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Hybrid Fuzzy Sets, Hybrid Intuitionistic Fuzzy Sets and Their Applications in MCDM Using Information Imputation
V Lakshmana Gomathi Nayagam and Bharanidharan R
Zadeh introduced fuzzy sets to study imprecision in real life after which many variants of fuzzy sets have been developed in literature. In this paper, new variants of fuzzy sets named Hybrid fuzzy sets and Hybrid intuitionistic fuzzy sets have been defined based on some real life scenarios where conventional fuzzy sets are not applicable for dealing Multi-Criteria Decision Making (MCDM) problems. Further, total ordering algorithms on those proposed sets based on scoring functions are defined and applied in MCDM problems where decision matrix is incomplete with respect to some criteria. The major drawback of MCDM problems is non-availability / missing of data values for some alternatives with respect to some criteria while collecting data from the experts. To overcome this, researchers infuse the missing data for one expert from the corresponding data collected from the other expert or deleting that criteria to form a single complete MCDM table. But there are situations in which decisions should be taken with single MCDM matrix with missing data points. In this paper, we have proposed a new method in which we find the unknown data from known values / other entries of the table using relative performances of the alternatives with respect to other criteria through which we attain a ranking of the alternatives of MCDM using total ordering defined on the hybrid intuitionistic fuzzy sets. Further, we proposed another method in which we obtain the score of missing values based on the scores defined on the hybrid intuitionistic fuzzy sets through which final decision / ranking is made. Finally, the applicabilities of new types of fuzzy sets and total ordering methods are established in the field of Fuzzy decision making by comparing with existing imputation methods in the literature.
Keywords: Hybrid fuzzy sets, generalization of fuzzy sets, fuzzy information imputation, hybrid intuitionistic fuzzy sets