Intuitionistic fuzzy MULTIMOORA approach for multi-criteria assessment of the energy storage technologies
Graphical abstract
Introduction
Multiple objectives need to be met when designing sustainable technologies and products as different domains of sustainability (economic, social and environmental) are often conflicting among themselves. For instance, cleaner technologies are often more expensive. In this regard, the use multi-criteria decision making (MCDM) techniques becomes an important issue. Indeed, MCDM techniques can be divided into the two classes depending on the nature of the data used for decision making [1], [2]. First, multi-objective decision making (MODM) techniques aim at identifying the most preferable decisions within a continuous set of feasible solutions (i.e. the number of alternatives considered is infinite) [3], [4], [5], [6]. Second, multi-attribute decision making (MADM) techniques focus on discrete sets of feasible alternatives. In the latter case, the number of solutions is limited by the number of alternatives considered. Usually, the single best alternative is identified. In this paper, we rely on MADM, yet, for sake of convenience, we stick to term MCDM when referring to multi-criteria analysis in the sequel.
The information of the performance of the alternatives under consideration is often imprecise due to the nature of the data, measurement errors or the underlying research question. For instance, subjective data provided by experts might be associated with different degrees of certainty based on their confidence. As regards the measurement issues, the results of measurement might vary depending on the assumptions taken and precision of measurement. The nature of the problem solved by MCDM determines the decision information in that problems involving higher amount of stochastic information require quantifying and imputing such data. The fuzzy set theory proposed by Zadeh [7] can be applied in case uncertain information is used in the decision making process. Atanassov [8] further generalized the fuzzy sets and proposed intuitionistic fuzzy sets which can be defined in terms of the degrees of membership and non-membership (the residual term is referred to as the degree of indeterminacy). Xu [9] defined the intuitionistic fuzzy numbers (IFNs) which can be used in the MADM to represent uncertain data.
There have been a number of MCDM techniques proposed. These techniques differ in the underlying principles of aggregation. For instance, Løken [10] considered MCDM methods based on the value function (utility function), reference point and outranking. One of the most important characteristics relevant to the sustainability problems is whether the approach applied is compensatory one or not [11]. The compensatory methods allow improving the values of the utility functions by altering a single decision variable without considering the values of the remaining variables. On the other hand, non-compensatory techniques prevent the utility functions from being increased if some variables remain at extremely low levels. Among the MCDM techniques, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) [12], and Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) [13], (1998) are the two methods relying on the reference point approach. In this regard, they do not allow for complete compensation among the attributes. The Simple Additive Weighting [14] is based on the value function and allows for complete compensation among the attributes. The Weighted Product approach [15] is similar, yet does not aloe for full compensation in the decision making. The WASPAS method combines the weighted sum and weighted product techniques [16], [17]. The ARAS technique is based on the reference point approach [18]. The Multi-objective Optimization by Ratio Analysis (MOORA) [19] and its extension – MOORA plus the Full Multiplicative Form (MULTIMOORA) [20] – is a comprehensive MCDM technique combining additive and multiplicative utility functions as well as the reference point approach. This implies it contains the properties of multiple classes of the MCDM techniques.
As the decision making often times involves uncertain information, the extension of the MCDM techniques with the IFNs has been carried out. Boran et al. [21], [22] and Aloini et al. [23], [24] applied intuitionistic fuzzy TOPSIS method for supplier selection, energy planning, and machine selection. Zhang and Xu [25] extended the fuzzy TOPSIS into interval-valued intuitionistic fuzzy environment and applied the proposed approach for group decision making. Chen [26] proposed the concept of inclusion for comparison of the interval-valued IFNs and applied it for TOPSIS-based decision making. Li and Chen [27] presented the TOPSIS technique for trapezoidal intuitionistic fuzzy information. Yue [28] proposed intuitionistic fuzzy TOPSIS technique involving additional negative ideal solution defined as the complement of the positive ideal solution. Gupta et al. [29] proposed interval-valued intuitionistic fuzzy TOPSIS where the weights of criteria re determined endogenously by means of linear programming model. Yang et al. [30] presented intuitionistic fuzzy TOPSIS for group decision making and discussed the possible choice of criterion weights. Zeng and Xiao [31] presented TOPSIS for hesitant fuzzy sets. Büyüközkan et al. [32] proposed group decision making framework involving Analytic Hierarchy Process and VIKOR technique in the intuitionistic fuzzy setting. Büyüközkan et al. [33] presented a series of MCDM techniques (COPRAS, VIKOR, and MULTIMOORA) for the interval-valued intuitionistic fuzzy information and applied them for choosing a cloud computing provider. Rostamzadeh et al. [34] proposed the ARAS method for fuzzy environment. Büyüközkan and Göçer [35] extended the ARAS technique into intuitionistic fuzzy environment. Devi [36] presented VIKOR method based on intuitionistic fuzzy information with application to robot selection. Wan et al. [37] developed VIKOR technique for triangular IFNs. Tavana et al. [38] and Wu et al. [39] presented VIKOR in stochastic and probabilistic settings, respectively. Zeng and Chen [40] proposed VIKOR method involving intuitionistic fuzzy induced aggregation operators. Yu [41] proposed aggregation operators for IFNs taking the confidence levels associated with expert assessments into consideration.
