1 Introduction

The concept of the smart city is based on integrating information and communication technologies (ICTs) into city infrastructure to collect data for allocating assets and resources as well as improving quality of life and sustainability. The problems and inefficient solutions in today’s cities increase the requirement for smart applications to address the current problems efficiently. In this context, smart city applications have attracted many researchers, engineers, urban planners, and even municipality members. Moreover, a wide spectrum of applications is available for the smart city concept in fields like urban planning, waste management, resource management, and municipality services.

Municipal solid waste management is one of the most important services for public health, aesthetics, and environmental protection. It includes all the activities and actions required to manage waste from the collection to the final disposal (Al-Khatib et al. 2007). For a waste management system to be sustainable, it is expected to be environmentally effective, economically affordable, and socially acceptable and should be accepted by the population directly affected by the system itself (Morrissey and Browne 2002). The identification of environmental, economic, and social criteria which are often conflicting and the list of alternatives is a crucial stage of a successful waste management plan. Particularly, solid waste collection system selection issue is a multi-criteria decision-making problem which should consider environmental, social, economic, and technical aspects simultaneously. Generally, collection and transportation are regarded as the most important and costly steps of the process due to the labor intensity of the work and the usage of the massive amount of vehicles in these processes (Amponsah and Salhi 2004). In many cities, waste collection and transportation systems focus on emptying containers and bins according to predefined schedules. However, the predefined scheduling introduces some problems such as early collection of the wastes from half-full bins and therefore, unnecessary fuel consumption of collection and transportation vehicles, a higher level of emission, poor use of city assets and resources. By using ICTs, smart solutions can be provided in terms of tracking waste levels, route optimization, and operational analytics. These solutions optimize waste management services, reduce operational costs, and better address the environmental issues associated with the inefficient waste collection. To increase efficiency and improve the quality of waste collection and transportation services, smart city solutions are developed by many companies and project groups.

Energy-efficient, eco-friendly and sustainable ICTs make increasingly significant contributions to the economy while protecting the environment. Wireless communications can be regarded as one of the most important components of modern ICTs with its fast-growing and very dynamic structure (Csáji et al. 2017). Wireless communication enables the connection and fast information transfer between the mobile users, machines, and vehicles although there is a considerable distance between them. In this regard, brand-new technique visible light communication (VLC) enables the ultra-fast communication between terminals using light bulbs and its becoming an important competitor for traditional radio-frequency (RF) communication such as Wi-Fi (Jovicic et al. 2013). VLC can provide interior lighting of a room and the data transfer at the same time without requiring any other communication system. Moreover, the human eye cannot recognize the difference between information bearing light and normal light (Rajagopal et al. 2012). VLC can be applied in many scenarios including light fidelity (Li-Fi), vehicle-to-vehicle communication, underwater communication, hospitals, and information displaying signboards, visible light ID systems as well as wireless local area networks. Li-Fi is a high speed two-way fully connected VLC system (Khan 2017). On the other hand, drone communication (DC) concept has become more and more popular with its promising applications in disaster management and aerial transport (Zeng et al. 2016). Moreover, drones can be employed to help the existing communication infrastructure to increase the wireless coverage within the service area. They can also be deployed to provide wireless connectivity between two or more distant terminals or groups of terminals, which do not have a reliable link between them, as well as to collect delay-tolerant information from sensors (Zeng et al. 2016).

The uncertainties arise if the parameters of the decision-making models are qualitative factors depending on personal preferences. Considering these uncertainties, using fuzzy methods provides efficient solutions in terms of decision making. To overcome the uncertainty of human evaluation, the concept of fuzzy set is first introduced by the Zadeh (1965). In fuzzy set theory, conversion scales are used to convert the linguistic terms into the fuzzy numbers. Fuzzy sets theory can be used to cope with social and technical complexity arising from human judgment, and there can be found many applications of this theory in artificial intelligence, computer science, medicine, control engineering, decision theory, management science, operations research, pattern recognition, as well as robotics, etc.

