 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘)𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡); 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖 is the threshold for achieving the i-th goal; 𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)� is a function of achievement degree of the i-th goal at moment t; 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−) is the PCI of the j-th goal in the k-th group of compatible goals, which has a negative influence on the i-th goal.
Calculation (by means of MGDEA) of the rating (relative estimation) of the decision variant corresponding to the l-th goal of the hierarchy at a certain moment of time t is, in essence, the determination of the difference between achievement degrees of the main goal 𝑑𝑑𝑑𝑑0(𝑡𝑡𝑡𝑡) under the condition of full achievement of all goals that correspond to decision variants intended for comparison 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿, 𝐿𝐿𝐿𝐿 = {𝑚𝑚𝑚𝑚. . 𝑛𝑛𝑛𝑛} and under the condition 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿\{𝑙𝑙𝑙𝑙}, 𝑑𝑑𝑑𝑑𝑙𝑙𝑙𝑙(𝑡𝑡𝑡𝑡) = 0. That is, the rating of this or that alternative (decision variant) is the difference between the degree of achievement of the main goal in the presence of the influence of this alternative upon the main goal and without it.
In order to expand the MGDEA functionality, it has been proposed to improve the method with the possibility to calculate the rating of alternatives not only in relation to the contribution to the achievement of the main goal of the hierarchy but also in relation to any chosen goal. This
, that is the degree of achievement of the i-th goal at the moment of time t, is determined by the following expression:
3.6. The Method of Goal Dynamic Evaluation of Alternatives
The Method of Goal Dynamic Evaluation of Alternatives (MGDEA) was developed for the evaluation of decision alternatives based on a goal-oriented hierarchical model (Totsenko, 2001).
And to improve and provide the opportunity of evaluating alternatives (projects, measures, decision variants) when building strategic plans (Tsyganok, 2013b). MGDEA is primarily intended for the evaluation of alternatives (decision variants, projects, measures) on a time interval in DSSs. Evaluation is carried out based on an expert-constructed subject domain model.
The method makes it possible to use the most general models of weakly structured subject domains, which fully and adequately reflect the peculiarities of one or another subject domain.
In contrast to other existing methods, for example, multi-criteria ones (Figueira, Salvatore,
& Ehrgott, 2005), where appropriate optimization methods are used (Steuer, 1992), MGDEA allows for the evaluation of heterogeneous projects, for which it is difficult or impossible to formulate a single set of criteria. In addition, MGDEA does not require an expert to master the entire problem as a whole, but instead allows decision-makers to involve expert groups. During the model construction, each expert only has full knowledge of some part of the subject domain.
Due to the aforementioned properties, MGDEA can be considered one of the fundamental methods in the field of expert decision-making support. The method makes it possible to calculate ratings (estimates) of decision variants (actions, measures, projects) based on KB.
The basis of MGDEA is a generalized procedure for determining the achievement degree of any goal in a hierarchy at a given moment in time t. As stated in Totsenko (2001), when determining the degree of achievement of a goal, it is necessary to analyze the degree of achievement of its immediate sub-goals (for each alternative subset of compatible sub-goals). So, 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡), that is the degree of achievement of the i-th goal at the moment of time t, is determined by the following expression:
𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) =
⎩⎪
⎪⎨
⎪⎪
⎧ 0, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖
𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)�, if 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖< 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
1, if 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
≤ 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) ≤ 1
, (2)
where 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝑘𝑘𝑘𝑘 ∑ 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘)𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡); 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖 is the threshold for achieving the i-th goal; 𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)� is a function of achievement degree of the i-th goal at moment t; 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−) is the PCI of the j-th goal in the k-th group of compatible goals, which has a negative influence on the i-th goal.
Calculation (by means of MGDEA) of the rating (relative estimation) of the decision variant corresponding to the l-th goal of the hierarchy at a certain moment of time t is, in essence, the determination of the difference between achievement degrees of the main goal 𝑑𝑑𝑑𝑑0(𝑡𝑡𝑡𝑡) under the condition of full achievement of all goals that correspond to decision variants intended for comparison 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿, 𝐿𝐿𝐿𝐿 = {𝑚𝑚𝑚𝑚. . 𝑛𝑛𝑛𝑛} and under the condition 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿\{𝑙𝑙𝑙𝑙}, 𝑑𝑑𝑑𝑑𝑙𝑙𝑙𝑙(𝑡𝑡𝑡𝑡) = 0. That is, the rating of this or that alternative (decision variant) is the difference between the degree of achievement of the main goal in the presence of the influence of this alternative upon the main goal and without it.
