Fuzzy multicriteria prioritization of Urban transformation projects for Istanbul

Abstract

Urban transformation projects are prepared with the purpose to rehabilitate urban areas and/or to mitigate disaster risk. Urban transformation projects should be realized in the cities where urbanization planning is not well-organized in the past and rapid perfunctory urbanization occurs. Selecting the appropriate urban transformation projects and prioritizing them is important in the cities where there are multiple problems such as earthquake risk, flood risk and landslide risk. Prioritization of transformation projects is a multicriteria decision making problem, in which multiple stakeholders have diverse perspectives. The fuzzy set theory enables us to make mathematical operations with the linguistic evaluations in a multicriteria decision making method. In urban transformation problems, especially for subjective criteria, stakeholders usually prefer making linguistic evaluations. When decision makers show hesitancy in their evaluations, hesitant fuzzy linguistic term sets (HFLTS) can be used to integrate various linguistic evaluations without losing any information. Istanbul is the largest metropolitan of Turkey where a probable earthquake is expected in the near future. In this paper, a new linguistic group decision making based hesitant fuzzy TOPSIS approach for evaluating urban transformation projects is proposed and a real world application for Istanbul is provided. Four urban transformation alternatives for Istanbul are prioritized by the proposed method and a sensitivity analysis is conducted.

Keywords

Multicriteria urban transformation linguistic term hesitant fuzzys TOPSIS

1 Introduction

Urbanization is defined as a population shift from rural to urban areas. Today urban areas host most of world’s population [27]. In order to deal with this fact, policy makers and authorities develop and execute urban plans for designing the cities. Sustainable urban development can only be achieved by considering various factors such as environmental (nature-based needs), social (human-interaction-based needs), and economic factors [19].

As the resources are limited, it is not possible to realize all of the urban transformation projects (UTPs). Thus prioritizing UTPs is one of the most vital decisions for local authorities. While prioritizing urban transformation projects, several decision makers, such as politicians, urban planners, citizens etc. should be included in the process and various factors representing their perspectives should be taken into account [17, 19]. The studies in the literature that focus on urban transformation are limited and majority of existing articles focus on improving the process of urban transformation and selecting the best project that should be applied for a specific territory. For instance in one of the recent papers, Lami and Vitti [15] propose using quality function deployment integrated with analytic network process with the aim of evaluating the urban development projects. The authors also provide a case study for a specific region in France. In another study, a decision model based on analytic network process is proposed for determining alternative projects for a specific region in Italy [7].

In the cities similar to Istanbul, prioritization of the transformation projects highly affects the direction of the change. As the level of change in a city increases, new problems may occur such as low standardsof living spaces, absence of social services, lack of green area usage and illegal rental of lands which belong to others. Overcrowded and faulty buildings with inadequate infrastructures cause the hazards to increase. All these problems can be limited by appropriately prioritizing existing transformation projects. However, the prioritization process is very hard since many subjective criteria and many stakeholders with different opinions are involved in the process.

There are many alternative projects for urban transformation in Istanbul. Besides, as the existing projects are completed, the new ones are added to the project list. Therefore a robust method which can be applied to the future transformation projects is necessary. Moreover the present decision makers may also change in elapse time and each decision maker may want to reflect his or her ideas to the prioritization process. Developing a new model for each new case is not practical. For this reason we aim at developing a robust multicriteria model which can be used for new cases. For the determination of the criteria weights, pairwise comparison matrices are used. It enables highly robust results but the process itself is tedious and takes time. After the weights are defined by the experts, these weights can be utilized for evaluating different projects by different decision makers.

The fuzzy sets theory, proposed by Zadeh [36], provides a representation of uncertainty and also enables developing formal techniques for modeling and solving problems with imprecision. Since uncertainty and imprecision is inevitable for real world problems, various techniques and applications of fuzzy sets are proposed in the literature [4 , 23]. However, in cases where more than one sources of vagueness exist, ordinary fuzzy sets may have shortcomings to represent the situation [20]. In order to deal with these kinds of situations, new extensions of fuzzy sets are proposed such as Type-2 fuzzy sets [6, 30], intuitionistic fuzzy sets [1], fuzzy multisets [35] and hesitant fuzzy sets [25]. One of the most recent and important approach is Hesitant fuzzy sets (HFSs) which is developed by Torra [29]. HFS approach allows more than one value to be assigned for defining the membership value of an element. In order to use linguistic terms for problem modeling and solution in hesitant fuzzy domain, hesitant fuzzy linguistic term sets (HFLTS) are proposed by Rodriquez et al. [25]. Humans are successful in approximate reasoning rather than making exact assessments. Besides, the criteria used in the evaluation of the urban transformation projects are mostly intangible and can be only evaluated by linguistic terms. HFLTS can take into account decision makers’ hesitancy and prevent loss of information during the evaluation process. In this paper, urban transformation project selection problem is handled by using HFLTS and a case study from Istanbul is provided. In the proposed methodology there are two phases; in the first phase the weights of the criteria are determined by pairwise comparisons; and in the second phase, hesitant fuzzy linguistic TOPSIS methodology is used to rank the alternatives. In terms of both the methodological approach and application area, this paper includes originalities; hence, to the best of our knowledge this is the first paper prioritizing the urban transformation projects using a hierarchical hesitant fuzzy linguistic TOPSIS.