Ordinary fuzzy sets, i.e., type-1 fuzzy sets, might not be sufficient to model uncertainties due to the high complexity of some problems and their crisp membership functions. In this context, type-2 fuzzy sets, whose membership functions are themselves fuzzy, could be considered as a viable technique to model higher uncertainties (Mendel and John 2002). Type-2 fuzzy sets were first introduced by Zadeh (1975) as an extension of the type-1 fuzzy sets. Although membership functions of type-1 fuzzy sets are two-dimensional, the membership function of a type-2 fuzzy set is three-dimensional, and the new third dimension enables new design degrees of freedom for handling higher uncertainties. When it is difficult to determine the exact membership function for a fuzzy set, type-2 fuzzy sets become useful. Interval type-2 fuzzy sets, each of which is characterized by the footprint of uncertainty, are very useful tools to show the decision information in the decision-making process. In the literature, there are many approaches which extend existing multi-criteria techniques into type-2 fuzzy environments: Chen and Lee (2010) presented an interval type-2 fuzzy TOPSIS method to handle fuzzy multiple attributes group decision-making problems based on interval type-2 fuzzy sets. Hu et al. (2013) proposed a new approach based on possibility degree to solve multi-criteria decision-making (MCDM) problems in which the criteria value takes the form of interval type-2 fuzzy number. Chen (2014) developed an ELECTRE-based outranking method for MCDM within the environment of interval type-2 fuzzy sets. Kahraman et al. (2014) suggested an interval type-2 fuzzy AHP method together with a new ranking method for type-2 fuzzy sets. Chen et al. (2013) proposed an extended QUALIFLEX method for handling MCDM problems in the context of interval type-2 fuzzy sets. Of these successful attempts, we have chosen to follow Chen and Lee’s (2010) type-2 fuzzy TOPSIS extension approach since it is one of the very early and most cited studies in the area.

Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is one of the most known techniques for solving MCDM problems. It is based on the idea that the selected alternative should have the shortest distance to positive ideal solution, which minimizes the cost criteria and maximizes the benefit criteria, and the largest distance to negative ideal solution (Nădăban et al. 2016). The concept of TOPSIS is developed and extended for solving MCDM problems by many researchers (Jahanshahloo et al. 2005). In real-word applications, due to incomplete and non-obtainable information arising from uncertainty of human judgment, it is not always possible to estimate the preference with an exact numerical data and the data (attributes) are often not so deterministic. Therefore, they can be fuzzy. In the MCDM literature, there are many successful extensions of TOPSIS technique in the context of type-1 fuzzy sets (Chen 2000; Shih et al. 2007; Wang et al. 2009; Abo-Sinna and Amer 2005). In their review article, Kahraman et al. (2015) showed that, fuzzy TOPSIS and fuzzy AHP are, by far the most popular fuzzy MCDM techniques in the literature with thousands of applications in areas like engineering, computer science, mathematics, business, and environmental science.

In this study, a type-2 fuzzy TOPSIS methodology is suggested for the evaluation and selection of municipal solid waste collection system in the context of smart cities. To do this, alternative concepts based on emerging ICTs are proposed. A real case study is provided from Eskişehir Tepebaşı district which has a great potential with currently ongoing smart city projects funded by European Union. The evaluation criteria were determined considering the local needs of municipal experts. A sensitivity analysis is also conducted to monitor the robustness of the findings to changes in the criteria weights.

The rest of the paper is organized as follows. In the next Section, a literature review is provided. Section 3 introduces the fundamental steps of the proposed type-2 fuzzy methodology. In Sect. 4, first, the current solid waste collection (SWC) practices in the study region are summarized. Then, the criteria and the proposed concepts are introduced. In Sect. 5, the findings are explained. Section 6 contains the sensitivity analysis. Finally, Sect. 7 is devoted to concluding remarks.

2 Literature review

The challenges in the current systems have led the researchers to design efficient waste collection and transportation systems for upcoming smart cities. Kim et al. (2006) addressed a real-life waste collection vehicle routing problem with time windows considering multiple factors including drivers’ lunch breaks. Similarly, Nuortio et al. (2006) studied the optimization of vehicle routes in Eastern Finland. A novel and innovative solution is suggested and tested by Vicentini et al. (2009) to monitor and handle waste in Pudong New Area region, Shanghai. Gutierrez et al. (2015) combined geographic information systems (GIS), applied graph theory, machine learning (ML), and Internet of Things (IoT) to design a waste collection system employing sensors in bins. In the proposed system, the data collected from the containers are sent to internet via Wi-Fi technology.

