An improved TODIM method based on the hesitant fuzzy psychological distance measure
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ORIGINAL ARTICLE
An improved TODIM method based on the hesitant fuzzy psychological distance measure Chenyang Song1,2 · Zeshui Xu3 · Jian Hou1 Received: 9 January 2020 / Accepted: 21 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The distance measure plays an important role in the hesitant fuzzy theory. Experts always focus on the attributes aggregation of hesitant fuzzy information, ignoring the preference relationships between alternatives. Therefore, it is necessary to consider the competition effect between alternatives and develop a more suitable distance measure. Considering the background information of the connections and competitive relationships between different alternatives, the hesitant fuzzy psychological distance measure is proposed. Based on which, a novel similarity measure for hesitant fuzzy information is also developed. Next, an improved TODIM based on the hesitant fuzzy psychological distance measure is proposed for decision making problems. At last but not least, we apply the proposed improved TODIM to the application of the temporary rescue airport decision making problem of the Arctic Northwest Passage. The results demonstrate the advantages of the proposed method in decision making under the hesitant fuzzy environment. Keywords Hesitant fuzzy set · Psychological distance measure · TODIM · Decision making
1 Introduction The widespread uncertainty of practical problems brings more challenges for decision making. In many situations, it is difficult to depict the similar information and competitive relationship of alternatives, which surely influences the experts’ attitudes and evaluations [1]. The uncertain knowledge makes it difficult to provide a certain consensus of the relationships between alternatives with sound reliability. The hesitant fuzzy set (HFS) [2, 3] is an effective tool to manage the cognitive uncertainty more comprehensively, which has been applied widely in the fields of decision making [4–9],
* Zeshui Xu [email protected] Chenyang Song [email protected] Jian Hou [email protected] 1
Army Aviation Institute, Beijing 101100, China
2
Command and Control Engineering College, Army Engineering University of PLA, Nanjing 211101, China
3
Business School, Sichuan University, Chengdu 610064, China
risk evaluation [10], pattern recognition [11, 12] and so on. It is a set consisting of several possible memberships to remain the original information and preference as much as possible. With the increasing of uncertain information and knowledge, it is necessary to encompass the massive data and preference information into a single HFS [13], which also expands its efficiency and applications. Since the experts always make use of the distance to measure the similarity between alternatives, many different kinds of distance measures under the hesitant fuzzy environment have been proposed. Inspired by the famous Hamming distance and Euclidean distance, Xu [14] defined the normalized Hamming distance and Euclidean dist
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