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The Application of Probabilistic Hesitation Fuzzy Lingustic in Urban Livability

With the continuous improvement of residents' living conditions and the improvement of spiritual civilization construction, urban livability has become the focus of attention of the government and urban residents, as well as a hot topic of research by experts and scholars at home and abroad. How to choose a suitable city to live in has become a group decision-making (GDM) problem that we have to deal with. However, the changeable decision environment leads to the fact that the decision information of the above GDM problem cannot be expressed by traditional display values. Therefore, we choose the probabilistic hesitation fuzzy linguistic term set (PHFLTS) and then study the consensus among preference relations (PRs). This paper will study the group consensus model based on PHFLTS. At present, it has been studied in supply chain management, public opinion prediction and other fields. This paper first defines the concept of PHFLTS and distance measure, then defines the similarity measure and the consistency index (CI) based on the distance measure, constructs the group consensus level (GCI), can express the uncertain preference information given by the decision maker more comprehensively. Finally, specific example is given to rank the cities and the future research direction is prospected.


Introduction
From slash-and-burn in the primitive society to the interconnection of everything in the information society, human beings have put forward higher and higher requirements for the livability of their gathering areas. As a symbol of carrying modern civilization, cities have highly developed secondary and tertiary industries. The development of these industries not only promotes human progress, but also inevitably tests the carrying capacity of urban environment: the one-sided pursuit of rapid industrial development, the extreme exploitation of natural resources, the urban environment level gradually deteriorated; With the continuous progress of urbanization, resulting in chaos of urban order and insufficient public resources [1] [1]. How to balance the contradiction between livability of cities and development pains is related to the effect of ecological civilization construction. A convenient and accurate assessment is needed to compare and evaluate the trend of sustainable performance of urban construction environment, so as to help people make decisions [2]. In group decision making, the personal preference and environmental factors such as the complex decision-making, decision makers often have different evaluation results, so according to the evaluation results of group decision makers are satisfied results of the ranking, need to consider whether or not the decision makers in a certain extent, reached the consensus level, so the consensus model was an important research field of group decision. probabilistic hesitant fuzzy preference relation (PHFPRs) improves the flexibility and richness of linguistic information expression. At present, many researches have focused on the consensus measures and consensus improvement methods of GDM, but some researches only consider the consensus measures and consider the consensus improvement methods. For example, Zhang et al. [3] proposed consensus measures based on allocation assessment without considering consensus improvement methods. In addition, most scholars divide GDM process into two processes [4]. In the process of reaching consensus, few papers consider consistency criteria before measuring the degree of consensus of the panel. For example, the consensus reaching process proposed by Garcia et al. [5] follows two important criteria, without considering the consistency of preference relations. This paper Taking four cities in Anhui province as examples and proposes a probabilistic hesitation based fuzzy linguistic evaluation method. This paper first defines the distance formula of the PHFPRs matrix, then defines the consensus measure of the PHFPRs matrix based on the distance formula, the consensus model is established and the livability of the four cities is ranked according to the score function, and finally gives a concrete example for verification.

Preliminaries
This section introduces the concept of PHFLTS and the concept of PHFPRs matrix. .

Group Consensus Description of Probabilistic Hesitant Fuzzy Linguistic
In this section, several distance formulas of the term set of probabilistic hesitant fuzzy linguistic are introduced. After completing the probabilistic information, another important consideration should be taken into account: given any two PHFE's, in most cases they tend to be of different lengths. In other words, two PHFE have different numbers of members, which may cause some difficulty in the calculation. This method does not change the properties of primary PHFE by using the model [8] and recording the probability of newly added fuzzy hesitating elements as 0.

Example Description
With the continuous improvement of residents' living conditions and the improvement of spiritual civilization construction, urban livability has become the focus of attention of the government and urban residents, as well as a hot topic of research by experts and scholars at home and abroad. Based on the availability of references and data, this paper selects four indicators The following algorithm steps are proposed.
Step 2: Use model [8] [7] And the probability of the new fuzzy hesitant element is recorded as 0, and the normalization probability hesitant fuzzy preference relation (NPHFLRPs) matrix   1,2,3 p Hp  is obtained.
Step 3: Calculate CI and GCI by using formula (1)(2)(3). If the calculated GCI is less than the GCI , Then perform step 4, and end otherwise.
Step 4: Use the preset consensus model [8] adjusts the matrix and performs the step 3 after adjustment.

 
, data can be obtained as shown in table 1, According to Figure ,

Comparative Analysis
Compared with literature [1], this paper cites probabilistic hesitation fuzzy linguistic. The method proposed in literature [9,10] only takes into account the consensus of HFLPRs and ignores the process of consistency check, which is improved in this paper by taking consistency check into consideration. Compared with literature [7] [8], this paper adds probability value for each membership degree on its basis, which can reflect expert preference and prevent information loss.

Conclusion
It can be concluded from the case that Hefei city of Anhui Province has the best livability. In this paper, the group consistency problem of decision matrix in probabilistic hesitation fuzzy linguistic is studied. Based on the newly defined distance measure, the group consensus measure, similarity measure and consistency index formula of probabilistic hesitation fuzzy language decision matrix are proposed, and these formulas are applied to group decision problems. We apply this algorithm to the actual GDM problems, and help people to choose suitable cities to live in. Finally, the influence of each parameter on the GCI is analyzed. In the following research, the concept of multi-granularity can be introduced into the model to explore more reasonable methods.