There is a vast literature on applications of fuzzy multi-criteria techniques in waste management area: Ekmekçioğlu et al. (2010) proposed a modified fuzzy TOPSIS methodology for the selection of appropriate disposal method and site for municipal solid waste. In the study of Xi et al. (2010), three scenarios are examined for waste management in Beijing and a fuzzy MCDA model is applied for analyzing the optimal solutions among the three alternatives. Mirzazadeh et al. (2018) investigated the utility level of waste disposal methods and suggested the most appropriate method considering geographical and environmental conditions of Mazandaran province of Iran using AHP and fuzzy AHP techniques. Estay-Ossandon et al. (2018) used fuzzy TOPSIS to rank the municipal solid waste treatment methods in the Canary territory. Ugurlu and Kahraman (2011) proposed a fuzzy VIKOR analysis for the selection of the most appropriate hazardous waste treatment methodology and showed the potential of the proposed methodology for the case of Istanbul. Vinodh et al. (2014) proposed an evaluation model based on the fuzzy AHP and TOPSIS to enable the industry players to perform performance evaluation in a fuzzy environment. Torkamani et al. (2002) used fuzzy TOPSIS as a tool for urban managers in decision-making process. Moreover, Wibowo and Deng (2015) developed an interactive fuzzy MCDM algorithm considering all the interest of individual decision makers in evaluating the performance of alternative e-waste recycling programs in terms of sustainability.

Table 1 Linguistic terms and the corresponding interval type-2 fuzzy sets
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There is also a growing literature on the applications of type-2 fuzzy in waste management area: Kahraman and Sarı (2012) used interval type-2 fuzzy TOPSIS for environmental risk evaluation and make a multi-criteria selection among the treatment alternatives of hazardous waste management. Ma et al. (2017) developed an integrated type-1 and type-2 fuzzy model for tackling regional MSW management problem and showed that their model is capable of helping decision makers to generate reasonable waste-allocation alternatives under uncertainties. Mohagheghi et al. (2016) developed a novel method to evaluate e-waste recycling programs under uncertainty. In the study, the concept of preference selection index is extended with type-2 fuzzy sets to increase the effectiveness of the process. Finally, in a recent study, Lajmi et al. (2017) presented the challenges of a high-performance in-car network traffic analyzer and used the analysis results as input data in type-2 fuzzy rule base system for road choice. Other than this study, to the authors’ knowledge, there is no study applying type-2 fuzzy decision techniques to decision problems in smart city environments. From this aspect, this study is the one of the first applications of type-2 fuzzy multi-criteria techniques for decision aid in the smart city environment. Moreover, this paper is the first study which evaluates the integration of VLC and drone communication technologies into solid waste collection systems.

3 Methodology

Assume that there are n alternatives, \(A=\{a_{1}\,,a_{2},\ldots \,,\,a_{n}\}\) , and m criteria, \(C=\{c_{1}\,,c_{2},\ldots \,,\,c_{m}\}\) . The set C of criteria is divided into two main groups \(C_{1}\) and \(C_{2},\) where \(C_{1}\) represents the benefit attributes and \(C_{2}\) represents the cost attributes. There are k experts, \(E_{1},\) \(E_{2},\ldots ,\) and \(E_{k}\).

Steps of the type-2 Fuzzy TOPSIS method can be summarized as follows:

  • Step 1: Using linguistic terms given in Table 1 (Lee and Chen 2008), obtain the decision matrix \(C_{p}\) of the pth expert:

    (1)

  • Step 2: Aggregate the experts’ opinions by obtaining the average decision matrix \(\bar{C.}\)

    $$\begin{aligned} \bar{C} = ({\widetilde{c_{\imath \jmath }})}_{m \times n}, \end{aligned}$$
    (2)

    where \(\widetilde{\widetilde{c_{\imath \jmath }}} = (\frac{\widetilde{\widetilde{c_{\imath \jmath }^{1}}}\oplus \widetilde{\widetilde{c_{\imath \jmath }^{2}}}\,\oplus \cdots \oplus \widetilde{\widetilde{c_{\imath \jmath }^{k}}}}{k})\), \(\widetilde{\widetilde{c_{\imath \jmath }}}\) is an interval type-2 fuzzy set, \(1\le i \le m,\,1\le j \le \,n,\,1\le p \le k\) (Chen and Lee 2010). Note that, the details of arithmetic operations in type-2 fuzzy sets including, summation, subtraction, and multiplication, can be found in (Lee and Chen 2008) and (Chen and Lee 2010).