Development of sustainable energy sector is a topical issue for contemporaneous economies [42], [43], [44], [45], [46], [47], [48], [49], [50]. In this regard, the promotion of smart grid technologies is important. Among different components of the smart grids, the energy storage technologies need to be properly chosen. The choice of the energy storage technology comprises a MCDM problem as multiple technologies are defined with respect to multiple conflicting criteria. Barin et al. [51], Raza et al. [52] and Ren [53] presented the cases of the choice of the energy storage technologies, yet those studies considered a limited number of technologies and/or criteria. What is more, MULTIMOORA technique has not been applied in spite of its appealing features (i.e. the use of three different utility functions and a mixture of compensatory and non-compensatory approaches). This paper aims to develop an MCDM approach based on MULTIMOORA extended into intuitionistic fuzzy environment which allows identifying the most preferable energy storage options based on economic, social and environmental criteria involving uncertainty. To do this, we firstly discuss the possible energy storage options. Second, we define the criteria which should be taken into consideration when choosing the energy storage technology. Third, we propose an MCDM procedure for aggregation of imprecise information describing the candidate energy storage technologies.
The proposed MCDM framework relies on the MULTIMOORA technique which is based on several aggregation principles (namely, additive utility function, reference point approach and the multiplicative utility function). The MULTIMOORA method was proposed by Brauers and Zavadskas [19], [20]. Recently, the method has been extended to handle hesitant fuzzy sets [54], neutrosophic fuzzy sets [55], Shannon’s entropy [56], dynamic environment [57]. The MULTIMOORA method has also been applied in engineering, see e.g. Souzangarzadeh et al. [58] and Büyüközkan et al. [33]. In this paper, we propose MULTIMOORA-IFN2 which is based on the intuitionistic fuzzy sets (IFSs) and allows aggregating the results provided by the three parts of MULTIMOORA. The use of IFSs enables one to fuse fuzzy and crisp data which is important in the case of the evaluation of the energy storage technologies due to the underlying uncertainties.
The contribution of this paper is threefold. First, we propose MULTIMOORA-IFN2 in the context of information fusion so that information of different types (e.g. crisp, interval, fuzzy, linguistic variables) could be transformed into IFNs. This allows for more comprehensive analysis of the alternatives under consideration with different patterns of uncertainty and vagueness. Second, we revise the MULTIMOORA-IFN by introducing aggregation of the three utility functions under the MULTIMOORA-IFN2 technique. This renders a more operational MCDM technique suitable for large-scale analysis. Third, the empirical case of the energy storage technology selection may contribute to improvement of effectiveness of decision making in microgrid management. While the procedure for information fusion used in this research is not a novel one, the extension of the MULTIMOORA-IFN technique contributes to the literature on soft computing.
The paper is structured as follows. Section 2 discusses the major types of the energy storage technologies along with the properties thereof. Section 3 identifies the criteria used to rank the energy storage technologies. Section 4 turns to the methodological issues. Specifically, the notions related to the intuitionistic fuzzy sets and principles for the fusion of hybrid data are presented. The proposed extension of the MULTIMOORA technique is also discussed. The results of empirical analysis are presented in Section 5.
Section snippets
Energy storage technologies
The energy storage technologies differ in their age: there have been such well-established technologies as pumped hydroelectric storage, whereas as batteries and flywheels only recently have appeared as tools for power system planning. Many storage technologies are still being developed and increasingly applied at a limited scale. The possible applications of different technologies vary with the scale of application. Taking the thermal energy storage (TES) as an example, one can note that TES
Criteria for the MCDM problem
The previous section discussed the different energy storage technologies. In this section, we focus on the criteria describing the performance of the energy storage systems in regards to the goals of sustainability and energy security. First, we present the indicator system and then apply it for the selected energy storage systems. This results in a decision matrix for MCDM problem.
As the energy storage technologies should contribute to improvement in energy sustainability, the EU priorities
Methodology
In this sub-section, we discuss the properties of the quantitative approach used in the paper. Specifically, we focus on the representation of the decision data by the intuitionistic fuzzy information. Then, we turn to the aggregation by the multi-criteria decision making technique MULTIMOORA-IFS.
Multi-criteria assessment of energy storage technologies
In this section, we apply the MULTIMOORA-IFN2 technique for ranking the energy storage technologies against a set of criteria belonging to different domains of sustainability. The analysis is carried out in two directions. First, we apply the MULTIMOORA-IFN2 with multiple weight vectors so as to check the sensitivity of the results with respect to changes in the importance of the criteria considered. Second, we compare the MULTIMOORA-IFN2 to the other MCDM techniques. Specifically, the VIKOR
Conclusions
In this paper, we proposed an intuitionistic fuzzy multi-criteria decision making approach for prioritizing the energy storage technologies. We have showed that there has been a number of competing energy storage technologies which feature different properties. In order to streamline the process of energy planning, one needs to consider all the considering criteria simultaneously. We, therefore, adapted the multi-criteria technique MULTIMOORA-IFN and proposed MULTIMOORA-IFN2 which allows
Acknowledgments
This paper is supported by National Natural Science Foundation of China (No. 71671165) and Statistical Scientific Research Project of China (No. 2018LY80).
Conflict of interest
The authors declare that there is no conflict of interest.
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