An extension of the new objective weight assessment methods CILOS and IDOCRIW to fuzzy MCDM

Abstract

Weights of criteria are playing a significant role in the wide range of MCDM (multiple criteria decision making) evaluation models. Results of evaluation significantly depend on magnitudes of weights as they proportionally transmit importance of each criterion to the final result of evaluation along with values of criteria placed in the decision matrix. There are two broad categories of methods for eliciting weights of criteria, subjective and objective. The former methods are based on opinions of experts, while the latter group of methods reflects the structure of data. The entropy method can be found within the most popular group of objective methods; it reflects the degree of diversification among values of criteria. Shortcomings of the entropy method are explained in the paper, especially the ones that are arising in the way of its extension to fuzzy MCDM. The authors propose extension of the earlier introduced criterion impact loss (CILOS) method to fuzzy MCDM that mitigate some shortcomings of the entropy. The latter method is based on the losses of values of criteria comparing to the ones that belong to the alternative with the best values. In the paper extension FIDOCRIW (Fuzzy Integrated Determination of Objective CRIteria Weights ) of the combination of both above-mentioned methods, entropy and CILOS, to fuzzy MCDM is proposed. Obstacles related to such extension are outlined and described. The paper provides a detailed explanation of the obstacles of extending the methods to fuzzy MCDM. Proposed in the paper FIDOCRIW method retains idea of the IDOCRIW method of combining the entropy with CILOS method. In contrast, the FIDOCRIW processes fuzzy numbers instead of real ones. This comprises uncertainty of data. The method allows to fully retain the fuzzy structure of the decision matrix along the full framework of the method. Resulting fuzzy weights allow to use the full scope of fuzzy MCDM methods, e.g. to comprise FIDOCRIW fuzzy weights with the fuzzy data that describe alternatives. Thus evaluation of alternatives in the environment with a degree of uncertainty can be performed.