  • Step 3: Find the weights of importance matrix \(W_{p}\) of the attributes of the \(p\hbox {th}\) expert. Then, obtain the average weighting matrix \(\bar{W}\) (Lee and Chen 2008):

    (3)
    $$\begin{aligned} \bar{W} = ({\widetilde{\widetilde{w_{\imath }}})}_{1{ xm}}, \end{aligned}$$
    (4)

    where \(\widetilde{\widetilde{w_{\imath }}} =(\frac{\widetilde{\widetilde{w_{\imath }^{1}}}\oplus \widetilde{\widetilde{w_{\imath }^{2}}}\,\oplus \cdots \oplus \widetilde{\widetilde{w_{\imath }^{k}}}}{k})\), \(\widetilde{\widetilde{w_{\imath }}}\) is an interval type-2 fuzzy set, \(1\le i\le {m},\,1\le p \le k\) and k denoting the number of experts.

  • Step 4: Compute the weighted decision matrix \(\bar{C}_{w}\) ,

    (5)

    Where \(\widetilde{\widetilde{v_{\imath \jmath }}}=\widetilde{\widetilde{w_{\imath }}} \oplus \,\widetilde{\widetilde{c\imath \jmath }}\) , \(1\le i\le m, 1\le j\le n\).

  • Step 5: Calculate the ranking value \(\text {Rank}(\widetilde{\widetilde{{v}_{\imath \jmath }}})\) of the interval type-2 fuzzy set \(\widetilde{\widetilde{v_{\imath \jmath }}},\) where \(1\le j \le n\). Then, find the ranking of the weighted decision matrix \(\bar{C}_{w}^{*}\) (Chen and Lee 2010):

    $$\begin{aligned} \text {Rank}(\widetilde{\widetilde{{A}_{\imath }}}= & {} M_{1}(\widetilde{A_{1}^{u})}+M_{1}(\widetilde{A_{\imath }^{L})}+M_{2}(\widetilde{A_{\imath }^{u})}+M_{2}(\widetilde{A_{\imath }^{L})} \nonumber \\&+M_{3}(\widetilde{A_{\imath }^{u})}+ M_{3}(\widetilde{A_{\imath }^{L})}-\frac{1}{4}(S_{1}(\widetilde{A_{\imath }^{u})} +S_{1}(\widetilde{A_{\imath }^{L})}\nonumber \\&+S_{2}(\widetilde{A_{\imath }^{u})}+S_{2}(\widetilde{A_{\imath }^{L})}+S_{3}(\widetilde{A_{\imath }^{u})} \nonumber \\&+ S_{3}(\widetilde{A_{\imath }^{L})} + S_{4}(\widetilde{A_{\imath }^{u})}+S_{4}(\widetilde{A_{\imath }^{L}))} + H_{1}(\widetilde{A_{\imath }^{u})} \nonumber \\&+H_{1}(\widetilde{A_{\imath }^{L})}+ H_{2}(\widetilde{A_{\imath }^{u})}+H_{2}(\widetilde{A_{\imath }^{L})} \end{aligned}$$
    (6)
    $$\begin{aligned} \bar{Y}_{w}^{*}= & {} (\text {Rank}(\widetilde{\widetilde{{v}_{\imath \jmath }}}))_{m \times n}, \end{aligned}$$
    (7)

    where \(1\le i\le m,\,1\le j \le n\).

  • Step 6: Compute the negative ideal solution (NIS) \(x^{-} =(v_{1}^{-},\,v_{2}^{-},\ldots ,\,v_{m}^{-})\) and the positive ideal solution (PIS) \(x^{+} =(v_{1}^{+},\,v_{2}^{+},\,\ldots ,\,v_{m}^{+})\) , where

    $$\begin{aligned} v_{i}^{{-}}\,= \left\{ {\begin{array}{l} \min \left\{ \left\{ \text {Rank}(\widetilde{\widetilde{v_{\imath \jmath }}}) \right\} ,\,if\,\,c_{i}\,\,\epsilon \,\,C_{1} \right. \\ \max \left\{ \left\{ \text {Rank}(\widetilde{\widetilde{v_{\imath \jmath }}}) \right\} {,} \right. \,if\,\,c_{i}\,\,\epsilon \,\,C_{2} \\ \end{array}} \right. 1\le j \le n \end{aligned}$$
    (8)

    and

    $$\begin{aligned} v_{i}^{+}= \left\{ {\begin{array}{l} \max \left\{ \left\{ \text {Rank}(\widetilde{\widetilde{v_{\imath \jmath }}}) \right\} ,if\,\,c_{i}\,\,\epsilon \,\, C_{1} \right. \\ \min \left\{ \left\{ \text {Rank}(\widetilde{\widetilde{v_{\imath \jmath }}}) \right\} , \right. if\,\,c_{i}\,\,\epsilon \,\, C_{2} \\ \end{array}} \right. 1\le j\le n \end{aligned}$$
    (9)

    where \(C_{1}\) and \(C_{2}\) stand for the set of benefit and cost attributes, respectively (Lee and Chen 2008).

