Abstract
Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a very common and useful method for solving multi-criteria decision making problems in certain and uncertain environments. Single valued neutrosophic hesitant fuzzy set (SVNHFS) and interval neutrosophic hesitant fuzzy set (INHFS) are developed on the integration of neutrosophic set and hesitant fuzzy set. In this paper, we extend TOPSIS method for multi-attribute decision making based on single valued neutrosophic hesitant fuzzy set and interval neutrosophic hesitant fuzzy set. Furthermore, we assume that the attribute weights are known, incompletely known or completely unknown. We establish two optimization models for SVNHFS and INHFS with the help of maximum deviation method. Finally, we provide two numerical examples to validate the proposed approach.
Highlights
Decision making is a popular field of study in the areas of Operations Research, Management Science, Medical Science, Data Mining, etc
Single valued neutrosophic hesitant fuzzy set (SVNHFS) Ye (2015a) developed the method to find out the best alternative under single valued neutrosophic hesitant fuzzy environment, and Sahin and Liu (2017) proposed correlation coefficient of single valued neutrosophic hesitant fuzzy set for Multi-attribute decision making (MADM)
Neutrosophic hesitant fuzzy set is flexible to deal with imprecise, indeterminate and incomplete information for MADM problems
Summary
Decision making is a popular field of study in the areas of Operations Research, Management Science, Medical Science, Data Mining, etc. Joshi and Kumar (2016) introduced Choquet integral based TOPSIS method for multi-criteria group decision making with interval valued intuitionistic hesitant fuzzy set. Hesitant fuzzy set can not present inconsistent, imprecise, inappropriate and incomplete information because the set has only truth hesitant membership degree to express any element to the set To handle this problem, Ye (2015b) introduced single valued neutrosophic hesitant fuzzy sets (SVNHFS) which have three hesitant membership functions – truth membership, indeterminacy membership and falsity membership functions. We observe that the TOPSIS method has not been studied earlier under SVNHFS as well as INHFS environment for solving MADM problems, when the weight information of the attribute is incompletely known or completely unknown.
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