The organization of the paper is as follows. Section 2 gives a review of urban transformation projects for Istanbul, In Section 3 a brief literature of HFSs is first given and then the steps of the methodology are introduced. In Section 4, a real world application case for Istanbul is provided and the alternative projects are prioritized. Finally in Section 5 the conclusions and future research suggestions are given.

2 Urban Transformation Projects (UTPs) for Istanbul

With a population over 14 million, Istanbul is by far the most crowded city of Turkey. Nowadays, it is under consideration for urban transformation projects. These projects are divided into two main categories: large scale transformation projects far from the city center and regeneration projects in historical areas in the inner city regions. Urban development process in Istanbul started in 1980’s and accelerated within the last two decades. This transformation has also taken the attention of international capital markets, resulting in purchasing the old buildings and valuable lands in both the center and suburbs of the city.

The present urban transformation projects in Istanbul are Galata, Esenler, Balat, and Tarlabaşı. The locations of these districts are shown by the arrows in Fig. 1. With urban transformation in Istanbul, some conflicts have occurred between commercial and collective interests. When the industrial organizations have moved to the suburbs of the city, no longer used buildings have become available. This study aims at developing a decision support tool for the prioritization of urban transformation projects using a fuzzy multiple criteria decision making methodology.

In the following the present UTPs for Istanbul are introduced:

Galata: This district is shown on the map with a dotted arrow in Fig. 1. The owners of the houses and buildings in Galata started to change in 1990’s since there was an increasing interest in the houses at the historical areas by new professionals. One of its main reasons was the low prices of houses and buildings. The new owners have now started to transform their old houses and buildings by reinforcing or rebuilding. Since 2000’s, small local investors and international investors have been active in the area. The transformation of Galata will take a long time since the area is rather large [12].

Tarlabasi: This district is shown on the map with a gray arrow in Fig. 1. Tarlabasi area is another transformation project. Tarlabasi Boulevard was opened in 1986 and this changed its naturel structure. The buildings in this area were at least 75 years old and many of them were no longer in use. This caused low-income people to rent apartments in this area with low rents. Next to Tarlabasi, Beyoglu became a nightlife center with its clubs and restaurants [12].

Fener - Balat – Ayvansaray: This district is shown on the map with a black arrow in Fig. 1. Fener-Balat and Ayvansaray is another transformation project. Demographic changes in this area are similar to Galata and Tarlabasi districts. The new owners started to apply renewal and restoration projects to their houses and buildings. However, the transformation in this area has taken much criticism because Fener-Balat and Ayvansaray is a tourist destination hosting the Greek orthodox Patriarch [12].

Esenler: This district is shown on the map with a dashed arrow in Fig. 1. Esenler area is another transformation project with its population with 460,000. Its first transformation has first time begun in 1980’s. Trans-European Highway increased the mobility in this area. The main problem in this area is the lack of spaces to build new and modern buildings. The existing building blocks in this area are too close to each other. The other problems with the buildings are poor quality materials and lack of maintenance [12].

3 Multicriteria HFLTS method

3.1 Literature review on hesitant fuzzy sets

Mathematical representation of uncertainty is maintained by the fuzzy set theory from the time it was first developed by Zadeh [36]. Since then, various new tools for handling problems under uncertainty have been proposed. Many existing crisp methods have also been enhanced using fuzzy sets to reach better results in the solutions of real-world problems. However, researchers [21, 25] have reported that ordinary fuzzy sets may have shortcomings in cases where the source of uncertainties are associated with words or more than one sources of vagueness appear at the same time. In situations where ordinary fuzzy sets have problems with defining membership functions, different generalizations and extensions of fuzzy sets such as type-2 fuzzy sets, intuitionistic fuzzy sets [9, 11], and hesitant fuzzy sets [10] can be utilized.