  • Step 7: Calculate the distances to PIS and NIS and find the degree of closeness \(\hbox {DoC}(x_{j})\) based on the equations below:

    $$\begin{aligned} d^{+}(x_{j})= & {} \sqrt{{\sum \limits _{i=1}^m {(\text {Rank}\left( \widetilde{\widetilde{v_{\imath \jmath }}} \right) -v_{i}^{+}})^{2}}}, \end{aligned}$$
    (10)
    $$\begin{aligned} d^{-}(x_{j})= & {} \sqrt{{\sum \limits _{i=1}^m {(\text {Rank}\left( \widetilde{\widetilde{v_{\imath \jmath }}} \right) -v_{i}^{-}})^{2}}}, \end{aligned}$$
    (11)
    $$\begin{aligned} \hbox {DoC}(x_{j})= & {} \frac{d^{-}(x_{j})}{d^{+}\left( x_{j} \right) {+}d^{-}(x_{j})}. \end{aligned}$$
    (12)

  • Step 8: Provide the rank order of the closeness scores \(\hbox {DoC}(x_{j})\) in a descending manner. Pick the alternative with the maximum \(\hbox {DoC}(x_{j})\) (Lee and Chen 2008; Chen and Lee 2010).

4 Municipal waste collection system selection: the case study

The collection and transportation of solid waste constitute the major services provided by municipalities in Turkey. Most of the management effort and budget is devoted to these services. It is important to note that there are two types of waste collection systems in Turkey. In the large cities of Turkey, curbside pickups are used for collection. In this collection system, waste collection truck travels and stops at each building to collect the solid wastes. This is repeated daily (if not twice a day). In smaller cities, community bins are used. In this system, the bins are emptied two or three times a week (Turan et al. 2009).

With an area of \(1403~\hbox {km}^{2}\), Tepebaşı district is located on the northwest side of Eskişehir. The district has a population of approximately 320.000. The population density of the district is 400–600 people per hectare (Etli and Aksoylu 2016). In Tepebaşı, collection and transportation of packing and domestic wastes are treated separately. Environmental Protection and Control Directorate of Tepebaşı  Municipality is responsible for the collection and transportation of packing wastes. On the other hand, the collection and transportation of domestic wastes are under the responsibility of Cleaning Services department. Domestic and packing wastes are not collected and transported by the municipality herself. Yearly auctions are held to decide the company to provide these services.

In 2017, approximately 10,000 tons of packing waste were collected and transported in Tepebaşı. This corresponds a monthly average amount of 800 tons of packing wastes. Twenty-four employees and nine trucks are employed in this service. To collect more wastes, each truck is equipped with a compressor. The packing wastes are collected from each household individually twice a week between 07:30 a.m. and 06:00 p.m. Yet, from supermarkets and shopping malls, the wastes are collected more frequently. In total, approximately 15,000 cardboard boxes are located for the collection of packing wastes in Tepebaşı . According to local authorities, 3000–4000 boxes are stolen by illegal collectors each year.

It is estimated that Tepebaşı households produce 295 tons of domestic wastes per day on an average. For the eight months of 2017, they produced 71,301 tons of domestic wastes in total. However, there is no any waste bin or container in Tepebasi. Rubbish bags are used to collect the domestic bags and households leave their rubbish bags to nearest trash dump on daily basis. Moreover, these wastes are collected on a daily basis by 24 dump trucks which are equipped with compressors. These trucks collect the wastes at nights, between 07:00 and 09:00 p.m, and five cleaning vehicles are employed in the mornings to clean the trash dumps. The number of workers employed in this service is 365. All the equipment, labor, and trucks are provided by the private company.

4.1 Research criteria

In this study, seven benefit criteria are used to evaluate the alternative collection solutions. It should be noted that the criteria were confirmed by the municipal experts to be consistent with the current needs and the situation of the region. These criteria are as follows:

  • Environmental friendliness \((C_{1})\) This criterion is used to evaluate the system in terms of the effects created by the system on the nature.

  • Operational feasibility \((C_{2})\) This criterion represents how feasible the system is.

  • Aesthetics \((C_{3})\) This criterion deals with the visual and physical aspects of the system.

