Mathematical Problems in Engineering

Volume 2016, Article ID 5620803, 11 pages

http://dx.doi.org/10.1155/2016/5620803

## Hesitant Cloud Model and Its Application in the Risk Assessment of “The Twenty-First Century Maritime Silk Road”

^{1}PLA University of Science and Technology, Meteorological and Oceanographic Institution, Nanjing 211101, China^{2}Collaborative Innovation Center on Forecast Meteorological Disaster Warning and Assessment, Nanjing University of Information Science & Technology, Nanjing 210044, China^{3}Chengdu Military Area Command, Surveying and Mapping Information Center, Chengdu 610000, China

Received 9 November 2015; Accepted 8 March 2016

Academic Editor: Laura Gardini

Copyright © 2016 Lizhi Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The evaluation of human environment risk is lacking quantitative data, while the qualitative knowledge cannot be easily quantified and synthesized. Furthermore, sometimes the experts are not well acknowledged with the whole indicator system or cannot reach an agreement on the comments. The conventional evaluation methods are not competent to solve the above aporia effectively. Thus the quantization of the human environment risk becomes a conundrum. The compatibility cloud model theory can set up a conversion model between the qualitative knowledge and quantitative value, which provides technique approaches to evaluating the risk of human environment. However, the hesitant opinion of experts stemming from the missing knowledge of the whole system or the branching opinions cannot be well solved by the traditional compatibility cloud model theory. Therefore, this paper brings in the theory of hesitant fuzzy set, combining with the cloud model theory, to try to construct a hesitant cloud model to achieve the quantitative assessment of human environment risk. And at last an experiment evaluation on the risk of maritime silk road is carried out.

#### 1. Introduction

Human environment risk such as political risk can only get access to some paperwork when it is quantitatively evaluated. There is always plenty of useful information involving different aspects and levels in the miscellaneous paperwork. As a result, if there is no mapping model from qualitative data to quantitative value, the merging of this useful information will be extremely difficult. The earliest techniques to cope with the above conundrum are expert scoring method and analytic hierarchy process while they are always criticized owing to their grave subjectivity. For example, the distinctions between the values graded are totally decided by the subjective sense of experts; that is, a single value means different varying with different experts; like “0.8” may mean “very good” with expert A while it may mean “just good” with expert B. Therefore, to deal with such uncertainty in risk analysis and assessment process, Nishiwaki et al. [1] firstly propose the possible application of fuzzy set theory in risk assessment. After that, Pokorádi [2], Dutta and Ali [3], Arunraj et al. [4], and Chen et al. [5] have explored such application deeply. Expert can choose the mathematical form that represents his evaluation via establishing membership function based on the fuzzy set theory, which is more reasonable than expert scoring method and analytical hierarchy process. However, with there being no objective criterion and basis for the choosing of membership function, it is usually done with experts’ sense of subjectivity. Moreover, the uncertainty of language concept contains two facets virtually, fuzziness and randomness [6], while only the fuzziness of expert comments can be expressed by the application of fuzzy set theory in risk assessment.

To establish the mapping model from qualitative data to quantitative value and cope with both “fuzziness” and “randomness” in language, academician Li [7] has set up the compatibility cloud to construct the conversion model between the qualitative data and quantitative value, which promote the research about the relationship between the connotation and extension of the human cognition concept. After that, the cloud model theory has been more rich and perfect thanks to the work of the research team of Li [6, 8, 9]. Because of its advantage in dealing with the conversion between the qualitative data and quantitative value, the compatibility cloud model theory has been prevalent in artificial intelligence field.

However, two situations often occur in the course of evaluation as follows: (i) limiting the range of his professional knowledge and the understanding degree about the object, expert cannot make his comment on part of the indicators; for example, there are seven evaluation indicators for one object, but the expert can only make comments on five indicators. (ii) Because of the hesitation between two variant comments, an expert cannot make a single and certain comment on one object; for instance, the expert may give two comments on one indicator because of his consideration about its property lying between “medium” and “moderately good.” The traditional methods for evaluation are of single value. That is to say, one expert must make comments, respectively, on all indicators. Besides, in conventional ways, a compromise would be the choice in the process of dealing with multiexperts’ comments. Therefore the traditional methods cannot be a good solution to the above problem. As the development of fuzzy mathematics, Torra and Narukawa have proposed hesitant fuzzy sets in 2009, which is an expansion of the fuzzy sets theory. Several possible values are tolerated in the membership of a single element which is the core idea of it. Torra and Narukawa [10, 11] have defined the hesitant fuzzy set and some of its basic operations; Xu and Xia [12, 13], Zhu et al. [14], Chen and Xu [15], and González-Arteaga et al. [16] have done great effort to improve and perfect its system info; Rodríguez et al. [17, 18] have provided an overview of the current extensions of the theory and some of the most important trends or challenges that should be achieved in such topics. The two difficulties in the course of evaluation can be well solved by the application of hesitant fuzzy set. Therefore it is gradually introduced into the research field of decision-making in recent years [19–22].

To sum up, it is difficult to quantify the qualitative data in human environment risk assessment, due to the lack of a model to convert the comments of experts to quantitative value. Moreover, in the process of human environment risk assessment, the knowledge of experts is always not comprehensive, and the judgement of experts on one object is hesitant. In view of above problems, this paper will construct a hesitant cloud model based upon hesitant fuzzy set and cloud model theory to make assessment on human environment risk, and a proper example will be brought in to test the practicability of this model.

#### 2. Principle and Theoretical Basis of Method

##### 2.1. Cloud Model Theory

The uncertainty of linguistic atoms contains two characters—randomness and fuzziness [6]. However, only one character is involved in the existing mathematical methods, like the probability theory dealing with randomness and the fuzzy set disposing fuzziness. To quantitatively represent the linguistic terms and effectively integrate the fuzziness and randomness of a linguistic term in a unified way, academician Li [7] proposed the theory of membership cloud based on probability theory and fuzzy set, whose basic idea is to let be the set, , as the universe of discourse, and a linguistic term associated with . As is a random implementation of , the membership degree of in to the linguistic term , , is a random number with a stable tendency. takes the values in . A compatibility cloud is a mapping from the universe of discourse to the unit interval . That is,

Due to each being a cloud drop, the overall shape of clouds is the representative of linguist term. Figure 1 shows appropriate compatibility clouds for the linguistic terms “about 20” and “teenage” from the term-set of the linguistic variable “Age.”