Torra [29] proposed Hesitant Fuzzy Sets (HFSs) in order to deal with cases where an element of a set can have more than one membership value. In the classical set theory, an element belongs to a set or not; in classical fuzzy sets this constraint is relaxed by the term membership degree and each element is allowed to have different membership values to different sets. However, especially in decision making problems, determining the membership values of a single element can be hard, and the case can become even worse in group decision making problems. Torra and Narukawa [28] propose hesitant fuzzy sets to be used in this kind of problems. In group decision making problems it is usual that decision makers have different evaluations about the membership degree of an element. Generally in traditional approach, an aggregation operator is used to transform these different membership degrees into a single value. However, by means of HFSs, the evaluations of different decision makers can be included in the decision making problem without any transformations [29].

HFS is defined by Torra [29] as follows: a HFS on a fixed set X is a function which returns a subset of [0, 1]when applied to X. Mathematical formula for HFS is given in Equation 1. $E = {< x, h_{E} (x) > | x \in X}$ (1)

where h_E (x) is hesitant fuzzy element (HFE) representing the possible membership degrees of the element x ∈ X to the set E. The lower and upper bounds of h_E (x) are given in Equations 2 and 3, respectively [29]: $h^{-} (x) = min h (x);$ (2) $h^{+} (x) = max h (x);$ (3)

Zhang and Wei [38] define the basic operation on HFEs. Let h_i represent a HFE. The following operations are valid: $h_{i}^{λ} = \cup_{γ \in h_{i}} {γ^{λ}};$ (4) $λ h_{i} = \cup_{γ \in h_{i}} {1 - (1 - γ)^{λ}};$ (5) $h_{1} \cup h_{2} = \cup_{γ_{1} \in h_{1}, γ_{2} \in h_{2},} max {γ_{1}, γ_{2}};$ (6) $h_{1} \cap h_{2} = \cup_{γ_{1} \in h_{1}, γ_{2} \in h_{2}}, min {γ_{1}, γ_{2}};$ (7) $h_{1} \oplus h_{2} = \cup_{γ_{1} \in h_{1}, γ_{2} \in h_{2},} {γ_{1} + γ_{2} - γ_{1} γ_{2}};$ (8) $h_{1} \otimes h_{2} = \cup_{γ_{1} \in h_{1}, γ_{2} \in h_{2}}, {γ_{1} γ_{2}};$ (9)

Measuring the distance between two HFEs is especially important for TOPSIS operations. There are different distance measures in the literature. Xu and Xia [34] give the following hesitant Euclidean distance: $d_{1} (h_{1}, h_{2}) = \sqrt{\frac{1}{l} \sum_{i = 1}^{l} {| h_{1_{σ (i)}} - h_{2_{σ (i)}} |}^{2}}$ (10)

Zhang and Wei [38] give the following Hamming distance: $d_{1} (h_{1}, h_{2}) = \frac{1}{l} \sum_{i = 1}^{l} | h_{1_{σ (i)}} - h_{2_{σ (i)}} |$ (11)

where h₁, h₂ are two HFEs and l is the length of the HFE which represents the number of elements in a HFE.

The lengths of HFEs may be different and the values also may not be ordered. In such situations, first the elements should be ordered. If the lengths are different, i.e. l_{h
₁} < l_{h
₂} then h₁ should be extended. This extension can be made by adding the minimum or maximum value to h₁ for obtaining the same number of elements. Optimist decision makers may add the maximum value, while pessimist decision makers may add the minimum value [33].

Although the initiation of the term is relatively new, HFSs have been widely used in multiattribute decision making area together with new aggregation and arithmetic operators. Zhao et al. [40] examine using hesitant triangular fuzzy information in group decision making problems and proposed six new operators based on Einstein operator. Zhang et al. [39] propose induced generalized hesitant fuzzy operators for multiattribute problems. Bedregal et al. [2] focus on the aggregation operators on the set of all possible membership degrees of HFS, and propose the class of finite hesitant triangular norms. Wei et al. [32] propose hesitant interval-valued fuzzy information. They develop a score function and six hesitant interval-valued fuzzy aggregation operators. Also many other forms of HFS are proposed in the literature such as Generalized HFS [24], Hesitant Triangular Fuzzy Sets [40], linguistic HFS [22], and Dual HFS [42] (Ye, 2014).

