Abstract
The linguistic interval-valued intuitionistic fuzzy (LIVIF) set is an efficient tool to represent data in the form of interval membership degrees in a qualitative rather than a quantitative manner. The LIVIF set combines the features of interval-valued intuitionistic fuzzy sets (IFSs) and the linguistic variables (LV) and hence provides more freedom to decision-makers. Under this environment, the main objective of this manuscript is to propose some new aggregation operators by capturing the prioritized relationship between the objects. For this, different weighted averaging and geometric aggregation operators are proposed in which preferences related to each object are expressed in terms of LIVIF numbers. Desirable properties of the proposed operators are studied. Further, a group decision-making (DM) approach is presented to solve the multi-attribute DM problems, and its efficiency has been verified with an illustrative example.
Highlights
Decision-making (DM) problems are the imperative part of modern decision theory, where a set of alternatives has to be assessed against multiple influential attributes before the best alternative is selected
interval-valued IFSs (IVIFSs) theory is a more efficient tool to deal with imprecise data, while the linguistic approach expresses the uncertainty in the qualitative aspect
By taking advantage of both, in this paper, LIVIFS is considered, which is the generalization of linguistic intuitionistic fuzzy set (LIFS) in which membership and non-membership degrees are represented by the interval-valued linguistic terms in order to better deal with fuzzy information under the qualitative aspect
Summary
Decision-making (DM) problems are the imperative part of modern decision theory, where a set of alternatives has to be assessed against multiple influential attributes before the best alternative is selected. Arora and Garg [34] presented prioritized averaging and geometric aggregation operators under intuitionistic fuzzy soft set information. Rani and Garg [35] presented power aggregation operators for the complex IFS As it is seen from the above study that LIFS theory is widely used by the researchers, due to the complexity of the DM problems, sometimes, decision-makers are not capable of providing their judgment in the form of crisp membership degrees (MDs) and non-membership degrees (NMDs). To provide more freedom to the decision-makers, Garg and Kumar [36] presented the concept of the linguistic interval-valued intuitionistic fuzzy (LIVIFS) set in which membership and non-membership degrees are represented by interval-valued linguistic terms.
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