In order to expand the MGDEA functionality, it has been proposed to improve the method with the possibility to calculate the rating of alternatives not only in relation to the contribution to the achievement of the main goal of the hierarchy but also in relation to any chosen goal. This
where
3.6. The Method of Goal Dynamic Evaluation of Alternatives
The Method of Goal Dynamic Evaluation of Alternatives (MGDEA) was developed for the evaluation of decision alternatives based on a goal-oriented hierarchical model (Totsenko, 2001).
And to improve and provide the opportunity of evaluating alternatives (projects, measures, decision variants) when building strategic plans (Tsyganok, 2013b). MGDEA is primarily intended for the evaluation of alternatives (decision variants, projects, measures) on a time interval in DSSs. Evaluation is carried out based on an expert-constructed subject domain model.
The method makes it possible to use the most general models of weakly structured subject domains, which fully and adequately reflect the peculiarities of one or another subject domain.
In contrast to other existing methods, for example, multi-criteria ones (Figueira, Salvatore,
& Ehrgott, 2005), where appropriate optimization methods are used (Steuer, 1992), MGDEA allows for the evaluation of heterogeneous projects, for which it is difficult or impossible to formulate a single set of criteria. In addition, MGDEA does not require an expert to master the entire problem as a whole, but instead allows decision-makers to involve expert groups. During the model construction, each expert only has full knowledge of some part of the subject domain.
Due to the aforementioned properties, MGDEA can be considered one of the fundamental methods in the field of expert decision-making support. The method makes it possible to calculate ratings (estimates) of decision variants (actions, measures, projects) based on KB.
The basis of MGDEA is a generalized procedure for determining the achievement degree of any goal in a hierarchy at a given moment in time t. As stated in Totsenko (2001), when determining the degree of achievement of a goal, it is necessary to analyze the degree of achievement of its immediate sub-goals (for each alternative subset of compatible sub-goals). So, 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡), that is the degree of achievement of the i-th goal at the moment of time t, is determined by the following expression:
𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) =
⎩⎪
⎪⎨
⎪⎪
⎧ 0, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖
𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖
𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)�, if 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖< 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
1, if 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
≤ 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) ≤ 1
, (2)
where 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝑘𝑘𝑘𝑘 ∑ 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘)𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡); 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖 is the threshold for achieving the i-th goal; 𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)� is a function of achievement degree of the i-th goal at moment t; 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−) is the PCI of the j-th goal in the k-th group of compatible goals, which has a negative influence on the i-th goal.
Calculation (by means of MGDEA) of the rating (relative estimation) of the decision variant corresponding to the l-th goal of the hierarchy at a certain moment of time t is, in essence, the determination of the difference between achievement degrees of the main goal 𝑑𝑑𝑑𝑑0(𝑡𝑡𝑡𝑡) under the condition of full achievement of all goals that correspond to decision variants intended for comparison 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿, 𝐿𝐿𝐿𝐿 = {𝑚𝑚𝑚𝑚. . 𝑛𝑛𝑛𝑛} and under the condition 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿\{𝑙𝑙𝑙𝑙}, 𝑑𝑑𝑑𝑑𝑙𝑙𝑙𝑙(𝑡𝑡𝑡𝑡) = 0. That is, the rating of this or that alternative (decision variant) is the difference between the degree of achievement of the main goal in the presence of the influence of this alternative upon the main goal and without it.
In order to expand the MGDEA functionality, it has been proposed to improve the method with the possibility to calculate the rating of alternatives not only in relation to the contribution to the achievement of the main goal of the hierarchy but also in relation to any chosen goal. This
is the threshold for achieving the i-th goal;
3.6. The Method of Goal Dynamic Evaluation of Alternatives
The Method of Goal Dynamic Evaluation of Alternatives (MGDEA) was developed for the evaluation of decision alternatives based on a goal-oriented hierarchical model (Totsenko, 2001).