On the other hand, the studies that extend the classical multicriteria decision making methods with hesitant fuzzy sets exist in the literature. TOPSIS and VIKOR are the first methods to be extended by HFS. Xu and Zhang [33] develop a model for using TOPSIS with hesitant fuzzy sets for cases where the weight information is incomplete. Zhang and Wei [38] extend VIKOR method based on hesitant fuzzy sets. Liao and Xu [18] propose hesitant fuzzy VIKOR method based on the terms; hesitant normalized Manhattan Lp — metric, the hesitant fuzzy group utility measure, the hesitant fuzzy individual regret measure, and the hesitant fuzzy compromise measure. Jin [13] extends ELECTRE and proposes hesitant fuzzy ELECTRE method which can work in decision environments where the decision makers provide hesitant fuzzy information. In another study, Zeng et al. [37] extend existing MULTIMOORA approach to facilitate with group decision making problems under fuzziness. The authors propose MULTIMOORA-HF which can work with HFSs. Wei [31] proposed a multicriteria group decision making method in hesitant fuzzy environment based on Grey Relational Analysis method. In one of the most recent studies, Onar et al. (2014) propose a MCDM model which integrate interval type-2 fuzzy AHP and hesitant fuzzy TOPSIS. The authors also provide a real world case study about strategic decision makingproblem.

3.2 Hesitant fuzzy linguistic term sets

It is very common that decision makers hesitate among several values when making assessments using linguistic variables. In such cases, ordinary fuzzy linguistic approaches which aim to use a single linguistic term are incapable of handling the situation. Rodriguez et al. [25] propose using Hesitant Fuzzy Linguistic Terms Sets (HFLTS) to deal with these situations. Using the HFLTS and related methodologies, decision making problems with multiple linguistic assessments can be mathematically represented and solved. The literature provides various studies about HFLTS. Weiet al. [32] define two aggregation operators, a hesitant fuzzy LWA operator and a hesitant fuzzy LOWA operator that can operate on HFLTS. The authors propose to use these operators in multicriteria decision making problems with known and unknown criteria weights. Lee and Chen [16] develop a new decision making method based on likelihood-based comparison relations of HFLTSs. In another study, four aggregation operators and a ranking method based on HFLTSs are proposed by Zhang et al. (2013). Beg and Rashid [3] extend the crisp TOPSIS method to be used in hesitant fuzzy environment using HFLTSs. Rodriguez et al. [26] propose a new group decision model based on HFLTS in order to enhance the elicitation of flexible and rich linguistic expressions. Zhu and Xu [41] define the concept of hesitant fuzzy linguistic preference relations (HFLPRs) which is a tool to collect and present decision makers’ evaluations. The authors also propose a consistency measure for HFLPRs so as to check the acceptability of an HFLPR.

Rodriguez et al. [25] list the basic definitions on HFLTS as follows:

Definition 1: An HFLTS, H_s, is an ordered finite subset of consecutive linguistic terms of a linguistic term set S which can be shown as S = {s₀, s₁, …, s_g}.

Definition 2: Assume that E_{G
_H} is a function that convert linguistic expressions into HFLTS, H_S. Let G_H be a context-free grammar that uses the linguistic term set S. Let S_u be the expression domain generated by G_H. This relation can be shown as E_{G
_H} : S_u → H_S.

Using the following transformations comparative linguistic expressions are converted into HFLTSs; $E_{G_{H}} (s_{i}) = {s_{i} | s_{i} \in S}$ (12) $E_{G_{H}} (at most s_{i}) = {s_{j} | s_{j} \in S and s_{j} \leq s_{i}}$ (13) $E_{G_{H}} (lower than s_{i}) = {s_{j} | s_{j} \in S and s_{j} < s_{i}}$ (14) $E_{G_{H}} (at least s_{i}) = {s_{j} | s_{j} \in S and s_{j} \geq s_{i}}$ (15) $E_{G_{H}} (greater then s_{i}) = {s_{j} | s_{j} \in S and s_{j} > s_{i}}$ (16)

$\begin{matrix} E_{G_{H}} (between s_{i} and s_{j}) \\ = {s_{k} | s_{k} \in S and s_{i} \leq s_{k} \leq s_{j}} \end{matrix}$ (17)

Definition 3: The envelope of an HFLTS is represent by env (H_S), and it is a linguistic interval whose limits are obtained by its maximum value and minimum value: $env (H_{S}) = [H_{S^{-}}, H_{S^{+}}], H_{S^{-}} \leq H_{S^{+}}$ (18)

where $H_{S^{-}} = min (s_{i}) = s_{j}, s_{i} \in H_{S} and s_{i} \geq s_{j} \forall_{i}$ $H_{S^{+}} = max (s_{i}) = s_{j}, s_{i} \in H_{S} and s_{i} \leq s_{j} \forall_{i}$

3.3 Proposed HFLTS TOPSIS methodology

In this study, a new linguistic group decision making based hesitant fuzzy TOPSIS approach is proposed. The proposed methodology which is applied to urban transformation contains two phases. In the first phase the weights of the criteria are determined using pairwise comparison based HFLTS method [26]; in the second phase the alternatives are evaluated by using TOPSIS extended by HFLTS.

