#!/usr/bin/env python
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# =============================================================================
# FUTURE
# =============================================================================

from __future__ import unicode_literals

# =============================================================================
# DOCS
# =============================================================================

__doc__ = """Simplests method of multi-criteria"""

__all__ = [
"WeightedSum",
"WeightedProduct"]

# =============================================================================
# IMPORTS
# =============================================================================

import numpy as np

from ..validate import criteriarr
from ..base import Data
from .. import norm, rank
from ..utils.doc_inherit import doc_inherit

from ._dmaker import DecisionMaker

# =============================================================================
# FUNCTIONS
# =============================================================================

def wsum(nmtx, ncriteria, nweights):
# invert the minimization criteria
nmtx = norm.invert_min(nmtx, ncriteria, axis=0)

# calculate raning by inner prodcut
rank_mtx = np.inner(nmtx, nweights)
points = np.squeeze(np.asarray(rank_mtx))

return rank.rankdata(points, reverse=True), points

def wprod(nmtx, ncriteria, nweights):
# invert the minimization criteria
nmtx = norm.invert_min(nmtx, ncriteria, axis=0)

# instead of multiply we sum the logarithms
lmtx = np.log10(nmtx)

# add the weights to the mtx
rank_mtx = np.multiply(lmtx, nweights)

points = np.sum(rank_mtx, axis=1)

return rank.rankdata(points, reverse=True), points

# =============================================================================
# OO
# =============================================================================

