Evaluation on connectivity of urban waterfront redevelopment under hesitant fuzzy linguistic environment

Ocean & Coastal Management 132 (2016) 101e110

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Evaluation on connectivity of urban waterfront redevelopment under hesitant fuzzy linguistic environment Ting Da a, *, Yejun Xu b a b

School of Landscape Architecture, Beijing Forestry University, Beijing, 100083, PR China Research Institute of Management Science, Business School, Hohai University, Nanjing 211100, PR China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 6 January 2016 Received in revised form 9 August 2016 Accepted 21 August 2016

“Connectivity” is the core planning strategy that is used to examine the features of functional and structural connections in urban waterfront redevelopment projects. According to SIA point of view, an index system of assessing urban waterfront redevelopment connectivity including 8 evaluation indexes is proposed from the hierarchy of ecological, social functional and contextual connections. In order to evaluate the connectivity of urban waterfront redevelopment, this paper proposes an interactive procedure for multi-attribute decision making under hesitant fuzzy linguistic environment, which allows the experts use several linguistic values to assess the connectivity index. A case study of typical redevelopment projects of Huangpu River Waterfront in Shanghai is analyzed to figure out the difference between landscape-restoration oriented projects and urban-exploitation projects. Theoretical analysis and computational results showed that the assessment index system is effective for measuring the social impacts generated by redeveloped projects. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Connectivity Social impact assessment (SIA) Urban waterfront redevelopment Hesitant fuzzy linguistic term set

1. Introduction Since 1992 United Nations Conference on Environment and Development has proposed a sustainable form of coastal development, the goals of coastal zone development projects and programs were translated into specific improvements in the bio-physical environment and those in the quality of life of human population (Olsen, 2003). Coastal zones are now viewed as the spatial and temporal context for jointly determined socio-economic and ecological systems on a co-evolutionary development path (Turner, 2000). Coastal zones are also looked as spatial unites (Portman et al., 2012), possessing unique flora and fauna, and providing human use of resources and habitation. The U.S. federal Coastal Zone Management Act (CZMA) of 1972 was put forward to provide a broad policy guidance to upgrade their capacity for coastal management. One of the five core objectives of CZMA was the revitalization of urban waterfronts (Hershman et al., 1999). In CZMA's definition of urban waterfront, it was referred to “any developed area that is densely populated and is being used for, or has been used for urban residential, recreational, commercial, shipping, or industrial purposes” (Goodwin, 1999). It suggested a broad concept of any shoreline adjacent to * Corresponding author. E-mail addresses: [email protected] (T. Da), [email protected] (Y. Xu). http://dx.doi.org/10.1016/j.ocecoaman.2016.08.014 0964-5691/© 2016 Elsevier Ltd. All rights reserved.

urban areas not only limited to marines but also to Great Lakes. It is clear that the concept of Urban Waterfront was defined from socioeconomic point of view, focusing on the use of the resources (wealth, creation) and habitation (quality of life aspects) in coastal zones. The urban waterfront studied in this paper is to base on CZMA's definition, which refers to the coastal urban areas adjacent to marine and estuaries. The revitalization of urban waterfront occurred mostly in those areas experiencing industrial changes (Hershman et al., 1999). Urban waterfront became a kind of transitional zone accompanied by social development. The purpose of urban waterfront revitalization is to establish a positive interaction between urban built-up area and nature water space (Hoyle, 2000), which was always looked as a problematic and controversial interface. In urban coastal area, it is necessary to set up a space for adaptation of multicultural collision and fusion to solve the conflicts and problems in urban development by functional conversion. According to policy guidance, the renaissance history in urban waterfront can be divided into 5 stages, namely reconstruction in 1950s, revitalization in 1960s, renewal in 1970s, redevelopment in 1980s and regeneration in 1990s (Roberts, 2000). Although the connotations of those ideals were different, the profound meaning of “connectivity” in urban waterfront redevelopment was widely accepted, which could promote the evolution of urban waterfront into a systematic and socialized space. Evaluations on connectivity

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were mainly focused on “landscape connectivity” to measure the stability and integrity of ecosystem in urban waterfront from an ecological point of view (Wu et al., 2000). However, researches on connectivity in urban waterfront as a planning strategy were mainly stayed on the qualitative description on its realization ways (Kunshan, 2006). There still lacks of assessment systems on implementation effects of urban waterfront redevelopment projects. “Landscape connectivity” could only represent the extent of the disturbances of human waterfront activity on natural environment, but could not measure the demands for social activities in urban waterfront. Therefore, it is necessary to establish a set of relatively standard assessment index system and method for urban waterfront redevelopment connectivity. Researches have been made to discuss the hierarchies and factor categories of assessment indexes in urban waterfront. Turner (2000) suggested an integrated assessment model for coastal systems including key environmental and socio-economic processes, which should contain three forms of sub-models: natural systems model, activity model and model with a valuation dimension. Da (2013) proposed an assessment index system of the threedimensional connectivity of urban waterfront redevelopment to evaluate the design level of redevelopment projects, which were ecological connection, social functional connection and contextual connection. The former one was set for evaluation of overall characteristics of coastal zone, while the later one was for single feature of waterfront assessment. Both of the hierarchy of assessment models had high coherence in natural environment, social function and valuation of urban waterfront. From the factor categories of assessment indexes point of view, Sairinen and Kumpulainen (2006) proposed an index system of urban waterfront plan based on social impact assessment. The index system was suggested to be divided into 4 categories, namely resources and identity, social status, access and activities as well as waterfront experience. Tang (2008) evaluated the factors of 46 California coastal zone land use plans, and proposed 4 categories of impact assessment, which were planning capacity, environmental sensitivity, public participation and contextual characteristics. Ali and Nawawi (2009) suggested that the conceptual framework of assessment might contain 6 index categories to figure out the characteristics of urban waterfront landscape, namely evaluating local identity, support activity, accessibility, open space, sustainable design and amenities. Although the studies have their own emphasis points, the indexes of assessment still could be summarized as 3 categories: characteristics of coastal environment, supportable social activities and cultural experience. From the methodology point of view, Hoyle and Wright (1999) proposed an evaluative framework for heritage-based revitalization in naval city ports, by means of semi-structured interviews, which offered a series of possible controversial propositions relating to the issues that researchers had great interests in. In order to avoid the distortion of the participants' intentions, further explanations of “agreement” or “disagreement” with the proposition might be given. To access the connectivity of urban waterfront redevelopment, the experts may use the linguistic variables. For example, to evaluate the environment safety, the experts may give his/her evaluation such as “high”, “very high” (Zadeh, 1975; Xu, 2009; Xu et al., 2013). However, there are some experts think environment safety is between “high” and “very high”, in such cases, the experts are hesitant about his evaluations, and which is called hesitant linguistic variable (Rodríguez et al., 2012a; Xu et al., 2015c). In order to deal with these situations, in this paper, we consider the multiple attribute decision making (MADM) problems, in which the information about attribute values is expressed in hesitant linguistic labels. MADM problem generally involves a set of m feasible