The proposed method is composed of two main phases and 12 steps. First six steps constitute Phase 1 which ends with determining the weights of the criteria and Phase 2 ranks the alternatives and selects the best one. The steps of the proposed algorithm are as follows:

3.3.1 Phase 1: Determining the Weights of the Criteria

Step 1. Define the semantics and syntax of the linguistic term set S and the context-free grammar G_H, where G_H = {V_N, V_T, I, P} $\begin{matrix} V_{N} = {〈 primary term 〉, 〈 composite term 〉, 〈 unary relation 〉, 〈 binary relation 〉, 〈 conjunction 〉} \\ V_{T} = {lower than, greater than, at least, at most, between, and s_{0}, s_{1}, \dots, s_{g}} \\ I \in V_{N} \end{matrix}$

The production rules can be given by Equation 19. $P = {\begin{matrix} I : : = 〈 primary term 〉 | 〈 composite term 〉, 〈 composite term 〉 : : = \\ 〈 unary relation 〉〈 primary term 〉 | 〈 binary relation 〉〈 primary term 〉〈 conjunction 〉〈 primary term 〉, \\ primary term : : = s_{0} | s_{1} | \dots | s_{g}, 〈 unary relation 〉 : : = lower then | greater than | at least | at most, \\ 〈 binary relation 〉 : : = between, 〈 conjunction 〉 : : = and \end{matrix}}$ (19)

Step 2. Gather the pairwise comparisons from the experts. In the domain of group decision making, m decision makers (E = {e₁, e₂, … , e_m}) try to select the best alternative among n alternatives (x = {x₁, x₂, …, x_n})where m > 1 and n > 1. In this case a matrix composed of preference relations (p^ks) are formed as shown in Equation (20). $p^{k} = (\begin{matrix} p_{11}^{k} & \dots & p_{1 m}^{k} \\ ⋮ & ⋱ & ⋮ \\ p_{n 1}^{k} & \dots & p_{nm}^{k} \end{matrix})$ (20)

where $p_{ij}^{k}$ shows the degree of preference of the alternative x_i over x_j according to expert e_k. In this step the preference matrix is constructed for the criteria.

Step 3. Transform the preference relations into HFLTS by using the transformation function E_{G
_H}. For each HFLTS obtain an envelope $[p_{ij}^{k -}, p_{ij}^{k +}]$ .

Step 4. Obtain the pessimistic and optimistic collective preference relations ( $P_{C}^{-}$ and $P_{C}^{+}$ ). Compute the pessimistic and optimistic collective preference for each alternative using 2-tuple sets. The 2-tuple set associated with S is defined as . The function is given in Equation 21. $Δ (β) = (s_{i}, α) with {\begin{matrix} i = round (β) \\ α = β - i \end{matrix}$ (21)

where round assigns to β the integer number i ∈ {0, 1, …, g} closest to β and is defined as shown in Equation 22. $Δ^{- 1} (s_{i}, α) = i + α$ (22)

Step 5. Build a vector of intervals $V^{R} = (p_{1}^{R}, p_{2}^{R}, \dots, p_{n}^{R})$ of collective preferences for the alternatives $p_{i}^{R} = [p_{i}^{-}, p_{i}^{+}]$ .

Step 6. Calculate the midpoints of the intervals and normalize the results in order to find the weights.

At the end of Step 6, which is the last step of Phase 1, the weights of the criteria are obtained.

3.3.2 Phase 2: Evaluating alternatives

In phase 2, the following steps should be followed to evaluate the alternatives using TOPSIS with HFLTS.

Step 7: Define context-free grammar for the evaluations of the alternatives and collect the evaluations of each decision makers. But this time the collection is not done using pairwise comparison format.

Step 8: Transform the expert evaluations into HFLTS and combine decision makers’ evaluations and form an envelope for each HFLTS.

Step 9: Transform the linguistic terms into membership values using a scale for linguistic terms and construct Hesitant Matrix and determine the positive and negative ideal solutions using Equation 23. And Equation 24 $A^{*} = {h_{1}^{*}, h_{2}^{*}, \dots, h_{n}^{*}};$ (23)

where

$\begin{matrix} h_{j}^{*} & = & \cup_{i = 1}^{m} h_{ij} = \cup_{γ 1 j \in h_{1 j, \dots,} γ_{mj} \in h_{mj}}, \\ max {γ_{1 j}, \dots γ_{mj}} j = 1, 2, \dots, n \\ A^{-} & = & {h_{1}^{-}, h_{2}^{-}, \dots, h_{n}^{-}}; \end{matrix}$ (24)

where $\begin{matrix} h_{j}^{*} & = & \cap_{i = 1}^{m} h_{ij} = \cap_{γ_{1_{j}} \in h_{1 j}, \dots, γ_{mj} \in h_{mj}}, \\ min {γ_{1 j}, \dots, γ_{mj}} j = 1, 2, \dots, n \end{matrix}$

