38
B. Uzun et al.
6.1 Introduction
Brans suggests the PROMETHEE approach and it is one form of method based on
an outrank relationship between alternate pairs (Brans 1982). The Promethean and
Gaia are best known in their concise additional geometrical analysis for interactive
help. Instead of pointing to a correct decision, the Promethean and Gaia approach
allows decision makers to find the best answer for their intent and understanding of
the problem (Brans and De Smet 2016). It offers an integrated and logical context in
which the decision problem can be organized, its contradictions and synergies defined
and quantified, action clusters, and the key alternatives and systematic thought underlying them. The Promethean and Gaia will refer to decisions in the following situations like Option (Select one alternative from a specified collection of alternatives,
typically when several decision criteria have been included.), Prioritization (Assess
the relative value of members of a set of alternatives as compared to the preference
of the particular one, or simply identify the alternative.), Allocation of resources to a
variety of choices., Classification (Adding a variety of alternatives to make Conflict
the most common.) and Resolution (Disagreements between seemingly conflicting
parties are settled.
The outranking test compares pairs of alternatives for any parameter. The
PROMETHEE approach produces the preferential function to define the disparity in
choice on each criterion between alternative pairs (Vincke and Brans 1985). Thus
preference functions are built up about the numerical difference between pairs of
alternatives to describe the preferential difference from the point of view of the decision maker. The value of such functions varies from 0 to 1. The greater the value of
the function, the greater will be the difference of preference. There’s no preferential
differential between pair of alternatives when the value is zero.
The steps of obtaining the ranking result via PROMETHEE technique is as follows
(Ozsahin et al. 2019):
Let a 1 , a 2 , . . . , a m be m alternatives and q 1 , q 2 , . . . , q n be n cardinal criteria and
let q i j be the value of j − th criteria of the i-th alternative (a i ). Let assume that all
parameters are to be maximized.
We use p j (a i, a k ) denoting preferential function on criterion j as calculated below;
P j (a i , a k ) =
0
q i j ≤ q k j
P
q i j − q k j
q i j > q k j
(6.1)
There are six different preference functions were adopted at Brans et al. study
based on various parameters (Fig. 6.1).
Clearly, various generic parameters reflect different altitudes against preference
structure and preference strength. Brans found that the linear preference function
was mainly used for functional use by users led by gauss preference function. For
these preference functions, the severity of the preference slowly increases from 0 to
1, while in the other preference functions, the severity of choice increases abruptly.
B. Uzun et al.
6.1 Introduction
Brans suggests the PROMETHEE approach and it is one form of method based on
an outrank relationship between alternate pairs (Brans 1982). The Promethean and
Gaia are best known in their concise additional geometrical analysis for interactive
help. Instead of pointing to a correct decision, the Promethean and Gaia approach
allows decision makers to find the best answer for their intent and understanding of
the problem (Brans and De Smet 2016). It offers an integrated and logical context in
which the decision problem can be organized, its contradictions and synergies defined
and quantified, action clusters, and the key alternatives and systematic thought underlying them. The Promethean and Gaia will refer to decisions in the following situations like Option (Select one alternative from a specified collection of alternatives,
typically when several decision criteria have been included.), Prioritization (Assess
the relative value of members of a set of alternatives as compared to the preference
of the particular one, or simply identify the alternative.), Allocation of resources to a
variety of choices., Classification (Adding a variety of alternatives to make Conflict
the most common.) and Resolution (Disagreements between seemingly conflicting
parties are settled.
The outranking test compares pairs of alternatives for any parameter. The
PROMETHEE approach produces the preferential function to define the disparity in
choice on each criterion between alternative pairs (Vincke and Brans 1985). Thus
preference functions are built up about the numerical difference between pairs of
alternatives to describe the preferential difference from the point of view of the decision maker. The value of such functions varies from 0 to 1. The greater the value of
the function, the greater will be the difference of preference. There’s no preferential
differential between pair of alternatives when the value is zero.
The steps of obtaining the ranking result via PROMETHEE technique is as follows
(Ozsahin et al. 2019):
Let a 1 , a 2 , . . . , a m be m alternatives and q 1 , q 2 , . . . , q n be n cardinal criteria and
let q i j be the value of j − th criteria of the i-th alternative (a i ). Let assume that all
parameters are to be maximized.
We use p j (a i, a k ) denoting preferential function on criterion j as calculated below;
P j (a i , a k ) =
0
q i j ≤ q k j
P
q i j − q k j
q i j > q k j
(6.1)
There are six different preference functions were adopted at Brans et al. study
based on various parameters (Fig. 6.1).
Clearly, various generic parameters reflect different altitudes against preference
structure and preference strength. Brans found that the linear preference function
was mainly used for functional use by users led by gauss preference function. For
these preference functions, the severity of the preference slowly increases from 0 to
1, while in the other preference functions, the severity of choice increases abruptly.