Since the Analytic network process (ANP) is much more flexible than the analytic hierarchy process (AHP) in handling the multiple criteria decision making (MCDM) problems in which the criteria or sub-criteria are interdependent, it has attracted many scholars’ attention and has been applied into many different areas. Given the powerfulness of intuitionistic fuzzy set in representing positive, negative and indeterminate information, this paper investigates the ANP framework for the MCDM problems in which all the pairwise comparison judgment information over the objects are represented by intuitionistic fuzzy numbers. We first justify the way to decompose the MCDM problem into a holarchy and network structure, based on which, the intuitionistic fuzzy preference relations (IFPRs) can be constructed through pairwise comparisons over the goals, criteria, clusters as well as the elements. Considering that not all the IFPRs are consistent, we then propose a new method to derive the priorities from the IFPRs no matter the IFPRs are consistent or not. After that, we address the way to construct the supermatrix for those interdependent elements. The complete algorithm of intuitionistic fuzzy ANP (IFANP) is given and illustrated by a flow chart. To show the applicability and efficiency of the IFANP, we implement the method to a case study concerning the brand management of the six golden flowers of Sichuan liquor. Some comparative analyses are given to clarify the advantages and invalidation of the IFANP.

In practice, the judgments of decision-makers are often uncertain and thus cannot be represented by accurate values. In this study, the opinions of decision-makers are collected based on grey linguistic variables and the data retains the grey nature throughout all the decision-making process. A grey best-worst method (GBWM) is developed for multiple experts multiple criteria decision-making problems that can employ grey linguistic variables as input data to cover uncertainty. An example is solved by the GBWM and then a sensitivity analysis is done to show the robustness of the method. Comparative analyses verify the validity and advantages of the GBWM.

Analytic Hierarchy Process (AHP), as one of the most important methods to tackle multiple criteria decision-making problems, has achieved much success over the past several decades. Given that linguistic expressions are much closer than numerical values or single linguistic terms to human way of thinking and cognition, this paper investigates the AHP with comparative linguistic expressions. After providing the snapshot of classical AHP and its fuzzy extensions, we propose the framework of hesitant fuzzy linguistic AHP, which shows how to yield a decision for qualitative decision-making problems with complex linguistic expressions. Firstly, the comparative linguistic expressions over criteria or alternatives are transformed into hesitant fuzzy linguistic elements and then the Hesitant Fuzzy Linguistic Preference Relations (HFLPRs) are constructed. Considering that HFLPRs may be inconsistent, we conduct consistency checking and improving processes after obtaining priorities from the HFLPRs based on a linear programming method. Regarding the consistency-improving process, we develop a new way to establish the perfectly consistent HFLPR. The procedure of the hesitant fuzzy linguistic AHP is given in stepwise. Finally, a numerical example concerning the used-car management in “lemon” market is given to illustrate the efficiency of the proposed hesitant fuzzy linguistic AHP method.