Step 10: Calculate the separation measures of each alternative from the ideal solution using weighted hesitant normalized Hamming distance. The distance of an alternative form positive ideal is calculated using Equation 25: $D_{i}^{+} = \sum_{j = 1}^{n} w_{j} ∥ h_{ij} - h_{j}^{*} ∥$ (25)

In Equation 25, w_j shows the weight of the criterion j which has been determined in Step 6.

Similar to the previous equation, the separation from the negative ideal solution is calculated using Equation 26. $D_{i}^{-} = \sum_{j = 1}^{n} w_{j} ∥ h_{ij} - h_{j}^{-} ∥$ (26)

The distance betwen two hesitant fuzzy numbers which are used both in Equations 25 and 26 is computed using Equation 27. $∥ h_{1} - h_{2} ∥ = \frac{1}{l} \sum_{j = 1}^{l} | h_{1 σ (j)} - h_{2 σ (j)} |$ (27)

Step 11: Calculate the relative closeness to the ideal solution by using Equation 28. $C_{i} = \frac{D_{i}^{-}}{D_{i}^{-} + D_{i}^{+}}$ (28)

Step 12: Rank the alternatives according their relative closeness values; the alternative with the highest value is selected as the best alternative.

The steps of the proposed method are given in Fig. 2.

4 Assessment of Urban transformation projects for Istanbul

In this study the decision criteria that are mentioned in Section 2 are used for prioritizing urban transformation projects. The considered projects are Esenler, Tarlabaşı, Galata, and Balat as mentioned in Section 2. The main criterion “Physical” is explained by three sub-criteria namely “Infrastructure”, “Building Structure” and “Open structures”. “Risk Factors” main criterion is explained by “Earthquake risk”, “Landslide risk”, and “Flood risk”. The other main criteria “Economical”,”Social-Cultural” and “Environmental” are explained by “Value Created & Cost of the project”, “Resistance to the project & Population” and “Traffics & Pollution”, respectively. Figure 3 presents the hierarchy.

In order to evaluate the criteria of the proposed decision model, a group of three experts has been formed. The experts in the decision making group are academicians whose expertise are mainly on urban design. The weights of the criteria are obtained by the pairwise comparisons. In order to obtain the weights of the main criteria, Table 1 is filled by the experts. Later the assessments of the experts are transformed into HFLTS as shown in Table 2.

Next HFLST intervals are shown in Table 3 and finally pessimistic and optimistic collective preferences are obtained as given in Table 4. The resulting weights of the main criteria with respect to the goal are presented in Table 5.

The weights of the sub-criteria are given in Tables 6–10.

In Table 11, the global weights of the criteria are listed. In the following steps, weighted scores of the alternatives are calculated by using these weights.

In Istanbul, decisions about urban transformation projects are given by the departments of Istanbul Municipality such as Directorate of Urban Transformation and Ministry of Environment and Urban Planning such as General Directorate of Infrastructure and Urban Transformation. Four decision makers from these departments evaluated the alternative projects. Table 12 gives the linguistic terms that are given to the alternatives by decision makers.

After defining the Linguistic Hesitant Fuzzy Sets the linguistic terms are transformed to their corresponding numerical values by using a predetermined set. In this example the transformation is made based on the values given in Table 14.

Table 15 shows the numerical hesitant fuzzy sets.

The results of the proposed method are given in Table 16.

According to the obtained ranking, the alternatives are sorted from the best to the worst as Esenler, Tarlabaşı, Balat, and Galata. Istanbul Metropolitan Municipality should consider these ranking while allocating the sources to the local municipalities. On the other hand the robustness of the results should be checked. This can be done through sensitivity analysis. In Fig. 4 the sensitivity analysis results are given. This figure shows the similarity to ideal solution coefficients with respect to the changing criteria. Our decision is insensitive to the infrastructure and landslide risk criteria whereas slightly sensitive to open areas, pollution, earth quake risk and flood risk. The other criteria building, value created, cost, population and traffic. When the criterion building structure is considered, the alternatives Esenler and Tarlabaşı have similar characteristics that indicate a more problematic building structure. Esenler district has different characteristics when compared to other districts in terms of landslide risk, traffic, value created, cost, and resistance criteria. Our decision for Galata district is insensitive to the changes in the weights of the landslide risk, flood risk, open areas, pollution, infrastructure and earthquake risk criteria and it takes the last order in each case.

