Research On Multiple Attribute Decision Making Methods With Hesitant Fuzzy Information

With the rapid development of modern society, the real-life decision environment that the decision makers (DMs) are facing is more and more complicated. Due to the lack of their own knowledge and experience, the DMs often hesitate when they evaluate the real-life complex decision problems. To this end, hesitant fuzzy element (HFE) which is an effective tool to describe hesitant fuzzy decision information is often used by the DMs to express their hesitant preference information. Therefore, the main goal of this paper is to deeply investigate and explore the complex multiple attribute decision making (MADM) (including multiple attribute group decision making, MAGDM) problems with hesitant fuzzy information, the main work is summarized as follows:(1) Motivated by the idea of classical TOPSIS method, a novel hesitant fuzzy TOPSIS approach based on the maximizing deviation model is developed for solving the MADM problems in which the attribute values take the form of HFEs and the weights of attributes are completely unknown or partially known. Furthermore, the extended results of the proposed method in interval-valued hesitant fuzzy situations are also pointed out.(2) To handle the MADM problem with hesitant fuzzy information in case of considering the DM’s psychological behavior, a hesitant fuzzy TODIM method based on the new measured functions is developed. Some novel measured functions of HFEs and interval-valued HFEs as well as the corresponding comparison methods are also proposed.(3) The hesitant index of HFE is defined and some novel hesitant fuzzy distance measures are proposed. Besides, a signed distance-based comparison method of HFEs is developed. On the basis of these novel concepts, the hesitant fuzzy QUALIFLEX approach with a signed distance-based comparison method is developed for solving the MADM problems in which both the attribute values and the weights of attributes take the form of HFEs.(4) In order to tackle the MAGDM problems with incomplete weight information in which the attribute values are HFEs and all pair-wise comparison judgements over alternatives are represented by interval numbers, a hesitant fuzzy LINMAP approach based on interval programming model is developed. On the other hand, considering the decision situation that all pair-wise comparison judgements are also expressed by HFEs, the LINMAP-based hesitant fuzzy programming method is proposed.(5) A novel approach based on consistency maximization model is proposed to solve the real-life MAGDM problems in which the attribute values are HFEs and the weights of attributes are completely known but the weights of experts are partially known or completely unknown. Meanwhile, noticing the fact that in some real-life decision problems, such as the supplier selection problem, the manager of a firm can not only want to find the best suppliers but also want to identify their optimum order quantities, this approach further integrates the multi-choice goal programming model to determine the optimum order quantities.(6) A deviation modeling method is developed to deal with the heterogeneous MAGDM problems with incomplete weight information in which the decision information is expressed as real numbers, interval numbers, linguistic variables, intuitionistic fuzzy numbers, HFEs and hesitant fuzzy linguistic term sets, which enriches the heterogeneous MAGDM theory.