afryca.ase.Snippet Library LPRAse Linguistic Preference Relation

//
// Linguistic preference relation class
//
// @param ids Labels
// @param n Number of alternatives
//


var LPRAse = function LPRAse(ids, n) {
	this.ids = ids; // Ids
	this.n = n; // Number of alternatives
	this.preference = new FPR(n);

	// Asociate value in internal FPR
	this.labelsValues = function() {
		var bucket = 1 / (ids.length - 1);
		var result = [];
		for (var i = 0; i < ids.length; i++) {
			result[ids[i]] = (i * bucket).toFixed(4)/1;
		}
		return result;
	}();
	
	// Beta of label value
	this.beta = function(value) {
		return (value * (this.ids.length - 1))
	}

	// Linguistic value of FPR pair
	this.linguisticValue = function(value) {
		var beta = this.beta(value);
		var i = Math.round(beta);
		var label = ids[i];
		var alpha  = (beta - i).toFixed(4)/1;
		var result = {s:label, alpha:alpha, lpr:this};
		result.toString = function() {
			return (result.alpha == 0) ? result.s : '(' + result.s + ', ' + result.alpha + ')';
		}
		return result;
	}

	// FPR value for linguistic value
	this.valueFor = function (label, alpha) {
		var value = NaN;
		if (typeof label == 'string') {
			value = this.labelsValues[label];
			if (typeof alpha == 'number') {
				value += (alpha * (1 / (this.ids.length - 1))).toFixed(2)/1;
			}
		}
		return value;
	}

	// Alternative value
	this.getValue = function (i, j) {
		var value = this.preference.getValue(i, j);
		return isNaN(value) ? NaN : this.linguisticValue(value);
	}

	// Set alternative value
	this.setValueSymmetrically = function (i, j, label, alpha) {
		this.preference.setValueSymmetrically(i | 0, j | 0, this.valueFor(label, alpha));
	}

	// LPR string value
	this.toString = function() {
		var result = [];
		var lengths = [];
		var value;
		for (var i = 0; i < this.n; i++) {
			result[i] = [];
			for (var j = 0; j < this.n; j++) {
				value = this.getValue(i | 0, j | 0).toString();
				result[i][j] = (i == j) ? '-' : ((value == 'NaN') ? '' : value);
				lengths[j] = (i == 0) ? result[i][j].length : Math.max(lengths[j], result[i][j].length);
			}
		}
		var output = '';
		for (var i = 0; i < this.n; i++) {
			for (var j = 0; j < this.n; j++) {
				if (j > 0) {
					output += ' ';
				}
				output += '| ' + result[i][j];
				for (var s = result[i][j].length; s < lengths[j]; s++) {
					output += ' ';
				}
			}
			output += ' |\n';
		}
		return output;
	}
}

//
// Xu's sum of two linguistic variables
//
// Deviation measures of linguistic preference relations in group decision making
// http://dx.doi.org/10.1016/j.omega.2004.04.008
//
// @param a Linguistic variable a
// @param b Linguistic variable b
//
LPRAse.xuSum = function(a, b) {
	if ((typeof a == 'undefined') || (typeof b == 'undefined')) {
		return NaN;
	}
	if ((typeof a.lpr == 'undefined') || (typeof b.lpr == 'undefined')) {
		return NaN;
	}
	if (a.lpr.ids != b.lpr.ids) {
		return NaN;
	}
	if (!( a.lpr.ids.length & 1 )) {
		return NaN;
	}
	var lpr = a.lpr;
	var T = lpr.ids.length;
	var adjustment = Math.round((T-1) / 2);
	var s_a = lpr.beta(lpr.valueFor(a.s)) + a.alpha - adjustment;
	var s_b = lpr.beta(lpr.valueFor(b.s)) + b.alpha - adjustment;
	return s_a + s_b;
}

//
// Xu's distance between two linguistic variables
//
// Deviation measures of linguistic preference relations in group decision making
// http://dx.doi.org/10.1016/j.omega.2004.04.008
//
// @param a Linguistic variable a
// @param b Linguistic variable b
//
LPRAse.xuDistanceBetweenTwoVariables = function(a, b) {
	var sum = LPRAse.xuSum(a, b);
	if (isNaN(sum)) {
		return NaN;
	}
	var T = a.lpr.ids.length;
	return (sum / T).toFixed(2)/1;
}

//
// Dong's distance between two LPR
//
// On consistency measures of linguistic preference relations - Definition 3
// doi:10.1016/j.ejor.2007.06.013
//
// @param lpr1 LPR 1
// @param lpr2 LPR 2
//
LPRAse.dongDistanceBetweenTwoLPR = function(lpr1, lpr2) {
	if ((typeof lpr1 == 'undefined') || (typeof lpr2 == 'undefined')) {
		return NaN;
	}
	if (lpr1.ids != lpr2.ids) {
		return NaN;
	}
	if (!(lpr1.ids.length & 1 )) {
		return NaN;
	}
	var result = 0;
	var a;
	var b;
	var n = lpr1.n;
	for (var i = 0; i < (n - 1); i++) {
		for (var j = i + 1; j < n; j++) {
			a = lpr1.getValue(i | 0, j | 0);
			b = lpr2.getValue(i | 0, j | 0);
			result += Math.pow(LPRAse.xuDistanceBetweenTwoVariables(a, b), 2);
		}
	}
	result *= 2 / (n * (n - 1));
	result = Math.sqrt(result).toFixed(2)/1;
	return result;
}

//
// Dong's average LPR
//
// On consistency measures of linguistic preference relations - Lemma 2
// doi:10.1016/j.ejor.2007.06.013
//
// @param lpr LPR
//
LPRAse.dongAverageLPR = function(lpr) {
	if (typeof lpr == 'undefined') {
		return NaN;
	}

	if (typeof lpr.preference == 'undefined') {
		return NaN;
	}

	if (!(lpr.ids.length & 1 )) {
		return NaN;
	}

	if (consistency.containsMissingValues(lpr.preference)) {
		return NaN;
	}

	var ids = lpr.ids;
	var T = ids.length;
	var n = lpr.n;
	var result = new LPRAse(ids, n);
	var aux;
	var a_i_c;
	var a_c_j;
	var adjustment = Math.round((T-1) / 2);
	for (var i = 0; i < (n - 1); i++) {
		for (var j = i + 1; j < n; j++) {
			aux = 0;
			for (var c = 0; c < n; c++) {
				a_i_c = lpr.getValue(i | 0, c | 0);
				a_c_j = lpr.getValue(c | 0, j | 0);
				aux += LPRAse.xuSum(a_i_c, a_c_j);
			}
			aux /= n;
			aux += adjustment;
			aux /= T-1;
			aux = lpr.linguisticValue(aux);
			result.setValueSymmetrically(i | 0, j | 0, aux.s, aux.alpha);
		}
	}
	return result;
}