And to improve and provide the opportunity of evaluating alternatives (projects, measures, decision variants) when building strategic plans (Tsyganok, 2013b). MGDEA is primarily intended for the evaluation of alternatives (decision variants, projects, measures) on a time interval in DSSs. Evaluation is carried out based on an expert-constructed subject domain model.
The method makes it possible to use the most general models of weakly structured subject domains, which fully and adequately reflect the peculiarities of one or another subject domain.
In contrast to other existing methods, for example, multi-criteria ones (Figueira, Salvatore,
& Ehrgott, 2005), where appropriate optimization methods are used (Steuer, 1992), MGDEA allows for the evaluation of heterogeneous projects, for which it is difficult or impossible to formulate a single set of criteria. In addition, MGDEA does not require an expert to master the entire problem as a whole, but instead allows decision-makers to involve expert groups. During the model construction, each expert only has full knowledge of some part of the subject domain.
Due to the aforementioned properties, MGDEA can be considered one of the fundamental methods in the field of expert decision-making support. The method makes it possible to calculate ratings (estimates) of decision variants (actions, measures, projects) based on KB.
The basis of MGDEA is a generalized procedure for determining the achievement degree of any goal in a hierarchy at a given moment in time t. As stated in Totsenko (2001), when determining the degree of achievement of a goal, it is necessary to analyze the degree of achievement of its immediate sub-goals (for each alternative subset of compatible sub-goals). So, 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡), that is the degree of achievement of the i-th goal at the moment of time t, is determined by the following expression:
𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) =
⎩⎪
⎪⎨
⎪⎪
⎧ 0, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖
𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖
𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)�, if 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖< 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
1, if 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
≤ 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) ≤ 1
, (2)
where 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝑘𝑘𝑘𝑘 ∑ 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘)𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡); 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖 is the threshold for achieving the i-th goal; 𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)� is a function of achievement degree of the i-th goal at moment t; 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−) is the PCI of the j-th goal in the k-th group of compatible goals, which has a negative influence on the i-th goal.
Calculation (by means of MGDEA) of the rating (relative estimation) of the decision variant corresponding to the l-th goal of the hierarchy at a certain moment of time t is, in essence, the determination of the difference between achievement degrees of the main goal 𝑑𝑑𝑑𝑑0(𝑡𝑡𝑡𝑡) under the condition of full achievement of all goals that correspond to decision variants intended for comparison 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿, 𝐿𝐿𝐿𝐿 = {𝑚𝑚𝑚𝑚. . 𝑛𝑛𝑛𝑛} and under the condition 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿\{𝑙𝑙𝑙𝑙}, 𝑑𝑑𝑑𝑑𝑙𝑙𝑙𝑙(𝑡𝑡𝑡𝑡) = 0. That is, the rating of this or that alternative (decision variant) is the difference between the degree of achievement of the main goal in the presence of the influence of this alternative upon the main goal and without it.
In order to expand the MGDEA functionality, it has been proposed to improve the method with the possibility to calculate the rating of alternatives not only in relation to the contribution to the achievement of the main goal of the hierarchy but also in relation to any chosen goal. This
is a function of achievement degree of the i-th goal at moment 3.6. The Method of Goal Dynamic Evaluation of Alternatives
The Method of Goal Dynamic Evaluation of Alternatives (MGDEA) was developed for the evaluation of decision alternatives based on a goal-oriented hierarchical model (Totsenko, 2001).
And to improve and provide the opportunity of evaluating alternatives (projects, measures, decision variants) when building strategic plans (Tsyganok, 2013b). MGDEA is primarily intended for the evaluation of alternatives (decision variants, projects, measures) on a time interval in DSSs. Evaluation is carried out based on an expert-constructed subject domain model.
The method makes it possible to use the most general models of weakly structured subject domains, which fully and adequately reflect the peculiarities of one or another subject domain.
In contrast to other existing methods, for example, multi-criteria ones (Figueira, Salvatore,
& Ehrgott, 2005), where appropriate optimization methods are used (Steuer, 1992), MGDEA allows for the evaluation of heterogeneous projects, for which it is difficult or impossible to formulate a single set of criteria. In addition, MGDEA does not require an expert to master the entire problem as a whole, but instead allows decision-makers to involve expert groups. During the model construction, each expert only has full knowledge of some part of the subject domain.