  • Innovativeness \((C_{4})\) This criterion is used to understand whether the system is innovative or not compared to the existing systems.

  • Maintenance efficiency \((C_{5})\) This criterion considers the efficiency of time and money spent on the system maintenance.

  • Sustainability \((C_{6})\) This attribute measures the aspects like the environmental, economic, and social sustainability of the system.

  • Setup cost advantage \((C_{7})\) This attribute stands for the efficiency of the investments made during the installation of the system.

Fig. 1
figure 1

Wi-Fi-based SWC system

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4.2 Concepts

In this section, four different concepts are introduced considering the existing problems in Tepebaşı. In this regard, we propose two smart city solid waste collection (SWC) concepts, in which VLC and DC are employed. Moreover, we use two existing smart city SWC concepts, in which Wi-Fi technology and cellular communication are used.

In all concepts, we consider smart bins, which are equipped with sensors, microcontrollers, batteries, compaction devices as well as solar panels. The bins are used to collect waste as well as the data of the waste. For this purpose, the sensors, which is located the top of the bins, measure the level of the waste and such measurement is stored at the microcontrollers. Moreover, when the bins become full, micro-controller communicates with a terminal and informs a server about bins’ situation via this terminal. The server processes the information and conducts a route optimization for garbage trucks as well as informs the garbage trucks about the bins to be emptied and the roads to be traveled. On the other hand, the transmission between microcontrollers and the terminals, which convey the bins’ information to the server, occurs in all concepts by using different technologies. It should be noted that how exactly the server conducts the route optimization is beyond the scope of the study.

Concept 1: Wi-Fi-based solid waste collection system

In this concept, Wi-Fi technology is considered, and the microcontrollers on the top of the bins are equipped with Wi-Fi wireless transceiver module and they communicate with a router to convey the bins’ information to the server.

The system model of a Wi-Fi-based SWC system is shown in Fig. 1. In this system, bins that are located in the same district communicate with the same router by using Wi-Fi technology. For example, the bins, which belong to district # 2, communicate only with Router # 2. As shown in Fig. 1, the system consists of a four-stage protocol. At the first stage, when the bin becomes full, it informs the corresponding router about its situation. Then, the router conveys this information to a server at the second stage. The server processes the information and constitutes a route optimization for available garbage trucks. Next, at the fourth stage, the server informs the garbage trucks about the bins to be emptied and routes to be traveled. Finally, the truck (s) departs to empty the full bin (s).

Concept 2: Cellular communication-based solid waste collection system

In the second concept, the microcontrollers are equipped with GSM modules and communicate with a base station to inform the server.

The system model of a cellular communication-based SWC system is shown in Fig. 2. Due to the coverage provided by the base station, it is assumed that all bins can communicate with the same base station. As it is seen in the figure, the system consists of a four-stage protocol. At the first stage, when the bin becomes full, it informs the base station about its situation. Then, the base station conveys this information to the server at the second stage. Server processes the information and constitutes a route optimization for available garbage trucks. Next, at the fourth stage, the server informs the garbage trucks about the bins to be emptied and routes to be traveled. Finally, the truck (s) departs to empty the full bin (s).

Fig. 2
figure 2

System model of cellular communication-based SWC

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Fig. 3
figure 3

Li-Fi-based SWC system

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Concept 3: Li-Fi-based solid waste collection system

In the third concept, we propose a VLC-based SWC procedure, which uses Li-Fi technology. In this concept, the microcontrollers communicate with streetlights and the streetlights convey the bins’ information to the server. The microcontrollers and streetlights are equipped with light-emitting diode (LED) transmitters and photodiodes, respectively. The microcontrollers send its information to the streetlight using their LEDs, and the streetlights communicate with each other and inform the server.

The system model of a Li-Fi-based SWC system is shown in Fig. 3. In this system, bins that are located in the same district communicate with the same streetlight by using VLC technology. Therefore, the direct link transmission is required between the bin and streetlight in this system. As seen from the figure, the system consists of five phases. At the first phase, when the bin becomes full, it informs the corresponding streetlight about its situation. Then, the streetlight conveys this information to a destination streetlight hop-by-hop via the other streetlights. It should be noted that the direct link transmission between streetlights is required for this system setup. At the third phase, the destination streetlight conveys the information to a server. Server processes the information and constitutes a route optimization for available garbage trucks. Next, at the fourth phase, the server informs the garbage trucks about the bins to be emptied and routes to be traveled. Finally, the truck departs to empty the full bin.