[docs]class WeightedSum(DecisionMaker): r"""The weighted sum model (WSM) is the best known and simplest multi-criteria decision analysis for evaluating a number of alternatives in terms of a number of decision criteria. It is very important to state here that it is applicable only when all the data are expressed in exactly the same unit. If this is not the case, then the final result is equivalent to "adding apples and oranges." To avoid this problem a previous normalization step is necesary. In general, suppose that a given MCDA problem is defined on :math:m alternatives and :math:n decision criteria. Furthermore, let us assume that all the criteria are benefit criteria, that is, the higher the values are, the better it is. Next suppose that :math:w_j denotes the relative weight of importance of the criterion :math:C_j and :math:a_{ij} is the performance value of alternative :math:A_i when it is evaluated in terms of criterion :math:C_j. Then, the total (i.e., when all the criteria are considered simultaneously) importance of alternative :math:A_i, denoted as :math:A_{i}^{WSM-score}, is defined as follows: .. math:: A_{i}^{WSM-score} = \sum_{j=1}^{n} w_j a_{ij},\ for\ i = 1,2,3,...,m For the maximization case, the best alternative is the one that yields the maximum total performance value. Notes ----- If some criteria is for minimization, this implementation calculates the inverse. Parameters ---------- mnorm : string, callable, optional (default="sum") Normalization method for the alternative matrix. wnorm : string, callable, optional (default="sum") Normalization method for the weights array. Returns ------- Decision : :py:class:skcriteria.madm.Decision With values: - **kernel_**: None - **rank_**: A ranking (start at 1) where the i-nth element represent the position of the i-nth alternative. - **best_alternative_**: The index of the best alternative. - **alpha_solution_**: True - **beta_solution_**: False - **gamma_solution_**: True - **e_**: Particular data created by this method. - **e_.points**: Array where the i-nth element represent the importance of the i-nth alternative. References ---------- .. [1] Fishburn, P. C. (1967). Letter to the editor—additive utilities with incomplete product sets: application to priorities and assignments. Operations Research, 15(3), 537-542. .. [2] Weighted sum model. In Wikipedia, The Free Encyclopedia. Retrieved from https://en.wikipedia.org/wiki/Weighted_sum_model .. [3] Tzeng, G. H., & Huang, J. J. (2011). Multiple attribute decision making: methods and applications. CRC press. """ def __init__(self, mnorm="sum", wnorm="sum"): super(WeightedSum, self).__init__(mnorm=mnorm, wnorm=wnorm)
[docs] @doc_inherit def solve(self, ndata): nmtx, ncriteria, nweights = ndata.mtx, ndata.criteria, ndata.weights rank, points = wsum(nmtx, ncriteria, nweights) return None, rank, {"points": points}
[docs]class WeightedProduct(DecisionMaker): """The weighted product model (WPM) is a popular multi-criteria decision analysis method. It is similar to the weighted sum model. The main difference is that instead of addition in the main mathematical operation now there is multiplication. In general, suppose that a given MCDA problem is defined on :math:m alternatives and :math:n decision criteria. Furthermore, let us assume that all the criteria are benefit criteria, that is, the higher the values are, the better it is. Next suppose that :math:w_j denotes the relative weight of importance of the criterion :math:C_j and :math:a_{ij} is the performance value of alternative :math:A_i when it is evaluated in terms of criterion :math:C_j. Then, the total (i.e., when all the criteria are considered simultaneously) importance of alternative :math:A_i, denoted as :math:A_{i}^{WPM-score}, is defined as follows: .. math:: A_{i}^{WPM-score} = \prod_{j=1}^{n} a_{ij}^{w_j},\ for\ i = 1,2,3,...,m To avoid underflow, instead the multiplication of the values we add the logarithms of the values; so :math:A_{i}^{WPM-score}, is finally defined as: .. math:: A_{i}^{WPM-score} = \sum_{j=1}^{n} w_j \log(a_{ij}),\ for\ i = 1,2,3,...,m For the maximization case, the best alternative is the one that yields the maximum total performance value. Notes ----- The implementation works as follow: - If we have some values of any criteria < 0 in the alternative-matrix we add the minimimun value of this criteria to all the criteria. - If we have some 0 in some criteria all the criteria is incremented by 1. - If some criteria is for minimization, this implementation calculates the inverse. - Instead the multiplication of the values we add the logarithms of the values to avoid underflow. Parameters ---------- mnorm : string, callable, optional (default="sum") Normalization method for the alternative matrix. wnorm : string, callable, optional (default="sum") Normalization method for the weights array. Returns ------- Decision : :py:class:skcriteria.madm.Decision With values: - **kernel_**: None - **rank_**: A ranking (start at 1) where the i-nth element represent the position of the i-nth alternative. - **best_alternative_**: The index of the best alternative. - **alpha_solution_**: True - **beta_solution_**: False - **gamma_solution_**: True - **e_**: Particular data created by this method. - **e_.points**: Array where the i-nth element represent the importance of the i-nth alternative. References ---------- .. [1] Bridgman, P.W. (1922). Dimensional Analysis. New Haven, CT, U.S.A.: Yale University Press. .. [2] Miller, D.W.; M.K. Starr (1969). Executive Decisions and Operations Research. Englewood Cliffs, NJ, U.S.A.: Prentice-Hall, Inc. .. [3] Wen, Y. (2007, September 16). Using log-transform to avoid underflow problem in computing posterior probabilities. from http://web.mit.edu/wenyang/www/log_transform_for_underflow.pdf """ def __init__(self, mnorm="sum", wnorm="sum"): super(WeightedProduct, self).__init__(mnorm=mnorm, wnorm=wnorm)
[docs] @doc_inherit def preprocess(self, data): non_negative = norm.push_negatives(data.mtx, axis=0) non_zero = norm.add1to0(non_negative, axis=0) nmtx = self._mnorm(non_zero, axis=0) ncriteria = criteriarr(data.criteria) nweights = ( self._wnorm(data.weights, criteria=data.criteria) if data.weights is not None else np.ones(data.criteria.shape)) return Data(mtx=nmtx, criteria=ncriteria, weights=nweights, anames=data.anames, cnames=data.cnames)
[docs] @doc_inherit def solve(self, ndata): nmtx, ncriteria, nweights = ndata.mtx, ndata.criteria, ndata.weights rank, points = wprod(nmtx, ncriteria, nweights) return None, rank, {"points": points}
# ============================================================================= # MAIN # ============================================================================= if __name__ == "__main__": print(__doc__)