Information Fusion 48 (2019) 39–54 Contents lists available at ScienceDirect Information Fusion journal homepage: www.elsevier.com/locate/inffus Score-HeDLiSF: A score function of hesitant fuzzy linguistic term set based on hesitant degrees and linguistic scale functions: An application to unbalanced hesitant fuzzy linguistic MULTIMOORA Huchang Liao a,b , Rui Qin a , Chenyuan Gao a , Xingli Wu a,∗ , Arian Hafezalkotob b , Francisco Herrera b,c a Business School, Sichuan University, Chengdu 610064, China b Andalusian Research Institute on Data Science and Computational Intelligence (DaSCI), University of Granada, Granada 18071, Spain c Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, Saudi Arabia a r t i c l e i n f o Keywords: Multiple criteria decision analysis Hesitant fuzzy linguistic term set Score function Hesitant degree Unbalanced HFL-MULTIMOORA Bicycle-sharing service a b s t r a c t The Hesitant Fuzzy Linguistic Term Set (HFLTS) is a powerful tool to depict experts’ cognitive complex linguistic information. This paper aims to propose a new score function of HFLTS to eliminate the defects of the subscript- based operations on HFLTSs. Hesitant degree is an intrinsic feature of HFLTS, and the greater the hesitant degree is, the lower the quality of the HFLTS will be. The asymmetric and non-uniform distributed linguistic term set is commonly used when expressing cognitive complex linguistic information. Considering both the hesitant degrees and the unbalanced linguistic terms in evaluations, a new score function of HFLTS, named the Score-HeDLiSF, is proposed based on the psychology of experts. The Score-HeDLiSF shows many advantages over the existing score function of HFLTS in terms of representing both the balanced and unbalanced linguistic information with hesitant degree and linguistic scale functions. Afterward, a hesitant degree-based weighting method is proposed to determine the weights of experts and criteria. To derive robust decision results, the MULTIMOORA method is improved by integrating the ORESTE method, and then we extend it to the unbalanced hesitant fuzzy linguistic context based on the introduced score function of HFLTS. Finally, an investment problem regarding the shared bicycles is solved by the proposed unbalanced HFL-MULTIMOORA method. The advantages of the unbalanced HFL-MULTIMOORA are highlighted by comparative analyses with two well-known multi-criteria decision-making methods. 1. Introduction A Multi-Experts Multi-Criteria Decision-Making (MEMCDM) prob- lem mainly includes two solution processes: (1) evaluating the per- formance of each alternative under different criteria and establishing the decision matrix; (2) aggregating the evaluations of each alternative and ranking the alternatives. When experts evaluate the performance of an alternative (criterion) based on their knowledge and experience for decision-making problems, their cognition usually cannot be quantified, but can be expressed in linguistic terms, such as “fast” spread, “extremely bad” quality and “very beautiful” appearance. How to represent experts’ linguistic evaluations exactly and make operations on these evaluation values are fundamental issues for decision-making. Zadeh [1] proposed the fuzzy linguistic approach, in which the evaluations are taken as lin- guistic terms rather than crisp numbers, to make linguistic evaluations ∗ Correspondence author. E-mail addresses: liaohuchang@163.com (H. Liao), 2631616499@qq.com (R. Qin), 1354992097@qq.com (C. Gao), xingliwusly@foxmail.com (X. Wu), hafez@correo.ugr.es (A. Hafezalkotob), herrera@decsai.ugr.es (F. Herrera). standardized, and introduced the model of computing with words to operate the linguistic terms. The traditional fuzzy linguistic approach is limited in dealing with complex linguistic evaluations since experts can only use singleton lin- guistic terms to make judgments. Due to the uncertainty of expert’s thinking and the complexity of subjective things, there are rich and com- plex linguistic evaluations such as “between good and very good”, “at least bad” and “more than high”. To respond to all possible linguistic expres- sions of experts completely, Rodríguez et al. [2] presented the concept of Hesitant Fuzzy Linguistic Term Set (HFLTS) which shows that the value of a linguistic variable is an ordered and continuous subset in a Linguistic Term Set (LTS). Later, Liao et al. [3] introduced the mathe- matical definition of HFLTSs and called the elements of the HFLTS as the Hesitant Fuzzy Linguistic Elements (HFLEs). The HFLTS is effective to describe both simple and complex linguistic evaluations. The HFLTS has https://doi.org/10.1016/j.inffus.2018.08.006 Received 28 May 2018; Received in revised form 17 August 2018; Accepted 20 August 2018 Available online 22 August 2018 1566-2535/© 2018 Published by Elsevier B.V.