Due to the aforementioned properties, MGDEA can be considered one of the fundamental methods in the field of expert decision-making support. The method makes it possible to calculate ratings (estimates) of decision variants (actions, measures, projects) based on KB.
The basis of MGDEA is a generalized procedure for determining the achievement degree of any goal in a hierarchy at a given moment in time t. As stated in Totsenko (2001), when determining the degree of achievement of a goal, it is necessary to analyze the degree of achievement of its immediate sub-goals (for each alternative subset of compatible sub-goals). So, 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡), that is the degree of achievement of the i-th goal at the moment of time t, is determined by the following expression:
𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) =
⎩⎪
⎪⎨
⎪⎪
⎧ 0, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖
𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)�, if 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖< 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
1, if 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
≤ 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) ≤ 1
, (2)
where 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝑘𝑘𝑘𝑘 ∑ 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘)𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡); 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖 is the threshold for achieving the i-th goal; 𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)� is a function of achievement degree of the i-th goal at moment t; 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−) is the PCI of the j-th goal in the k-th group of compatible goals, which has a negative influence on the i-th goal.
Calculation (by means of MGDEA) of the rating (relative estimation) of the decision variant corresponding to the l-th goal of the hierarchy at a certain moment of time t is, in essence, the determination of the difference between achievement degrees of the main goal 𝑑𝑑𝑑𝑑0(𝑡𝑡𝑡𝑡) under the condition of full achievement of all goals that correspond to decision variants intended for comparison 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿, 𝐿𝐿𝐿𝐿 = {𝑚𝑚𝑚𝑚. . 𝑛𝑛𝑛𝑛} and under the condition 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿\{𝑙𝑙𝑙𝑙}, 𝑑𝑑𝑑𝑑𝑙𝑙𝑙𝑙(𝑡𝑡𝑡𝑡) = 0. That is, the rating of this or that alternative (decision variant) is the difference between the degree of achievement of the main goal in the presence of the influence of this alternative upon the main goal and without it.
In order to expand the MGDEA functionality, it has been proposed to improve the method with the possibility to calculate the rating of alternatives not only in relation to the contribution to the achievement of the main goal of the hierarchy but also in relation to any chosen goal. This is the PCI of the j-th goal in the k-th group of compatible goals, which has
a negative influence on the i-th goal.
Calculation (by means of MGDEA) of the rating (relative estimation) of the decision variant corresponding to the l-th goal of the hierarchy at a certain moment of time t is, in essence, the determination of the difference between achievement degrees of the main goal
3.6. The Method of Goal Dynamic Evaluation of Alternatives
The Method of Goal Dynamic Evaluation of Alternatives (MGDEA) was developed for the evaluation of decision alternatives based on a goal-oriented hierarchical model (Totsenko, 2001).
And to improve and provide the opportunity of evaluating alternatives (projects, measures, decision variants) when building strategic plans (Tsyganok, 2013b). MGDEA is primarily intended for the evaluation of alternatives (decision variants, projects, measures) on a time interval in DSSs. Evaluation is carried out based on an expert-constructed subject domain model.
The method makes it possible to use the most general models of weakly structured subject domains, which fully and adequately reflect the peculiarities of one or another subject domain.
In contrast to other existing methods, for example, multi-criteria ones (Figueira, Salvatore,
& Ehrgott, 2005), where appropriate optimization methods are used (Steuer, 1992), MGDEA allows for the evaluation of heterogeneous projects, for which it is difficult or impossible to formulate a single set of criteria. In addition, MGDEA does not require an expert to master the entire problem as a whole, but instead allows decision-makers to involve expert groups. During the model construction, each expert only has full knowledge of some part of the subject domain.
Due to the aforementioned properties, MGDEA can be considered one of the fundamental methods in the field of expert decision-making support. The method makes it possible to calculate ratings (estimates) of decision variants (actions, measures, projects) based on KB.
