Intuitionistic fuzzy variables: Concepts and applications in decision making

The present paper aims at advancing the well-recognized uncertainty theory built upon the credibility measure. In face of the increasing level of uncertainty embedded within the real world problem solving, it is discovered that the fuzzy variables defined in the credibility space are far from adequate to reflect the hesitance incurred during decision making. Although more complex fuzzy quantities are introduced, such as the fuzzy possibility space based type-2 fuzzy variables, the area of intuitionistic fuzzy variables is still a largely unexplored territory. Therefore, a novel concept of intuitionistic fuzzy variable is introduced hereby as an attempt to extend the uncertainty theory, which possesses a decent self-dual property compared with the fuzzy set theory. Unlike the intuitionistic fuzzy set theory, which has been widely implemented in various application fields, the intuitionistic fuzzy variables have hardly been employed in practices, especially the decision making sector. To bridge the gap, three outranking methods are developed to help evaluate intuitionistic fuzzy variables. The sufficient conditions of the three methods in distinguishing different fuzzy variables are also proved in the present work. The benefits of ranking with the three methods include the minimum amount of defuzzification, which prevents the information loss to a significant extent. Furthermore, in order to validate the proposed methods, a numerical study is performed. And the consistency of the ranking outputs from the three proposed methods is analyzed afterward. Besides, several managerial insights are presented regarding the sensitivity analysis of each ranking method.