4. Hesitant Fuzzy Multiple Criteria Decision Analysis Based on LINMAP

The LINMAP technique is one of the most representative methods for handling the MCDM or MCGDM problems with respect to the preference information over alternatives. This chapter utilizes the main structure of LINMAP to develop the hesitant fuzzy group LINMAP technique with interval programming model and the hesitant fuzzy programming model-based LINMAP technique. The former is mainly used to solve the MCGDM problems in which the ratings of alternatives with respect to criteria are taken as HFEs, and all pair-wise comparison judgments are represented by interval numbers. While the latter is mainly utilized to address the MCDM problems with incomplete weight information in which the ratings of alternatives with each criterion are taken as HFEs and the incomplete judgments on pair-wise comparisons of alternatives with hesitant degrees are also represented by HFEs. The main contributions of this chapter are that (1) the developed techniques not only can take sufficiently into account the experts’ hesitancy in expressing their assessment information for criteria values by using HFEs but also can simultaneously consider the uncertainty of preference information over alternatives by using interval numbers or HFEs; (2) the concept of hesitant fuzzy programming model in which both the objective function and the constraints’ coefficients take the form of HFEs has been proposed, and an effective technique to solve this sort of model is developed; (3) the bi-objective programming model has been constructed to address the issues of incomplete and inconsistent weights of the criteria.