The basis of MGDEA is a generalized procedure for determining the achievement degree of any goal in a hierarchy at a given moment in time t. As stated in Totsenko (2001), when determining the degree of achievement of a goal, it is necessary to analyze the degree of achievement of its immediate sub-goals (for each alternative subset of compatible sub-goals). So, 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡), that is the degree of achievement of the i-th goal at the moment of time t, is determined by the following expression:
𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) =
⎩⎪
⎪⎨
⎪⎪
⎧ 0, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖
𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖
𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)�, if 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖< 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
1, if 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
≤ 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) ≤ 1
, (2)
where 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝑘𝑘𝑘𝑘 ∑ 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘)𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡); 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖 is the threshold for achieving the i-th goal; 𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)� is a function of achievement degree of the i-th goal at moment t; 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−) is the PCI of the j-th goal in the k-th group of compatible goals, which has a negative influence on the i-th goal.
Calculation (by means of MGDEA) of the rating (relative estimation) of the decision variant corresponding to the l-th goal of the hierarchy at a certain moment of time t is, in essence, the determination of the difference between achievement degrees of the main goal 𝑑𝑑𝑑𝑑0(𝑡𝑡𝑡𝑡) under the condition of full achievement of all goals that correspond to decision variants intended for comparison 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿, 𝐿𝐿𝐿𝐿 = {𝑚𝑚𝑚𝑚. . 𝑛𝑛𝑛𝑛} and under the condition 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿\{𝑙𝑙𝑙𝑙}, 𝑑𝑑𝑑𝑑𝑙𝑙𝑙𝑙(𝑡𝑡𝑡𝑡) = 0. That is, the rating of this or that alternative (decision variant) is the difference between the degree of achievement of the main goal in the presence of the influence of this alternative upon the main goal and without it.
In order to expand the MGDEA functionality, it has been proposed to improve the method with the possibility to calculate the rating of alternatives not only in relation to the contribution to the achievement of the main goal of the hierarchy but also in relation to any chosen goal. This
under the condition of full achievement of all goals that correspond to decision variants intended for comparison
3.6. The Method of Goal Dynamic Evaluation of Alternatives
The Method of Goal Dynamic Evaluation of Alternatives (MGDEA) was developed for the evaluation of decision alternatives based on a goal-oriented hierarchical model (Totsenko, 2001).
And to improve and provide the opportunity of evaluating alternatives (projects, measures, decision variants) when building strategic plans (Tsyganok, 2013b). MGDEA is primarily intended for the evaluation of alternatives (decision variants, projects, measures) on a time interval in DSSs. Evaluation is carried out based on an expert-constructed subject domain model.
The method makes it possible to use the most general models of weakly structured subject domains, which fully and adequately reflect the peculiarities of one or another subject domain.
In contrast to other existing methods, for example, multi-criteria ones (Figueira, Salvatore,
& Ehrgott, 2005), where appropriate optimization methods are used (Steuer, 1992), MGDEA allows for the evaluation of heterogeneous projects, for which it is difficult or impossible to formulate a single set of criteria. In addition, MGDEA does not require an expert to master the entire problem as a whole, but instead allows decision-makers to involve expert groups. During the model construction, each expert only has full knowledge of some part of the subject domain.
Due to the aforementioned properties, MGDEA can be considered one of the fundamental methods in the field of expert decision-making support. The method makes it possible to calculate ratings (estimates) of decision variants (actions, measures, projects) based on KB.
The basis of MGDEA is a generalized procedure for determining the achievement degree of any goal in a hierarchy at a given moment in time t. As stated in Totsenko (2001), when determining the degree of achievement of a goal, it is necessary to analyze the degree of achievement of its immediate sub-goals (for each alternative subset of compatible sub-goals). So, 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡), that is the degree of achievement of the i-th goal at the moment of time t, is determined by the following expression:
𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) =
⎩⎪
⎪⎨
⎪⎪
⎧ 0, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖
𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)�, if 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖< 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
1, if 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
≤ 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) ≤ 1
, (2)
where 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝑘𝑘𝑘𝑘 ∑ 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘)𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡); 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖 is the threshold for achieving the i-th goal; 𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)� is a function of achievement degree of the i-th goal at moment t; 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−) is the PCI of the j-th goal in the k-th group of compatible goals, which has a negative influence on the i-th goal.
