A PRINCIPLE OF PREFERENCE CONCENTRATION APPLIED TO THE UNSUPERVISED EVALUATION OF THE IMPORTANCE OF MULTIPLE CRITERIA

SantAnna, Annibal Parracho; Sant’Anna, Joana Lezan

doi:10.1590/0101-7438.2019.039.02.0317

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Articles • Pesqui. Oper. 39 (2) • May-Aug 2019 • https://doi.org/10.1590/0101-7438.2019.039.02.0317 copy

A PRINCIPLE OF PREFERENCE CONCENTRATION APPLIED TO THE UNSUPERVISED EVALUATION OF THE IMPORTANCE OF MULTIPLE CRITERIA

Authorship SCIMAGO INSTITUTIONS RANKINGS

ABSTRACT

The influence of a principle of preference concentration in the process of decision making in different contexts is discussed here. A procedure exploring the concentration of preferences to derive probabilities and another to derive, with higher generality, Choquet capacities are presented. An important feature of this last procedure is that it derives capacities in a space of criteria only from matrices of probabilities of preference according to each criterion, precluding the effort of directly trying to measure the interactions between them.

Keywords:
multiple criteria analysis; preferences; Choquet integral

	S	O	D
Alternative1	0.6	0.2	0.6
Alternative2	0.4	0.8	0.4

	*{ S, O* }**	*{ S, D* }**	*{ O, D* }**	*{ S, O, D* }**
Alternative1	$1 - 0.4 * 0.8 = 0.68$	$1 - 0.4 * 0.4 = .0.84$	$1 - 0.8 * 0.4 = 0.68$	$1 - .4 * .8 * .4 = 0.872$
Alternative2	$1 - 0.6 * 0.2 = 0.88$	$1 - 0.6 * 0.6 = 0.64$	$1 - 0.2 * 0.6 = 0.88$	$1 - .6 * .2 * .6 = 0.928$

	S	O	D	*{ S, O* }**	*{ S, D* }**	*{ O, D* }**	*{ S, O, D* }**
$q = 3$ Maxima	0.6	0.8	0.6	0.88	0.84	0.88	0.928
$q = 3$ Capacities	0.647	0.862	0.647	0.948	0.905	0.948	1
$q = 2$ Maxima	0.6	0.8	0.6	0.88	0.84	0.88
$q = 2$ Capacities	0.682	0.909	0.682	1	0.955	1	1

	S	O	D	*{ S, O* }**	*{ S, D* }**	*{ O, D* }**	*{ S, O, D* }**
$q = 3$ Maxima	0.5	0.6	0.5	0.64	0.75	0.64	0.8
$q = 3$ Capacities	0.625	0.75	0.625	0.8	0.9375	0.8	1
$q = 2$ Maxima	0.5	0.6	0.5	0.64	0.75	0.64
$q = 2$ Capacities	0.667	0.8	0.667	0.853	1	0.853	1

	Eng	Com	Alg	Ana	Phy
Concentration	0.13	0.17	0.30	0.09	0.31
Entropy	0.21	0.21	0.19	0.19	0.19

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Eng	0.39	Eng-Com	0.48	Eng-Com-Alg	0.62	Eng-Com-Alg-Ana	0.63
Com	0.42	Eng-Alg	0.52	Eng-Com-Ana	0.50	Eng-Com-Alg-Phy	0.99
Alg	0.43	Eng-Ana	0.44	Eng-Com-Phy	0.63	Eng-Com-Ana-Phy	0.64
Ana	0.37	Eng-Phy	0.51	Eng-Alg-Ana	0.55	Eng-Alg-Ana-Phy	0.90
Phy	0.45	Com-Alg	0.55	Eng-Alg-Phy	0.89	Com-Alg-Ana-Phy	0.94
		Com-Ana	0.45	Eng-Ana-Phy	0.52
		Com-Phy	0.57	Com-Alg-Ana	0.56
		Alg-Ana	0.45	Com-Alg-Phy	0.93
		Alg-Phy	0.83	Com-Ana-Phy	0.58
		Ana-Phy	0.46	Alg-Ana-Phy	0.84