Proposition of NON-probabilistic entropy as reliability index for decision making

After the definition of probabilistic entropy proposed by Shannon, many other authors have adapted this theory to the domain of the non-probabilistic entropy and the fuzzy sets towards the fuzzy entropy theory. The main goal of the fuzzy entropy is to provide an index so that the fuzzy degree (fuzziness) of a non-probabilistic set could be quantified. The mathematical expression proposed by DeLuca and Termini for the calculation of the concept of fuzziness was based in that also proposed by Shannon since it is considered as a reference in the domain of uncertainty measure and information. However, other function families have been introduced as measures of uncertainty not only in the classic concept of information theory but also in other areas like decision making and model recognition. The fuzziness indexes are widely used with great relevance in the field of uncertainty management applied to complex systems. Most of those indexes are proposed in decision-making theory so as to discern between two exclusive choices. We proposed in this paper an index that could express the reliability of making a decision taking in account the information provided by a non-probabilistic set of alternatives.