alternatives X ¼ fx1 ; x2 ; …; xm g, with respect to a set of n predefined attributes, C ¼ fc1 ; c2 ; :::; cn g. We establish a practical interactive procedure for selecting the most desirable alternative(s). The interactive process can be realized by giving and revising the satisfactory degrees of alternatives till an optimum satisfactory solution is achieved. In this paper, the evaluation index system and method for urban waterfront redevelopment proposed is based on the theory of social impact assessment. And the evaluation of this paper belongs to post-evaluation. The rest of the paper is organized as follows. Section 2 presents the evaluation index system based on social impact assessment. Section 3 gives some basic concepts of hesitant fuzzy linguistic sets. Section 4 develops an interactive procedure to solve the MADM problem under hesitant fuzzy linguistic environment. A case study on Huangpu River Waterfront redevelopment is provided in Section 5. Section 6 concludes the paper.

2. Assessment index system based on social impact assessment 2.1. Social impact assessment There isn't a uniform standard on Social Impact Assessment (SIA) until now. According to the definitions of Social Impact Assessment by International Association for Impact Assessment, as a prediction step in environmental assessment framework, Social Impact Assessment was originally the part of Environmental Impact Assessment (EIA)(Esteves et al., 2012). SIA is now thought as a process, assessing the social consequence of planned interventions (projects) or events, analyzing positive or negative social impacts carried by projects (IAIA2003)(Esteves et al., 2012), and developing strategies for monitoring and managing impacts. Social impacts have broad contextual features that represent complex social relations and dynamics. It is believed that there is no distinction between social change process and social impact (Vanclay, 2002). Social impacts are related to the change of local social context, such as the transition of cultural, political, economic and historic of the community. Social changes are also seen as the result of proposed policies, plans and projects. Direct social impacts are result from social change process, and indirect social impacts are the result of biophysical environment change. The goal of social impact assessment is to make better understand of social consequences for social changes, and to provide critical inputs for impact prediction (Burdge, 2003). Thus, to some extent, Social Impact Assessment is to examine the ecological, economic (Thabrew et al., 2009) and cultural (Slootweg et al., 2001) values of projects from social point of view. Urban waterfronts are always considered as one of strategic areas in urban development. The transformation and regeneration of urban waterfronts are related to the image of the city and the reshaping of green spaces in urban structure, which might cause direct or indirect influences on social equity for the distribution of shoreline resources for communities. Sairinen and Kumpulainen (2006) suggested that the social impact assessment of urban waterfront plans was to examine different ways of using and experiencing waterfronts by communities in order to make a good understanding on physical, recreational and cultural aspects of urban waterfront by planners and decision-makers. Hence, in a strict sense, evaluation on connectivity of urban waterfront belongs to the category of SIA. It is established to answer the questions about whether the connections are available for urban waterfront redevelopment projects (or plans), as well as to examine the features of social functions on functional and structural connectivity in projects of urban waterfront redevelopment.

T. Da, Y. Xu / Ocean & Coastal Management 132 (2016) 101e110

2.2. Assessment index system The establishment of evaluation index system of urban waterfront redevelopment connectivity is based on an analysis of earlier urban waterfront studies and SIA studies. According to the SIA point of view, the hierarchy of assessment index system of urban waterfront redevelopment connectivity can be divided into three levels, which are ecological connection, social functional connection and contextual connection. Ecological connection evaluates social role of ecological functions; social functional connection evaluates the role of social functions in physical space; and contextual connection evaluates the role of cultural function in spiritual space. The foundations of evaluation factors of urban waterfront redevelopment connectivity proposed in this paper are the strategies of urban waterfront revitalization. In CZMA's literature, it can be seen that the goals of urban waterfront revitalization are focused on giving priority to water-depended industry, conserving historic sites and buildings, increasing public access, increasing public use, education, etc. In order to achieve the goals in urban waterfront revitalization, many programs and projects were carried out under the guidance of CZMA. Goodwin had summarized the planning strategies of the programs. He suggested that the planning strategies might be public access, marine activity, historical and cultural structures & sites conserved, clean-up and environmental restoration, and festival or maritime events (Goodwin, 1999). These strategies were proposed for increasing the diversity of social functions of urban waterfront redevelopment plans as well as protecting and promoting natural and historical environment in urban waterfront. Such achievement is endorsed in this paper. The evaluation system of urban waterfront redevelopment connectivity is as follows: 2.2.1. Hierarchy of ecological connection From an ecological point of view, the urban waterfront should be regarded as a riparian ecosystem located in the river ecosystem and terrestrial ecosystem communities coupling zone (Naiman et al., 2001). The ecological connection of urban waterfront is associated with species and flow characteristic. Considering that the urban waterfront is the joint action zone of nature and urban area (Sun and Wang, 2000), we believe that the meaning of ecological connection in urban waterfront not only is restricted to improving its ecosystem, but also includes all types of ecological functions for social activities in urban waterfront (Slootweg et al., 2001). The riparian ecosystem in urban waterfront has multi-functions such as agriculture, water transportation, recreation, balance of the nature water level variation and naturally scenic sightseeing. Since the mode of ecological connection and social-functional connection is changed with social values, the assessment of ecological connection should be stressed on the ecological characteristics of urban waterfront, especially focused on the social functions carried out by environmental background and ecological aesthetic features. Therefore, taking the environmental optimization & beautification and environmental safety as the evaluation indexes, as well as the environmental safety and ecological improvement as the basic premise of urban waterfront redevelopment, we can measure the supportable degree for social activities in waterfront by ecological connection. 2.2.2. Hierarchy of social functional connection In social functional level, the urban waterfront redevelopment is concerned with how to use the open space in urban waterfront to release people's mental pressure in high-density urban environment as well as to recreate and organize the public life in urban waterfront. Two typical different redevelopment modes are formed in urban waterfront redevelopment projects. One is for landscape-