Calculation (by means of MGDEA) of the rating (relative estimation) of the decision variant corresponding to the l-th goal of the hierarchy at a certain moment of time t is, in essence, the determination of the difference between achievement degrees of the main goal 𝑑𝑑𝑑𝑑0(𝑡𝑡𝑡𝑡) under the condition of full achievement of all goals that correspond to decision variants intended for comparison 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿, 𝐿𝐿𝐿𝐿 = {𝑚𝑚𝑚𝑚. . 𝑛𝑛𝑛𝑛} and under the condition 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿\{𝑙𝑙𝑙𝑙}, 𝑑𝑑𝑑𝑑𝑙𝑙𝑙𝑙(𝑡𝑡𝑡𝑡) = 0. That is, the rating of this or that alternative (decision variant) is the difference between the degree of achievement of the main goal in the presence of the influence of this alternative upon the main goal and without it.
In order to expand the MGDEA functionality, it has been proposed to improve the method with the possibility to calculate the rating of alternatives not only in relation to the contribution to the achievement of the main goal of the hierarchy but also in relation to any chosen goal. This
, and under the condition
3.6. The Method of Goal Dynamic Evaluation of Alternatives
The Method of Goal Dynamic Evaluation of Alternatives (MGDEA) was developed for the evaluation of decision alternatives based on a goal-oriented hierarchical model (Totsenko, 2001).
And to improve and provide the opportunity of evaluating alternatives (projects, measures, decision variants) when building strategic plans (Tsyganok, 2013b). MGDEA is primarily intended for the evaluation of alternatives (decision variants, projects, measures) on a time interval in DSSs. Evaluation is carried out based on an expert-constructed subject domain model.
The method makes it possible to use the most general models of weakly structured subject domains, which fully and adequately reflect the peculiarities of one or another subject domain.
In contrast to other existing methods, for example, multi-criteria ones (Figueira, Salvatore,
& Ehrgott, 2005), where appropriate optimization methods are used (Steuer, 1992), MGDEA allows for the evaluation of heterogeneous projects, for which it is difficult or impossible to formulate a single set of criteria. In addition, MGDEA does not require an expert to master the entire problem as a whole, but instead allows decision-makers to involve expert groups. During the model construction, each expert only has full knowledge of some part of the subject domain.
Due to the aforementioned properties, MGDEA can be considered one of the fundamental methods in the field of expert decision-making support. The method makes it possible to calculate ratings (estimates) of decision variants (actions, measures, projects) based on KB.
The basis of MGDEA is a generalized procedure for determining the achievement degree of any goal in a hierarchy at a given moment in time t. As stated in Totsenko (2001), when determining the degree of achievement of a goal, it is necessary to analyze the degree of achievement of its immediate sub-goals (for each alternative subset of compatible sub-goals). So, 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡), that is the degree of achievement of the i-th goal at the moment of time t, is determined by the following expression:
𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) =
⎩⎪
⎪⎨
⎪⎪
⎧ 0, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖
𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖
𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)�, if 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖< 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
1, if 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
≤ 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) ≤ 1
, (2)
where 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝑘𝑘𝑘𝑘 ∑ 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘)𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡); 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖 is the threshold for achieving the i-th goal; 𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)� is a function of achievement degree of the i-th goal at moment t; 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−) is the PCI of the j-th goal in the k-th group of compatible goals, which has a negative influence on the i-th goal.
Calculation (by means of MGDEA) of the rating (relative estimation) of the decision variant corresponding to the l-th goal of the hierarchy at a certain moment of time t is, in essence, the determination of the difference between achievement degrees of the main goal 𝑑𝑑𝑑𝑑0(𝑡𝑡𝑡𝑡) under the condition of full achievement of all goals that correspond to decision variants intended for comparison 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿, 𝐿𝐿𝐿𝐿 = {𝑚𝑚𝑚𝑚. . 𝑛𝑛𝑛𝑛} and under the condition 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿\{𝑙𝑙𝑙𝑙}, 𝑑𝑑𝑑𝑑𝑙𝑙𝑙𝑙(𝑡𝑡𝑡𝑡) = 0. That is, the rating of this or that alternative (decision variant) is the difference between the degree of achievement of the main goal in the presence of the influence of this alternative upon the main goal and without it.
In order to expand the MGDEA functionality, it has been proposed to improve the method with the possibility to calculate the rating of alternatives not only in relation to the contribution to the achievement of the main goal of the hierarchy but also in relation to any chosen goal. This
,
3.6. The Method of Goal Dynamic Evaluation of Alternatives
The Method of Goal Dynamic Evaluation of Alternatives (MGDEA) was developed for the evaluation of decision alternatives based on a goal-oriented hierarchical model (Totsenko, 2001).
