Distance and distance induced intuitionistic entropy of generalized intuitionistic fuzzy soft sets

This paper examines the generalized intuitionistic fuzzy soft set (GIFSS) model which is an intuitively straightforward extension of the intuitionistic fuzzy soft set (IFSS) model. This concept which arises from IFSSs, is generalized by including a moderator’s opinion regarding the validity of the information at hand, thus making it highly suitable for use in decision-making problems that involve uncertain, vague and/or unreliable data. In this paper, we introduce the tools that measure the distance, similarity and the degree of fuzziness of GIFSSs. The axiomatic definitions of the distance measure is introduced and subsequently used to define the similarity measure and intuitionistic entropy induced by this distance measure. Some of the algebraic properties of these measures are also verified. The well-known Hamming, normalized Hamming, Euclidean and normalized Euclidean distances are generalized to make them compatible with the concept of GIFSSs. Subsequently, some relations among these information measures are proposed and verified. These results indicate how these measures are related and how they can be deduced from one another. Finally, we demonstrate the application of the information measure between GIFSSs by applying it to a case study related to the moderation of school-based assessment components of students in externally accredited academic programs.