Fig. 4
figure 4

SWC system with drones

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Concept 4: Waste management collection and transportation with drones

In the last concept, we propose a DC-based SWC system which uses drones to convey information. In this concept, a drone flies over the bins and communicate with them by using Wi-Fi technology.

The system model of an SWC with drones is shown in Fig. 4. In this system, a drone travels around all districts and receives information from the waste bins. The system consists of four phases. It is assumed that the capacity of drone’s battery is enough to travel around three districts and receive information from the bins of these districts. At the first phase, the drone travels around the districts one-by-one and receives information from the bins if they become full. At the second phase, the drone conveys the information to a server. Server processes the information and constitutes a route optimization for available garbage trucks. Next, at the fourth phase, the server informs the garbage trucks about the bins to be emptied and routes to be traveled. Finally, the truck departs to empty the full bin.

Table 2 The importance level of the criteria \(({\varvec{C}}_{{\varvec{i}}})\) according to experts’ evaluations
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Table 3 type-2 fuzzy weights \((\widetilde{\widetilde{{\varvec{w}}}}_{{\varvec{i}}})\) for the evaluation criteria \(({\varvec{C}}_{{\varvec{i}}})\)
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5 Findings

In this section, the findings of the waste collection concept selection for Tepebaşı  municipality are described. To determine the importance level of the criteria, the evaluators used the seven-point scale given in Table 1. By using Tables 1 and 2, weights \((\widetilde{\widetilde{{\varvec{w}}}}_{{\varvec{i}}})\) of the evaluation criteria \((\mathbf {{\varvec{C}}}_{{\varvec{i}}})\) are calculated as given in Table 3.

Then, in order to decide the most suitable collection system for the district, the proposed type-2 fuzzy TOPSIS procedure is applied. First of all, the experts evaluated proposed concepts \((a_{1},a_{2},a_{3},a_{4})\) in the light of the criteria given in Table 1. Evaluation scores of the alternatives are given in Table 4.

Later, type-2 fuzzy weighted evaluation matrix is calculated by using Eqs. (3–5). After that, as given in Table 5, the ranks \((\text {rank}(\widetilde{\widetilde{{\varvec{v}}}}_{{\varvec{ij}}}))\) of the alternatives are obtained by making use of Eqs. (6–9).

In the following step, the ranks for the positive ideal and negative ideal solutions are obtained as in Table 6.

The distances from positive ideal solutions and negative ideal solutions are calculated as in Table 7 by using Eqs. (10, 11). In the final step, closeness index and ranking among the collection alternatives are obtained by using Eq. (12) as in Table 8.

Table 4 Evaluation scores of the alternatives
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Table 5 The ranks \((\text {rank}(\widetilde{\widetilde{{\varvec{v}}}}_{{\varvec{ij}}}))\) for the alternatives
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Table 6 The ranks for the positive ideal and negative ideal solutions
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Table 7 Distances from the positive and negative ideal solution
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Table 8 The closeness index \((C^{*})\) and the rankings
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According to Table 8, the best alternative for the waste collection system is a waste collection with drones. The second best concept is Li-Fi-based solid waste collection system. The third best and the last concepts become Wi-Fi-based and cellular communication-based solid waste collection systems, respectively.

A comparative analysis is also conducted to see the validity of the obtained results compared to type-1 fuzzy TOPSIS methodology. To do this, we use type-1 fuzzy extension of TOPSIS proposed by Chen (2000). Linguistic variables are expressed in positive triangular fuzzy numbers using the suggested conversion tables given by Chen (2000). Following the steps in (Chen 2000), the closeness index (\(C^{*}\)) for the concepts is obtained as follows:

Table 9 The closeness index \((C^{*})\) based on type-1 fuzzy TOPSIS
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Table 9 shows that the closeness index, \(C^{*}\), figures are significantly different from those of type-2 fuzzy TOPSIS methodology given in Table 8. Moreover, \(C^{*}\), figures given in Table 9 are very close to each other. Therefore, it is hard to reach a preference order with type-1 fuzzy TOPSIS methodology. This comparative analysis shows that type-2 fuzzy TOPSIS separates the closeness figures more effectively and provides a better preference order compared to type-1 fuzzy TOPSIS technique.