5 Conclusion and further research

Istanbul is a metropolitan with many perfunctory urbanized areas. Currently more than 15 urban transformation projects exist in Istanbul where our study considers four projects that Istanbul Metropolitan Municipality recently handles. Several criteria such as natural risks, social needs, and economic factors should be considered while prioritizing these projects. Evaluation of urban transformation projects generally involves intangible criteria and their linguistic terms. There is a need for a powerful tool that is capable of taking all these criteria in to account. HFLTS are very successful in collecting and aggregating different opinions of different experts without any information loss. The originality of the paper comes from integrating a hierarchical hesitant fuzzy linguistic weighting approach and hesitant fuzzy linguistic TOPSIS method.

Prioritizing urban transformation projects can be modeled as a multicriteria decision making problem since there are various criteria involved and HFLTS based methods are very appropriate for this type of problem. Our proposed method has evaluated the considered urban transformation projects effectively without any loss of information. The decision makers of the Istanbul Metropolitan Municipality confirmed the consistency of the results with their expectations.

Since Istanbul is a highly dynamic metropolitan, new transformation projects will possibly be considered within few years. The proposed method is a robust method which can be applied to these new projects. This will improve the prioritization process and enable a faster solution. The results of our proposed method can be compared with the ones obtained from Type 2 fuzzy TOPSIS or intuitionistic fuzzy TOPSIS.

References

Atanassov

K.T.

, Intuitionistic fuzzy sets, Fuzzy Set Syst20 (1986), 87–96.

Bedregal

, Reiser

, Bustince

, López-Molina

and Torra

, Aggregating functions for typical hesitant fuzzy elements and the action of automorphisms, Inform Sci256(1) (2014), 82–97.

Beg

and Rashid

, TOPSIS for hesitant fuzzy linguistic term sets, International Journal of Intelligent Systems28(12) (2013), 1162–1171.

Behret

, Oztaysi

and Kahraman

, A fuzzy inference system for supply chain risk management, Practical Applications of Intelligent Systems, Springer, 2012, pp. 429–438.

Çevik Onar

, Öztayşi

and Kahraman

, Strategic decision selection using hesitant fuzzy TOPSIS and interval type-2 fuzzy AHP: A case study, International Journal of Computational Intelligent Systems7(5) (2014), 1002–1021.

Dubois

and Prade

, Fuzzy Sets and Systems: Theory and Applications, New York, Kluwer, 1980.

Ferri

and Maturo

, Decisional models for a holistic perspective of Risk in urban regeneration projects, A Case Study in Pescara (Italy), International Journal of Risk Theory3(1) (2013), 37–53.

Hara

, Thaitakoo

and Takeuchi

, Landform transformation on the urban fringe of Bangkok: The need to review land-use planning processes with consideration of the flow of fill materials to developing areas, Landscape and Urban Planning84(1) (2008), 74–91.

Y.D.

, Chen

H.Y.

, Zhou

L.G.

, Liu

J.P.

and Tao

Z.F.

, Intuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making,a), Information Sciences259 (2014), 142–159.

10.

Y.D.

, He

, Wang

G.D.

and Chen

H.Y.

, Hesitant fuzzy power bonferroni means and their application to multiple attribute decision making, IEEE Transactions on Fuzzy Systems (2014b) DOI: 10.1109/TFUZZ.2014.2372074

11.

Y.D.

, He

and Chen

H.Y.

, Intuitionistic fuzzy interaction bonferroni means and its application to multiple attribute decision making, IEEE Transactions on Cybernetics45 (2015), 116–128.

12.

Inceoglu

and Yürekli

, Urban transformation in Istanbul: Potentials for a better city, Enhr Conference 2011, Toulouse, 2011.

13.

Jin

, ELECTRE method for multiple attributes decision making problem with hesitant fuzzy information, Journal of Intelligent and Fuzzy Systems (2013). DOI: 10.3233/IFS-131081

14.

Kahraman

, Multi-criteria decision making methods and fuzzy sets, Fuzzy Multi-Criteria Decision Making, Springer, 2008, pp. 1–18.

15.

Lami

and Vitti

E.L.

, A combination of Quality Function Deployment and Analytic Network Process to evaluate urban redevelopment projects: An application to the Belle de Mai – La Friche of Marseille, France, Journal of Applied Operational Research3(1) (2011), 2–12.

16.

Lee

L.W.

and Chen

S.M.

, Fuzzy decision making based on hesitant fuzzy linguistic term sets, Lecture Notes in Computer Science Intelligent Information and Database SystemsVolume 7802, 2013, pp. 21–30.

