Source code for skcriteria.madm.closeness

#!/usr/bin/env python
# -*- coding: utf-8 -*-

# Copyright (c) 2016-2017, Cabral, Juan; Luczywo, Nadia
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# =============================================================================
# FUTURE & DOCS
# =============================================================================

from __future__ import unicode_literals


__doc__ = """Methods based on an aggregating function representing
“closeness to the ideal”.


"""

__all__ = ['TOPSIS']


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

import numpy as np

from .. import rank
from ..validate import MIN, MAX
from ..utils.doc_inherit import doc_inherit

from ._dmaker import DecisionMaker


# =============================================================================
# Function
# =============================================================================

def topsis(nmtx, ncriteria, nweights):

    # apply weights
    wmtx = np.multiply(nmtx, nweights)

    # extract mins and maxes
    mins = np.min(wmtx, axis=0)
    maxs = np.max(wmtx, axis=0)

    # create the ideal and the anti ideal arrays
    ideal = np.where(ncriteria == MAX, maxs, mins)
    anti_ideal = np.where(ncriteria == MIN, maxs, mins)

    # calculate distances
    d_better = np.sqrt(np.sum(np.power(wmtx - ideal, 2), axis=1))
    d_worst = np.sqrt(np.sum(np.power(wmtx - anti_ideal, 2), axis=1))

    # relative closeness
    closeness = d_worst / (d_better + d_worst)

    # compute the rank and return the result
    return rank.rankdata(closeness, reverse=True), ideal, anti_ideal, closeness


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

[docs]class TOPSIS(DecisionMaker): """TOPSIS is based on the concept that the chosen alternative should have the shortest geometric distance from the ideal solution and the longest euclidean distance from the worst solution. An assumption of TOPSIS is that the criteria are monotonically increasing or decreasing, and also allow trade-offs between criteria, where a poor result in one criterion can be negated by a good result in another criterion. Parameters ---------- mnorm : string, callable, optional (default="vector") 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_.closeness**: Array where the i-nth element represent the closenees of the i-nth alternative to ideal and worst solution. References ---------- .. [1] Yoon, K., & Hwang, C. L. (1981). Multiple attribute decision making: methods and applications. SPRINGER-VERLAG BERLIN AN. .. [2] TOPSIS. In Wikipedia, The Free Encyclopedia. Retrieved from https://en.wikipedia.org/wiki/TOPSIS .. [3] Tzeng, G. H., & Huang, J. J. (2011). Multiple attribute decision making: methods and applications. CRC press. """ def __init__(self, mnorm="vector", wnorm="sum"): super(TOPSIS, self).__init__(mnorm=mnorm, wnorm=wnorm)
[docs] @doc_inherit def solve(self, ndata): nmtx, ncriteria, nweights = ndata.mtx, ndata.criteria, ndata.weights rank, ideal, anti_ideal, closeness = topsis(nmtx, ncriteria, nweights) extra = { "ideal": ideal, "anti_ideal": anti_ideal, "closeness": closeness} return None, rank, extra