6 Sensitivity analysis

To understand the sensitivity of the figures to changes for the different weight scenarios, a sensitivity analysis is conducted. Table 10 shows the different weight cases which will be used in the sensitivity analysis. To calculate the closeness indexes for each case, at first, we convert the linguistic importance levels given in Table 10 to type-2 fuzzy weights using Table 1. Then, using Eqs. (3–12), the closeness indexes corresponding to each case are calculated. The closeness indexes \((C^{*})\), which are calculated for different cases, are demonstrated in Table 11.

Table 10 Importance levels of criteria for different cases
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As mentioned before, in the current case (CC), the best alternative is \(a_{4}\) (SWC with drones), followed by \(a_{3}\) (Li-Fi-based SWC) and \(a_{1}\) (Wi-Fi-based SWC), respectively. In Case 1, we set all the criteria weights fixed at a level of “medium” importance. As seen from Fig. 5, only increase is observed in the closeness index of \(a_{3}\) and the closeness indexes of all other alternatives decrease. Hence, the ranking among the alternatives changes, and the best alternative becomes \(a_{3}\), followed by \(a_{4}\) and \(a_{1}\) or \(\,a_{2}\), which have the same closeness index, respectively. Compared to Case 1, the importance level of \(C_{7}\) (Setup cost) is increased significantly in Case 2. Figure 5 shows that this change leads to increase in the closeness indexes of \(a_{1}\), \(a_{2}\), or \(a_{3}\). However, the closeness index of \(a_{1}\) dramatically decreases in this case. Moreover, compared to CC, the rankings of \(a_{1}\) and \(a_{2}\) are replaced by each other and the rankings of \(a_{3}\) and \(a_{4}\) remain unchanged in Case 2. In Case 3, we increase the importance levels of \(C_{5}\) (Maintenance efficiency) and \(C_{7}\) (Setup cost advantage) significantly. Such changes in Case 3 made the closeness indexes of \(a_{2}\) and \(a_{3}\) equal and lead to changes in the ranking among \(a_{1}\), \(a_{2}\), and \(a_{3}\). On the other hand, \(a_{4}\) is still the best alternative in this case as in CC. Finally, in Case 4, when the importance levels of \(C_{2}\) (Operational feasibility) and \(C_{3}\) (Aesthetics) are decreased significantly compared to Case 3, the ranking among alternatives becomes the same as Case 3 with increasing closeness index of \(a_{4}\) and decreasing closeness index of \(a_{1}\). It is important to note that the ranking among \(a_{3}\) and \(a_{4}\) does not change in the most of the scenarios.

Hence, sensitivity analysis shows that the ranking among \(a_{3}\) and \(a_{4}\) is robust to changes in importance levels. On the other hand, it can be said that the rankings among \(a_{1}\) and \(a_{2}\) are sensitive to significant changes in the weights of certain attributes.

Table 11 The closeness index (\(C^{*}\)) for alternatives with respect to different cases
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Fig. 5
figure 5

Sensitivity analysis

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7 Conclusion

In this study, alternative municipal SWC systems which are based on different ICTs are evaluated and ranked using a type-2 fuzzy decision aid method. Taking the current situation and needs of a study region into consideration, alternative SWC concepts are designed based on Wi-Fi, cellular communication, Li-Fi, and drone technologies. The case study is conducted in a region the municipal authorities of which support the smart city approach and ongoing smart city projects exist.

While applying the suggested type-2 fuzzy TOPSIS methodology, attributes like environmental friendliness, operational feasibility, aesthetics, innovativeness, sustainability, maintenance efficiency, and setup cost advantage are considered. Analysis results showed that the drone and the visible light communication-based collection systems are the most appropriate systems for the study area. VLC is an environmentally friendly and efficient technology which allows ultra-fast information transfer between humans, machines, and vehicles. Similarly, drone-based technologies are becoming increasingly useful in improving connectivity and coverage indifferent application areas. The results of this study show that these technologies can be preferred and used in the smart city environment, particularly in the solid waste collection context. Usage of fuzzy sets enabled us to successfully convert the vagueness and uncertainty in the judgments of local decision makers and scientific experts. Comparative analysis showed that type-2 fuzzy TOPSIS method served better decision aid compared to that of type-1 fuzzy TOPSIS by providing more dispersed closeness index figures. Finally, to monitor the stability of the results to changes in the attribute weights, a sensitivity analysis is conducted. The results showed that the rankings were almost robust to weight changes.

In the future studies, the suggested type-2 fuzzy TOPSIS methodology proposed here can be applied to solid waste collection problems of other cities and regions. With minor modifications in the criteria structure, the technique can be used in different waste management problems in the context of smart cities.