And to improve and provide the opportunity of evaluating alternatives (projects, measures, decision variants) when building strategic plans (Tsyganok, 2013b). MGDEA is primarily intended for the evaluation of alternatives (decision variants, projects, measures) on a time interval in DSSs. Evaluation is carried out based on an expert-constructed subject domain model.
The method makes it possible to use the most general models of weakly structured subject domains, which fully and adequately reflect the peculiarities of one or another subject domain.
In contrast to other existing methods, for example, multi-criteria ones (Figueira, Salvatore,
& Ehrgott, 2005), where appropriate optimization methods are used (Steuer, 1992), MGDEA allows for the evaluation of heterogeneous projects, for which it is difficult or impossible to formulate a single set of criteria. In addition, MGDEA does not require an expert to master the entire problem as a whole, but instead allows decision-makers to involve expert groups. During the model construction, each expert only has full knowledge of some part of the subject domain.
Due to the aforementioned properties, MGDEA can be considered one of the fundamental methods in the field of expert decision-making support. The method makes it possible to calculate ratings (estimates) of decision variants (actions, measures, projects) based on KB.
The basis of MGDEA is a generalized procedure for determining the achievement degree of any goal in a hierarchy at a given moment in time t. As stated in Totsenko (2001), when determining the degree of achievement of a goal, it is necessary to analyze the degree of achievement of its immediate sub-goals (for each alternative subset of compatible sub-goals). So, 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡), that is the degree of achievement of the i-th goal at the moment of time t, is determined by the following expression:
𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) =
⎩⎪
⎪⎨
⎪⎪
⎧ 0, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖
𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖, if 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖
𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)�, if 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖< 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) < 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
1, if 1 − ��𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−)�
𝑖𝑖𝑖𝑖
≤ 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) ≤ 1
, (2)
where 𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝑘𝑘𝑘𝑘 ∑ 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘)𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡); 𝑇𝑇𝑇𝑇𝑖𝑖𝑖𝑖 is the threshold for achieving the i-th goal; 𝑓𝑓𝑓𝑓�𝐷𝐷𝐷𝐷𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡)� is a function of achievement degree of the i-th goal at moment t; 𝑤𝑤𝑤𝑤𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖(𝑘𝑘𝑘𝑘−) is the PCI of the j-th goal in the k-th group of compatible goals, which has a negative influence on the i-th goal.
Calculation (by means of MGDEA) of the rating (relative estimation) of the decision variant corresponding to the l-th goal of the hierarchy at a certain moment of time t is, in essence, the determination of the difference between achievement degrees of the main goal 𝑑𝑑𝑑𝑑0(𝑡𝑡𝑡𝑡) under the condition of full achievement of all goals that correspond to decision variants intended for comparison 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿, 𝐿𝐿𝐿𝐿 = {𝑚𝑚𝑚𝑚. . 𝑛𝑛𝑛𝑛} and under the condition 𝑑𝑑𝑑𝑑𝑖𝑖𝑖𝑖(𝑡𝑡𝑡𝑡) = 1, 𝑖𝑖𝑖𝑖 ∈ 𝐿𝐿𝐿𝐿\{𝑙𝑙𝑙𝑙}, 𝑑𝑑𝑑𝑑𝑙𝑙𝑙𝑙(𝑡𝑡𝑡𝑡) = 0. That is, the rating of this or that alternative (decision variant) is the difference between the degree of achievement of the main goal in the presence of the influence of this alternative upon the main goal and without it.
In order to expand the MGDEA functionality, it has been proposed to improve the method with the possibility to calculate the rating of alternatives not only in relation to the contribution to the achievement of the main goal of the hierarchy but also in relation to any chosen goal. This
. That is, the rating of this or that alternative (decision variant) is the difference between the degree of achievement of the main goal in the presence of the influence of this alternative upon the main goal and without it.
In order to expand the MGDEA functionality, it has been proposed to improve the method with the possibility to calculate the rating of alternatives not only in relation to the contribution to the achievement of the main goal of the hierarchy but also in relation to any chosen goal. This allows us to compare the influence of alternative decision variants on intermediate goals in the general domain model.
(2)