An extension of grey relational analysis for interval-valued fuzzy soft sets

Abstract

Background: Neither any analytical (nor numerical) nor any statistical approach is often helpful in a situation where every person has his/her own choice. To cope with such situations usually we have to use fuzzy sets in combination with soft sets, which consist of predicates and approximate value sets as their images. Material: Choice values and comparison table techniques are two common decision-making techniques, which often don’t result in same preference order or optimal choice. To overcome this kind of situation in decision-making problems, grey relational analysis method is used to get on a final decision. Method: Here we have used grey relational analysis method involving “interval-valued fuzzy soft sets” and “AND operation” to deal with such kind of problems. Our approach is also a correction to the method used by Kong et al.(1), where the Uni-Int technique is incorrectly used in case of soft sets instead of fuzzy soft sets. Result: The proposed method is effective in seeking an optimal choice in the case when common decision-making techniques fail to get on a final decision. Conclusion: By using grey relational analysis, a suitable method to choose one object from different choices has been proposed. It overcomes the grayness in decision-making problems for getting on a final decision when one gets too many options and finds it difficult to choose an optimal choice. Keywords: Fuzzy soft set; Grey relational analysis; Un-Int; interval-valued fuzzy soft set