Cognitive fuzzy sets for decision making

The intuitionistic fuzzy set (IFS) is useful in information expression but the cognitive overlap of people might cause the situation where the membership degree plus non-membership degree is greater than 1. The linear programming techniques for multidimensional analysis of preference (LINMAP) method is a well-known decision-making approach but little research focused on the interactive multiple criteria decision making (MCDM) problems within the LINMAP framework. This paper aims to propose a cognitive fuzzy set (CFS) to overcome the drawbacks of IFSs, and then develop an interactive cognitive fuzzy LINMAP (CF-LINMAP) method. To achieve these goals, the joint degree, which is caused by the cognitive overlap, of an IFS is interpreted, and then the concept of the CFS is proposed. We define the distance measure and comparison of CFSs, based on which, the cognitive fuzzy consistency and inconsistency indexes are calculated. The irrational index, which represents the irrational degree of experts, is introduced to improve the consistency and inconsistency indexes at each decision-making stage. Afterwards, an interactive CF-LINMAP method is proposed to deal with MCDM problems. An illustration concerning the hospital internal supply chain selection is given to show the applicability of the interactive CF-LINMAP method. Finally, the sensitivity analysis is done to demonstrate the reliability of the results. (C) 2020 Elsevier B.V. All rights reserved.