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restoration oriented aiming to build the waterfront parks. The other one is for urban-exploitation oriented aiming to combine the functions of shopping, exhibition, conference, leisure, recreation, tourism, local office, residential, hotel and others into an integrated one by mixed development (Kunshan, 2006). It is thought that the diversification of function types in waterfront can bring about the variety of urban waterfront recreation. Although the two modes are totally different which present very different spatial forms, both of them take for improving the quality of space in waterfront. It is suggested that the redevelopment purpose can be reached by reasonable organization of social functions in urban waterfront to implement the complementary and extension of social functions between water and city. Therefore, the assessment criteria for both of them are unified. Sairinen and Kumpulainen (2006) proposed that the indexes of social impact assessment for urban waterfront redevelopment can be divided into four dimensions depending on different usage ways in urban waterfront, which were resources and identity, social status, access & activities, and waterfront experience. While Ali and Nawawi (2009) presented six social impact assessment indexes for urban waterfront landscape, namely local identity, support activity, accessibility, open space, sustainable design and amenities. Although scholars emphasized on different fields, it still can be seen from the researches that urban waterfront social status, accessibility and support activities are the key factors affecting social functions. Thus, the evaluation indexes of social functional connection should be stressed on the interpenetration of waterfront events and social life. The compatibility of social functions in waterfront community, accessibility and diversity of recreational activities are the evaluation indexes in this paper. 2.2.3. Hierarchy of contextual connection Contextual function is concerning with cultural interactions between residence and water which are hidden in the phenomena of a variety of constructions in urban waterfront. In context level, the contextual connection was established to reflect the continuity and succession of urban waterfront development (Zhou and Shen, 2011) and to increase the sense of place. The historical development and cultural cognition were taken as secondary indicators of contextual connection in Da and Xu (2014)'s research. Although the formal evaluation indicators could measure the historical context and cultural enlightenment functions to some extent, it is difficult to measure whether the evolutionary approach of historical development in site is clear and reasonable by those indicators since the complexity of original site type and contextual interpretation accompanied by the diversity of site transformation was not fully considered. Given that the cultural context has physical and non-physical characteristics, the evaluation of contextual connection should focus on the maintenance of sense of history and the establishment of authenticity in urban waterfront redevelopment. It is important to evaluate contextual connection by whether the original characteristics of site pattern is retained or restored, the buildings and structures with historic significance in site are retained or reproduced, and the traditional cultural activities are continued or not. We suggest that cultural cognition, sense of history and continuation of waterdependent activities are the evaluation indexes for contextual connection. By measuring the materiality characteristic of site pattern's historical context, the retention and reuse of buildings and structures, the perfect degree of landscape facilities and identification systems, as well as the active degree of non-physical waterfront activities, the connectivity in spiritual and cultural aspects for urban waterfront redevelopment could be measured. In summary, the evaluation indexes of urban waterfront redevelopment connectivity could be the eight ones, which are depicted in Table 1.

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T. Da, Y. Xu / Ocean & Coastal Management 132 (2016) 101e110

Table 1 The indexes of urban waterfront redevelopment connectivity. Index

Interpretation

Environmental optimization & beautification (c1) Environmental safety (c2) Compatibility of social functions in marine community (c3) Accessibility (c4) Diversity of recreational activities (c5) Cultural cognition (c6) Sense of history (c7) Continuation of water-dependent activities (c8)

The degree of helping to improve the waterfront environment in biodiversity, vegetation coverage, water system density, and environment beautification. The degree of helping to improve the environmental pollution, land deterioration, and water level adjustment. The degree of helping to improve social functions in marine community. The The The The The

degree degree degree degree degree

of of of of of

helping to improve accessibility and walking continuity. helping to conduct activities such as tourism, sightseeing, sports and etc. perfecting the interpretation system of spatial succession and natural evolution. retention and reproduction of the site pattern as well as the important buildings and structures. activities of formal maritime entertainment and cultural activities.

According to the interpretation of indexes, the evaluation indexes above are qualitative indexes. It is necessary to follow the expert's judgment of qualitative reviews for quantitative evaluation. The expert comment could be divided into 7 levels: perfect, very high, high, medium, low, very low, nothing. For example, the criteria of index (c1) are as follow (the rest criteria will not be given due to space limitation): “Perfect” means high vegetation coverage, rich species, high density of water network, high efficiency of ecological environment benefits, and most suitable for human waterfront recreation activities; “high” means relatively high vegetation coverage, abundant species, relatively high density of water network, relatively high efficiency of ecological environment benefits, and suitable for human waterfront recreation activities; “medium” means moderate vegetation coverage, relatively abundant species, general density of water network, general efficiency of ecological environment benefits, and the appearance of unsuitable factors for human waterfront recreation activities; “low” means polluted environment, poor condition, and poor environment for human waterfront recreation activities, “nothing” means that there is no way to take advantage of the waterfront green spaces and water bodies to carry out human waterfront recreation activities; and so on. 3. Hesitant fuzzy linguistic term sets In this section, we review some basic concepts of hesitant fuzzy linguistic term sets. We consider a finite and totally ordered linguistic term set S ¼ fs0 ; s1 ; …; sg g with odd cardinality and the midterm representing an assessment of “approximately 0.5”, and with the rest of the terms being placed symmetrically around it. For example, a set S of seven terms could be given as follows:

S ¼ fs0 ¼ nothing; s1 ¼ very low; s2 ¼ low; s3 ¼ medium; s4 ¼ high; s5 ¼ very high; s6 ¼ perfectg Moreover, it is usually required that the linguistic term set satisfies the following characteristics: (1) There is a negation operator: negðsi Þ ¼ sgi , where g þ 1 is the cardinality of the term set; (2) The set is ordered: si  sj ⇔i  j. (3) There exists a maximization operator: maxðsi ; sj Þ ¼ si , if sj  si ; (4) There exists as minimization operator: minðsi ; sj Þ ¼ si if si  sj . Xu (2005)
extended the discrete term set S to a continuous term set S ¼ fsi
i2½0; tg, where t (t > g)is a sufficiently large positive integer. If si 2S, then we call sa the original term, otherwise, we call

si the virtual term. Consider any two linguistic variables sa ; sb 2S and l2½0; 1, we define the following operational laws (Xu, 2004): (1) sa 4sb ¼ saþb ; (2) lsa ¼ sla :

Definition 1. (Xu, 2005). Let sa ; sb 2S be two linguistic variables, then the deviation degree between sa and sb is defined as follows:

 ja  b j  d sa ; sb ¼ g

(1)

whereg þ 1 is the number of linguistic terms in the set S. Due to the complexity of the real world decision making problems, it is often that decision makers hesitant among several linguistic terms to express their knowledge and they would like to use more than one linguistic term to express their opinions. In order to deal with these hesitant situations, Rodríguez et al. (2012b) introduced the concept of HFLTS which is based on hesitant fuzzy sets (Torra, 2010; Xia and Xu, 2011; Xu et al., 2015a, 2016). Definition 2. (Rodríguez et al., 2012b). Let S ¼ fs0 ; s1 ; …; sg g be a linguistic term set, a HFLTS hS is an ordered finite subset of the consecutive linguistic terms of S. Example 1. Let S ¼ fs0 ¼ nothing; s1 ¼ very low; s3 ¼ medium; s4 ¼ high; s5 ¼ very high; s6 ¼ perfectg be a linguistic term set, then h1 ¼ fmedium; highg ¼ fs3 ; s4 g; h2 ¼ fvery low; low; mediumg ¼ fs1 ; s2 ; s3 g, are two HFLTS on S. Definition 3. Let S ¼ fs0 ; s1 ; …; sg g be a linguistic term set, and h be an arbitrary HFLTS on S, then (1) The upper bound: hþ ¼ maxðsi Þ ¼ sj ; si 2h and si  sj , ci; (2) The lower bound: h ¼ minðsi Þ ¼ sj ; si 2h and si  sj , ci. From Example 1, we can see that different HFLTSs have different numbers of linguistic terms in most cases. In order to operate correctly when comparing two HFLTSs, Zhu and Xu (2014) introduced a method to add linguistic terms in a HFLTS. Definition 4. (Zhu and Xu, 2014). Assume a HFLTS h ¼ fhl jl ¼ 1; 2; …;#hg, where #h is the number of elements in the set h, let hþ and h be the maximum and minimum linguistic term in h respectively, and 2ð0  2  1Þ be an optimized parameter, then we can add the linguistic term

h ¼ 2hþ þ ð1  2Þh into the HFLTS.

(2)

T. Da, Y. Xu / Ocean & Coastal Management 132 (2016) 101e110

For any two HFLTSs h1 ¼ fsa1 ; sa2 ; …; san g and h2 ¼ fsb1 ; sb2 ; …; sbn g (suppose the number of each HFLTS's elements is the same), we can define three operations as follows: Definition 5. (Xu et al., 2015b). Let hi (#hi ¼ #h, for all i ¼ 1; 2; …; n) be a collection of HFLTSs, and let HFLWA: Un /U, if

HFLWAðh1 ; h2 ; …; hn Þ ¼ w1 h1 4w2 h2 4…4wn hn

(3)

then HFLWA is called a hesitant fuzzy linguistic weighted average (HFLWA) operator, where wi is the weighting vector of hi , P w ¼ ðw1 ; w2 ; …; wn ÞT with wi 2½0; 1 and ni¼1 wi ¼ 1; respectively.

2

h11 6 h21 H¼6 4 « hm1 where

105

3 h1n h2n 7 7 « 5 hmn

::: ::: 1 :::

h12 h22 « hm2



hij ¼ ∪s l 2hij fsdl

l ¼ 1; 2; …; #hij g(i ¼ 1; 2; …; m, d

j ¼ 1; 2;

ij

ij

…; n) is a HFLTS, denoting the degree that alternative xi satisfies the criterion cj . For each HFLTS hij , according to Definition 3, we can obtain the lower bound h ij ¼ minl¼1;…;#hij fsdl g and the upper bound ij

(1) (2) (3) (4) (5)

hþ ¼ maxl¼1;…;#hij fsdl g. Then, we define the positive ideal solution ij

empty HFLTS: hS ðsa Þ ¼ fg; full HFLTS: hS ðsa Þ ¼ S; lh1 ¼ fsla1 ; sla2 ; …; slan g; h1 4h2 ¼ fsa1 þb1 ; sa2 þb2 ; …; san þbn g; h1 4h2 ¼ h2 4h1 :

ij

(PIS) and the negative ideal solution (NIS) under hesitant fuzzy linguistic environment as follows:

Let S ¼ fs0 ; s1 ; …; sg g be a linguistic term set,

h1 ðxi Þ ¼ ∪s l 2h1 fsdl
l ¼ 1; 2; …; #h1 g (#h1 be the number of lind 1 1

guistic terms in h1 ) and h2 ðxi Þ ¼ ∪s l 2h2 fsdl
l ¼ 1; 2; …; #h2 g(#h2 d

2

2

be the number of linguistic terms in h2 ) be two HFLTSs on X ¼ fx1 ; x2 ; …; xn g, where #h1 ¼ #h2 ¼ L (otherwise, we can extend the shorter one by adding the linguistic terms by Eq. (2)). Suppose that the linguistic terms are arranged in ascending order, then the Hamming distance of h1 ðxi Þ and h2 ðxi Þ can be defined as:




l l
L
d  d
X 1 2 1 dðh1 ðxi Þ; h2 ðxi ÞÞ ¼ L g

o n þ þ hþ ¼ hþ ; h ; …; h n 1 2

(5)

o n   h ¼ h 1 ; h2 ; …; hn

(6)

where

hþ j ¼

8 max hþ ¼ > > i¼1;2;…;m ij > > < > > > > :

min

i¼1;2;…;m

h ij

max

i¼1;2;…;m l¼1;…;#hij

¼

min

  sdl

for benefit criterion cj

ij

i¼1;2;…;m l¼1;…;#hij

  sdl ij

; j ¼ 1; 2; …; n for cost criterion cj

(4)

(7)

l¼1

and Definition 6. For a HFLTS h ¼ fsdl jl ¼ 1; 2; …; #hg where #h is the P#h l 1 number of linguistic terms in h, hðhÞ ¼ #h d is called the score l¼1 function of h. For two HFLTS h1 and h2 , if hðh1 Þ > hðh2 Þ, then h1 > h2 ; if hðh1 Þ ¼ hðh2 Þ, then h1 ¼ h2 .

4. An interactive procedure for hesitant fuzzy linguistic MADM problems In the following, we represent the multiple attribute decision making problems under hesitant fuzzy linguistic environment. Let X ¼ fx1 ; x2 ; …; xm g be a discrete set of alternatives, C ¼ fc1 ; c2 ; …; cn g be a discrete set of attributes. Let w ¼ ðw1 ; w2 ; …; wn ÞT 2F be the weight vector of attributes, where P wj  0, j ¼ 1; 2; …; n, nj¼1 wj ¼ 1, F is the set of the known weight information, which can be constructed by the following forms (Park and Kim, 1997; Kim et al., 1999; Xu and Da, 2008): (1) (2) (3) (4) (5)

A weak ranking: fwi  wj g; A strict ranking: fwi  wj  ai g; A ranking with multiples: fwi  ai wj g; An interval form: fai  wi  ai þ εi g; A ranking of differences: fwi  wj  wk  wl g; for jsksl.

Let H ¼ ðhij Þmn be the hesitant fuzzy linguistic decision matrix, where hij is a HFLTS on S and represents the linguistic assessment provided by the decision maker for the alternative xi with respect to the criterion cj . The hesitant fuzzy decision matrix H can be written as:

h j ¼

8 min h ¼ ij > > i¼1;2;…;m > > < > > > > :

max hþ i¼1;2;…;m ij

¼

min

i¼1;2;…;m l¼1;…;#hij

max

i¼1;2;…;m l¼1;…;#hij

  sdl ij

  sdl ij

for benefit criterion cj ; j ¼ 1; 2; …; n for cost criterion cj (8)

Based on the hesitant fuzzy linguistic decision matrix H ¼ ðhij Þmn , the overall value of the alternative xj can be expressed as

zi ðwÞ ¼ w1 hi1 4w2 hi2 4…4wn hin ;

i ¼ 1; 2; …; m

(9)

It is obvious that the greater the value zi ðwÞ, the better the alternative xi is. Especially, we get the overall values corresponding the hesitant fuzzy linguistic ideal point and the hesitant fuzzy linguistic negative ideal point as follows, respectively: þ þ zþ ðwÞ ¼ w1 hþ 1 4w2 h2 4…4wn hn

(10)

  z ðwÞ ¼ w1 h 1 4w2 h2 4…4wn hn

(11)

dðzþ ðwÞ; z ðwÞÞ

By Eq. (4), we let be the distance between the overall value zi ðwÞ of the alternative xi and the overall value z ðwÞ corresponding to the hesitant fuzzy linguistic negative ideal point h , then the greater the value dðzþ ðwÞ; z ðwÞÞ, the better the alternative xi is. Definition 7. Let dðzþ ðwÞ; z ðwÞÞ be the distance between the overall value zþ ðwÞ corresponding to the hesitant fuzzy linguistic

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positive ideal point hþ and the overall value z ðwÞ corresponding to the hesitant fuzzy linguistic negative ideal point h , then we call

  d zi ðwÞ; z ðwÞ  d zþ ðwÞ; z ðwÞ

mðzi ðwÞÞ ¼ 

(12)

the satisfactory degree of the alternative xi . From Definition 7, we know that the satisfactory degree mðzi ðwÞÞ of the alternative xi is the ratio of the distance between the overall value zi ðwÞ of the alternative xi and the overall value z ðwÞ of the hesitant linguistic negative ideal point h to the distance between the overall value zþ ðwÞ of the hesitant fuzzy linguistic positive ideal point hþ and the overall value z ðwÞ of the hesitant fuzzy linguistic negative ideal point h . Obviously, the greater the distance between the overall value zi ðwÞ of the alternative xi and the overall value z ðwÞ of the hesitant fuzzy linguistic negative ideal point h , the higher the satisfactory degree mðzi ðwÞÞ of the alternative xi is, that is, the satisfactory degree mðzi ðwÞÞ of the alternative xi is a strictly monotone increasing function with respect to dðzþ ðwÞ; z ðwÞÞ. Therefore, the higher the satisfactory degree mðzi ðwÞÞ, the better the alternative xi is. As a result, we establish the following optimization model:

ðM  1Þ maxmðwÞ ¼ ðmðz1 ðwÞÞ; mðz2 ðwÞÞ; …; mðzm ðwÞÞÞ s:t: w2F n X wj  0; j ¼ 1; 2; …; n; wj ¼ 1:

5. A case study

j¼1

We can integrate the satisfactory degrees of all alternatives with the max-min operator proposed by, i.e., the optimization model is as follows:

