Generalized intuitionistic fuzzy soft sets with applications in decision-making

• Intuitionistic fuzzy soft sets are generalized with the inclusion of moderator's opinion about the original evaluation.
• The properties and operations for Generalized intuitionistic fuzzy soft set (GIFSS) are presented.
• The notion of generalized intuitionistic fuzzy soft relations is devised.
• A score function and similarity relation for GIFSS are proposed.
• We show the application of GIFSS in real supplier selection and medical diagnosis problems.

The concept of intuitionistic fuzzy soft set (IFSS) arising from intuitionistic fuzzy set (IFS) is generalized by including a parameter reflecting a moderator's opinion about the validity of the information provided. The resulting generalized intuitionistic fuzzy soft set (GIFSS) finds a special role in the decision making applications. It can evaluate the given criteria along with the moderator's assessment of the furnished data. The properties of GIFSS are investigated and the associated relations called generalized intuitionistic fuzzy soft relations (GIFSR) are given. A similarity measure is given to compare two GIFSSs. As this is not applicable to fuzzy numbers, a new score function is devised to compare two intuitionistic fuzzy numbers (IFNs), the components of IFS. The effectiveness of the proposed GIFSS in decision making is demonstrated on four case studies.