Methods for Solving Decision Making Problems Under Neutrosophic Environment

Abstract

Multiple-criteria decision-making (MCDM) problems are the imperative part of modern decision theory where a set of alternatives has to be assessed against the multiple influential attributes before the best alternative is selected. In a decision-making (DM) process, an important problem is how to express the preference value. Due to the increasing complexity of the socioeconomic environment and the lack of knowledge or the data about the DM problems, it is difficult for the decision maker to give the exact decision as there is always an imprecise, vague or uncertain information. To deal with this, the theory of the fuzzy sets (FSs) or its extensions such as intuitionistic fuzzy sets (IFSs), interval-valued intuitionistic fuzzy sets (IVIFSs), type-2 fuzzy sets (T2FSs), etc., are widely used by the researchers so as to minimize the uncertainty level. During the last decades, the researchers are paying more attention to these theories and have successfully applied it to the various situations in the DM process. Nevertheless, neither the FS nor IFS theory is able to deal with indeterminate and inconsistent information. For instance, we take a person giving their opinion about an object with 0.5 being the possibility that the statement is true, 0.7 is the possibility that the statement is false and 0.2 being the possibility that he or she is not sure. To resolve this, Smarandache in 1998, introduced a new component called the ``indeterminacy-membership function' and added the ``truth membership function' and ``falsity membership function', all which are independent components lying in ] 0^-, 1^+ [, and hence the corresponding set is known as a neutrosophic set (NS), which is the generalization of the IFS and FS. However, without specification, NSs are difficult to apply to real-life problems. Thus, a particular case of the NS called a single-valued NS (SVNS) and the interval neutrosophic set (INS) has been proposed by the researchers. After this pioneering work, researchers have been engaged in extensions and appli