ðM  2Þ max l s:t: mðzi ðwÞÞ  l; i ¼ 1; 2; …; m; w2F; n X wj  0; j ¼ 1; 2; …; n; wj ¼ 1 j¼1

where l ¼ min mðzi ðwÞÞ. i

By solving the model (M-2), we get the original optimal solution ð0Þ

ð0Þ

ð0Þ

wð0Þ ¼ ðw1 ; w2 ; …; wn ÞT , and then calculate the satisfactory degrees mðzi ðwð0Þ ÞÞ ði ¼ 1; 2; …; mÞ of the alternatives xi ði ¼ 1; 2; …; mÞ. The DMs then provide the lower bounds

lð0Þ ði ¼ 1; 2; …; mÞ of the satisfactory degrees of the alternatives xi j (i ¼ 1; 2; …; m) according to mðzi ðwð0Þ ÞÞ (i ¼ 1; 2; …; m) in the process. Then, we can get the new optimization model as follows:

ðM  3Þ

max J ¼

m P i¼1

s:t:

li

mðzi ðwÞÞ  li  lið0Þ ; i ¼ 1; 2; …; m w2F wj  0; j ¼ 1; 2; …; n;

n X

wj ¼ 1

j¼1

Calculating the model (M-3), then the DMs need to reconsider ð0Þ

Step 1. Extend the elements in the matrices by Eq. (2). Then the length of all hij will be the same, and we obtain the normalized hesitant decision matrix. Step 2. Utilize Eq. (5) and Eq. (7) to get the hesitant fuzzy linguistic positive ideal solution hþ and the hesitant fuzzy linguistic negative ideal solution h , respectively. Step 3. Utilize the model (M-2) to derive the original optimal ð0Þ ð0Þ ð0Þ solution wð0Þ ¼ ðw1 ; w2 ; …; wn ÞT , and then calculate the satisð0Þ factory degrees mðzi ðw ÞÞ(i ¼ 1; 2; …; m) of the alternatives xi ð0Þ (i ¼ 1; 2; …; m). The DMs give the lower bounds li (i ¼ 1; 2; …; m) of the satisfactory degrees of the alternatives according to the satisfactory degrees mðzi ðwð0Þ ÞÞ (i ¼ 1; 2; …; m). Let k ¼ 1. Step 4. Utilize the model (M-3) to derive the weight vector ð0Þ ð0Þ ð0Þ wð0Þ ¼ ðw1 ; w2 ; …; wn ÞT and calculate the satisfactory degrees mðzi ðwðkÞ ÞÞ (i ¼ 1; 2; …; m) of the alternatives xi (i ¼ 1; 2; …; m). Step 5. If the DMs are satisfied with the result obtained by Step 3, calculate the overall values zi ðwÞ(i ¼ 1; 2; …; m) of the alternatives xi (i ¼ 1; 2; …; m) by HFLWA operator Eq. (3), and go to next Step. If the DMs are not satisfied with the result, then the DM should increase the satisfactory degrees of some alternatives, and decrease the satisfactory degrees of some other alternatives. Let k ¼ k þ 1, and go to Step2. Step 6. Compute the score values hðzi Þ (i ¼ 1; 2; …; m) of alternatives xi (i ¼ 1; 2; …; m) by Definition 6. Step 7. Ranking the alternatives according to the score values hðzi Þ (i ¼ 1; 2; …; m).

the lower bounds li (i ¼ 1; 2; …; m) of the satisfactory degrees of the alternatives xi (i ¼ 1; 2; …; m) till getting the optimal solution if there exists no optimal solution. Based on the above interactive procedure, the algorithm and process of the multi-attribute group decision making problem under hesitant fuzzy linguistic environment is summarized as follows.

Since port opening in Shanghai, Huangpu River Waterfront has been closely linked to the development of urban space, which experienced the period of industry, warehousing, transportation occupying urban waterfront, and is moving to the age of financial and trade, tourism and cultural, ecology and residential. Huangpu River Waterfront redevelopment aims at achieving social functional transformation and urban scene enhancement by means of improving the environment and reconstructing the functions in urban waterfront, optimizing the space resources along the riverside, and improving the environment. Urban space of Shanghai is developing to a multi-center style at present. Many revitalization nodes are divided along the shoreline. By redeveloping those waterfront districts, the revitalization of shoreline space can be achieved, thus to undergo development of adjacent communities. Houtan Park, Bai Lianjin Park and Xu Jiahui Waterfront on the west side of Huangpu River are adjacent to the formal World Expo site. Under the World Expo drive, both of them are re-built through landscape restoration to improve ecology and social functions and to reconstruct public space in waterfront. However, the East Bund and North Bund on west side of Huangpu River were the cradle of modern industry and “the largest industrial zone of riverside” after 1950s. Although the sites are located in waterfront in city center and adjacent to the Bund, they have become the shanty area since the original industry declined. To meet the requirement of the development of international shipping industry, Oriental Fisherman's Wharf and Shanghai Port International Cruise Terminal are re-constructed through urban-exploitation. The riverside marina and complex buildings with functions such as exhibition, business, tourism service, restaurant and etc. are built to create public activity space, which can provide social functional support for surrounding upscale residential community and adjacent corporate headquarters and R & D base (See Fig. 1). Take five xi (i ¼ 1; 2; …; 5) typical redevelopment cases in Shanghai Huangpu River waterfront as research objects, where x1 ; x2 ; x3 ; x4 ; x5 represent Houtan Park, Bai Lianjin Park, Xu Jiahui Waterfront, Oriental Fisherman's Wharf and Shanghai Port

T. Da, Y. Xu / Ocean & Coastal Management 132 (2016) 101e110

International Cruise Terminal, respectively. Experts were chosen according to the need of evaluation issues. The invited experts came from different professional fields, including landscape architecture, architecture and urban planning. Landscape architects were good at eco-design. Architects had good knowledge of old building and facilities reuse and protection. While urban planners were expert in land-use and traffic organization. They had a wealth of experience in assessments. The expert evaluates these redevelopment cases using the linguistic term set S and provides the assessment information on alternatives x1 ; x2 ; x3 ; x4 ; x5 and criteria c1 ; c2 ; …; c8 (which is listed in Table 1), which is depicted in Table 2. In order to select the best alternative, we use the procedure proposed in Section 4. Suppose that the known weight information is as follows, which is offered by the experts in advance.

107

Fig. 1. Urban waterfront redevelopment projects sites in Huangpu River Waterfront, Shanghai.

