Incomplete linguistic q-rung orthopair fuzzy preference relations and their application to multi-criteria decision making

Abstract

With the development of social and economic research, the judgements that people deal with are full of fuzziness and vagueness. It is convenient to use the linguistic q-rung orthopair fuzzy numbers to offer the qualitative uncertain information. Consequently, in this paper, we mainly study linguistic q-rung orthopair fuzzy preference relations (Lq-ROFPRs) and apply them to a multi-criteria decision-making (MCDM) problem. The multiplicative consistency of Lq-ROFPRs is first introduced, then a consistency-based model is established to derive the normalized linguistic q-rung orthopair fuzzy priority weight vector. The concept of acceptably multiplicative consistency is further defined, and an optimization model is formulated to repair the unacceptably multiplicative consistent Lq-ROFPR. To cope with the incomplete Lq-ROFPR, another programming model is built to ascertain the missing values. The weights of criteria are determined by constructing a possibility degree matrix. Subsequently, an MCDM problem with incomplete Lq-ROFPRs is considered and a step-by-step algorithm is put forward. Finally, the proposed method is applied to three examples, and the advantages of this new approach are also demonstrated.