17.

Lefebvre

, Metropolitan government and governance in western countries, a critical review, Int Urban Reg Res22(1) (1998), 9–25.

18.

Liao

and Xu

, A VIKOR-based method for hesitant fuzzy multi-criteria decision making, Fuzzy Optimization and Decision Making12(4) (2013), 373–392.

19.

Matsuoka

R.H.

and Kaplan

, People needs in the urban landscape: Analysis of Landscape And Urban Planning contributions, Landscape and Urban Planning84(1) (2008), 7–19.

20.

Mendel

J.M.

, Uncertainty, fuzzy logic, and signal processing, Signal Proc J80 (2000), 913–933.

21.

Mendel

J.M.

, John

R.I.

and Liu

F.L.

, Interval type-2 fuzzy logical systems made simple, IEEE Transactions on Fuzzy Systems14(6) (2006), 808–821.

22.

Meng

, Chen

and Zhang

, Multi-attribute decision analysis under a linguistic hesitant fuzzy environment, Information Sciences (2014). DOI: https://dx-doi-org.web.bisu.edu.cn/10.1016/j.ins.2014.02.012

23.

Oztaysi

and Ucal

, Comparing MADM techniques for use in performance measurement, ISAHP Proceedings, The 10th International Symposium on the Analytic Hierarchy Process, 2009, pp. 1–11.

24.

Qian

, Wang

and Feng

, Generalized hesitant fuzzy sets and their application in decision support system, Knowledge-Based Systems37 (2013), 357–365.

25.

Rodriguez

R.M.

, Martinez

and Herrera

, Hesitant fuzzy linguistic term sets for decision making, IEEE Transactions on Fuzzy Systems20(1) (2012), 109–19.

26.

Rodriguez

R.M.

, Martinez

and Herrera

, A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets, Information Sciences241 (2013), 28–42.

27.

Shi

and Yu

, Assessing urban environmental resources and services of Shenzhen, China: A landscape-based approach for urban planning and sustainability, Landscape and Urban Planning125 (2014), 290–297.

28.

Torra

and Narukawa

, On Hesitant Fuzzy Sets and Decision, FUZZ-IEEE 2009, Korea, 2009, pp. 20–24.

29.

Torra

, Hesitant fuzzy sets, International Journal of Intelligent Systems25 (2010), 529–539.

30.

Uçal Sari

, Oztaysi

and Kahraman

, Fuzzy analytic hierarchy process using type-2 fuzzy sets: An application to warehouse location selection, Multicriteria Decision Aid and Artificial Intelligence, Wiley, 2013, pp. 285–308.

31.

Wei

, GRA method for multiple criteria group decision making with incomplete weight information under hesitant fuzzy setting, Journal of Intelligent and Fuzzy Systems (2013). DOI: 10.3233/IFS-131073

32.

Wei

, Zhao

and Lin

, Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making, Knowledge-Based Systems46 (2013), 43–53.

33.

and Zhang

, Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information, Knowledge-Based Systems52 (2013), 53–64.

34.

Z.S.

and Xia

M.M.

, Distance and similarity measures for hesitant fuzzy sets, Information Sciences181 (2011), 2128–2138.

35.

Yager

R.R.

, On the theory of bags, Int J Gener Syst13 (1986), 23–37.

36.

Zadeh

L.A.

, Fuzzy sets, Information and Control8(3) (1965), 338–353.

37.

Zeng

, Balezentis

and Su

, The multi-criteria hesitant fuzzy group decision making with multimoora method, Economic Computation & Economic Cybernetics Studies & Research47(3) (2013), 171–184. 14.

38.

Zhang

and Wei

, Extension of VIKOR method for decision making problem based on hesitant fuzzy set, Applied Mathematica[1]l Modeling37 (2013), 4938–4947.

39.

Zhang

, Wang

, Tian

and Li

, Induced generalized hesitant fuzzy operators and their application to multiple attribute group decision making, Comput Ind Eng67 (2014), 116–138.

40.

Zhao

, Lin

and Wei

, Hesitant triangular fuzzy information aggregation based on Einstein operations and their application to multiple attribute decision making, ExpertSystems with Applications41/4(1) (2014), 1086–1094.

41.

Zhu

and Xu

, Consistency measures for hesitant fuzzy linguistic preference relations, IEEE Transactions on Fuzzy Systems22(1) (2014), 35–45.

42.

Zhu

, Xu

, Xia

, Dual hesitant fuzzy sets, Journal of Applied Mathematics2012 (2012). DOI: https://dx-doi-org.web.bisu.edu.cn/10.1155/2012/879629