F ¼ f0:08  w1  0:2; 0:1  w2  0:2; 0:08  w3  0:15; w4  1:5w3 ; w4  0:2; 0:05  w5  0:15; w6  0:12; w6  w7  0:05; w7  0:2; 0:1  w8  0:2g

Step 1. Extend the elements in the matrices by Eq. (2) until all the elements have the same length. Assume that 2 ¼ 1, then we get the following normalized decision matrix, which is listed in Table 3.

h ¼ ðfs2 g; fs3 g; fs3 g; fs3 g; fs0 g; fs1 g; fs0 g; fs1 gÞ Step 3. Utilize the model (M-2) to establish the following optimization model:

maxl s:t 1 11w1 þ 8w2 þ 3w3 þ 5w4 þ 12w5 þ 15w6 þ 17w7 þ 8w8 ,  l; 3 4w1 þ 3w2 þ 3w3 þ 2w4 þ 5w5 þ 5w6 þ 6w7 þ 3w8 1 6w1 þ 5w2 þ 2w3 þ 3w4 þ 8w5 þ 9w6 þ 14w7 þ 8w8 ,  l; 3 4w1 þ 3w2 þ 3w3 þ 2w4 þ 5w5 þ 5w6 þ 6w7 þ 3w8 1 5w1 þ 3w2 þ 5w3 þ 0w4 þ 3w5 þ 2w6 þ 3w7 þ 3w8 ,  l; 3 4w1 þ 3w2 þ 3w3 þ 2w4 þ 5w5 þ 5w6 þ 6w7 þ 3w8 1 3w1 þ 5w2 þ 6w3 þ 2w4 þ 11w5 þ 9w6 þ 2w7 þ 5w8 ,  l; 3 4w1 þ 3w2 þ 3w3 þ 2w4 þ 5w5 þ 5w6 þ 6w7 þ 3w8 1 8w1 þ 3w2 þ 3w3 þ 5w4 þ 14w5 þ 5w6 þ 6w7 þ 5w8 ,  l; 3 4w1 þ 3w2 þ 3w3 þ 2w4 þ 5w5 þ 5w6 þ 6w7 þ 3w8 0:08  w1  0:2; 0:1  w2  0:2; 0:08  w3  0:15; w4  1:5w3 ; w4  0:2; 0:05  w5  0:15; w6  0:12; w6  w7  0:05; w7  0:2; 0:1  w8  0:2; 8 P

wj ¼ 1;

wj  0;

j ¼ 1; 2; …; 8

j¼1

Step 2. By Eqs. (5)e(8), we get the hesitant fuzzy linguistic positive ideal solution hþ and the hesitant fuzzy linguistic negative ideal solution h as follows:

hþ ¼ ðfs6 g; fs6 g; fs6 g; fs5 g; fs5 g; fs6 g; fs6 g; fs4 gÞ

 

m z1 wð0Þ



Solving this model, we obtain the attribute weight vector

wð0Þ ¼ ð0:2; 0:2; 0:08; 0:12; 0:05; 0:12; 0:07; 0:16ÞT and obtain the satisfactory degrees mðzi ðwð0Þ ÞÞ (i ¼ 1; 2; …; 5) of the alternatives xi (i ¼ 1; 2; …; 5)

            ¼ 0:8733; m z2 wð0Þ ¼ 0:5932; m z3 wð0Þ ¼ 0:2829; m z4 wð0Þ ¼ 0:4491; m z5 wð0Þ ¼ 0:5106:

108

T. Da, Y. Xu / Ocean & Coastal Management 132 (2016) 101e110

Table 2 The decision matrix.

x1 x2 x3 x4 x5

c1

c2

c3

c4

c5

c6

c7

c8

{s5,s6} {s3,s4,s5} {s3,s4} {s2,s3,s4} {s4,s5}

{s5,s6} {s4,s5} {s3,s4,s5} {s4,s5} {s3,s4,s5}

{s3,s4,s5} {s3,s4} {s4,s5} {s4,s5,s6} {s3,s4,s5}

{s4,s5} {s3,s4,s5} {s3} {s3,s4} {s4,s5}

{s3,s4,s5} {s2,s3} {s0,s1,s2} {s3,s4} {s4,s5}

{s6} {s3,s4,s5} {s1,s2} {s4} {s2,s3}

{s5,s6} {s4,s5} {s1} {s0,s1} {s1,s2,s3}

{s3,s4} {s3,s4} {s1,s2,s3} {s2,s3} {s2,s3}

c1

c2

c3

c4

c5

c6

c7

c8

{s5,s6,s6} {s3,s4,s5} {s3,s4,s4} {s2,s3,s4} {s4,s5,s5}

{s5,s6,s6} {s4,s5,s5} {s3,s4,s5} {s4,s5,s5} {s3,s4,s5}

{s3,s4,s5} {s3,s4,s4} {s4,s5,s5} {s4,s5,s6} {s3,s4,s5}

{s4,s5,s5} {s3,s4,s5} {s3,s3,s3} {s3,s4,s4} {s4,s5,s5}

{s3,s4,s5} {s2,s3,s3} {s0,s1,s2} {s3,s4,s4} {s4,s5,s5}

{s6,s6,s6} {s3,s4,s5} {s1,s2,s2} {s4,s4,s4} {s2,s3,s3}

{s5,s6,s6} {s4,s5,s5} {s1,s1,s1} {s0,s1,s1} {s1,s2,s3}

{s3,s4,s4} {s3,s4,s4} {s1,s2,s3} {s2,s3,s3} {s2,s3,s3}

Table 3 The normalized decision matrix.

x1 x2 x3 x4 x5

ð0Þ

he DM gives the lower bounds li (i ¼ 1; 2; …; 5) of satisfactory degrees of the alternatives xi (i ¼ 1; 2; …; 5) according to the satisfactory degrees mðzi ðwð0Þ Þ (i ¼ 1; 2; …; 5):

and the satisfactory degrees mðzi ðwð1Þ ÞÞ (i ¼ 1; 2; …; 5) of the alternatives xi (i ¼ 1;2; :::; 5)

 

m z1 wð1Þ



l1ð0Þ ¼ 0:85; l2ð0Þ ¼ 0:60; l3ð0Þ ¼ 0:28; l4ð0Þ ¼ 0:45; l5ð0Þ ¼ 0:50:

¼ 0:5311:

Step 4. By the model (M-3), we establish the following optimization model:

maxJ ¼

5 P i¼1

s:t:

      ¼ 0:8712; m z2 wð1Þ ¼ 0:6032; m z3 wð1Þ       ¼ 0:4546; m z5 wð1Þ ¼ 0:28; m z4 wð1Þ

li

1 11w1 þ 8w2 þ 3w3 þ 5w4 þ 12w5 þ 15w6 þ 17w7 þ 8w8 ,  l1  0:85; 3 4w1 þ 3w2 þ 3w3 þ 2w4 þ 5w5 þ 5w6 þ 6w7 þ 3w8

1 6w1 þ 5w2 þ 2w3 þ 3w4 þ 8w5 þ 9w6 þ 14w7 þ 8w8 ,  l2  0:60; 3 4w1 þ 3w2 þ 3w3 þ 2w4 þ 5w5 þ 5w6 þ 6w7 þ 3w8 1 5w1 þ 3w2 þ 5w3 þ 0w4 þ 3w5 þ 2w6 þ 3w7 þ 3w8 ,  l3  0:28; 3 4w1 þ 3w2 þ 3w3 þ 2w4 þ 5w5 þ 5w6 þ 6w7 þ 3w8 1 3w1 þ 5w2 þ 6w3 þ 2w4 þ 11w5 þ 9w6 þ 2w7 þ 5w8 ,  l4  0:45; 3 4w1 þ 3w2 þ 3w3 þ 2w4 þ 5w5 þ 5w6 þ 6w7 þ 3w8 1 8w1 þ 3w2 þ 3w3 þ 5w4 þ 14w5 þ 5w6 þ 6w7 þ 5w8 ,  l5  0:50; 3 4w1 þ 3w2 þ 3w3 þ 2w4 þ 5w5 þ 5w6 þ 6w7 þ 3w8 0:08  w1  0:2; 0:1  w2  0:2; 0:08  w3  0:15; w4  1:5w3 ; w4  0:2; 0:05  w5  0:15; w6  0:12; w6  w7  0:05; w7  0:2; 0:1  w8  0:2

Solving this model, we get the attribute weight vector:

wð1Þ ¼ ð0:2; 0:1417; 0:08; 0:12; 0:0683; 0:12; 0:07; 0:2ÞT

Step 5. The DM is satisfied with this result. Therefore, we can calculate the overall values zi ðwÞ(i ¼ 1; 2; …; m) of the alternatives xi (i ¼ 1; 2; …; m) by HFLWA operator Eq. (3):

    z1 wð1Þ ¼ fs3:7634 ; s4:4634 ; s4:6117 g; z2 wð1Þ ¼ fs2:6034 ; s3:4234 ; s3:8634 g;     z3 wð1Þ ¼ fs1:9151 ; s2:5451 ; s2:7751 g; z4 wð1Þ ¼ fs2:4917 ; s3:1917 ; s3:5917 g;   z5 wð1Þ ¼ fs2:5683 ; s3:3883 ; s3:6800 g:

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Step 6. Calculate the score values hðzi Þ of alternatives xi (i ¼ 1; 2; …; m).

hðz1 Þ ¼ 4:2795; hðz2 Þ ¼ 3:2967; hðz3 Þ ¼ 2:4118; hðz4 Þ ¼ 3:0917; hðz5 Þ ¼ 3:2122: Step 7. Rank the alternatives according to the score values, we have

x1 _x2 _x5 _x4 _x3 Thus, the best alternative is Houtan Park (x1 ). From the above procedure, we can see that the experts generally may give some possible linguistic evaluation values. The hesitant fuzzy linguistic provides a more flexible way for the experts to express their opinions. Finally, the evaluation results are also the hesitant fuzzy linguistic values. In order to compare them, we propose a score function to compare them, and finally to select the best alternative. As can be seen from the results of the evaluation cases above, although the Houtan Park belongs to landscape-restoration oriented project, it focused on retaining the original site environment context and has constructed a successful public recreation place that people loved on the basis of brownfield governance. So that its social functions are restored, and becomes the most successful redevelopment case. In comparison, Xu Jiahui Waterfront also belongs to landscape-restoration oriented project. Because of the waterfront has been taken as a green belt-shaped open space exclusively, its social functional and contextual connections do not play good social roles, which make it getting the lowest connectivity in evaluation. Moreover, despite the Oriental Fisherman's Wharf has focused on the transformation of its social functions in waterfront, there is no site pattern retained in redevelopment, almost all the buildings in site are demolished and reconstructed, it achieves the poorest contextual connection and makes the evaluation results relatively poor. Although there are two different types of urban waterfront redevelopment projects, if the landscape-restoration oriented project can solve social functional and contextual connections well, and the urban-exploitation projects can solve the ecological and contextual connections well, the better connectivity in urban waterfront redevelopment can still be achieved. Therefore, it is not necessary to restrict the cases to redevelopment types when evaluating their connectivity.

6. Conclusions In this paper, we have built a standard assessment index system for urban waterfront connectivity. By analyzing urban waterfront connectivity, we can measure the social impacts generated by redeveloped projects to figure out the difference between landscape-restoration oriented projects and urban-exploitation projects. It is a comprehensive evaluation, providing a systematic analysis method for improving the functional and structural connection in urban waterfront. Considering that the experts may give his evaluation value by hesitant fuzzy linguistic term sets, this paper develops an interactive procedure for solving the MADM problems. The interactive process can be realized by giving and revising the satisfactory degree of alternative till an optimum satisfactory solution is achieved. The procedure has been applied to urban waterfront redevelopment projects sites in Huangpu River Waterfront, Shanghai. Theoretical analysis and computational results showed that the developed method is robust and effectiveness for solving the MADM problems with hesitant fuzzy linguistic information.

109

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