A novel integrated fuzzy DEA–artificial intelligence approach for assessing environmental efficiency and predicting CO2 emissions

1 A novel integrated fuzzy DEA-artificial intelligence approach for assessing environmental efficiency and predicting CO2 emissions Majid Zadmirzaei1*, Fahimeh Hasanzadeh2, Andres Susaeta3, Ester Gutiérrez4 1* Corresponding author, Department of forestry, Faculty of Natural Resources, University of Guilan, P.O. Box 1144, Sowmeh Sara, Iran, Email: [email protected]; majid.zadmirza[email protected] 2Department of Mathematics and Computer Science, Lorestan University, Khorramabad, Lorestan, Iran, Email: f.hasanza[email protected] 3 Department of Forest Engineering, Resources and Management, Oregon State University, 344 Peavy Forest Science Center, Corvallis, OR 97331, USA. Email: [email protected]du 4 Department of Industrial Management, Escuela Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos, s/n, 41092 Seville, Spain, Email: [email protected] Abstract Undesirable output of industrial economic activities-carbon dioxide (CO2) and other pollutantshave been become global concern because of their harmful effects on the climate, especially for environmentally sustainable production systems which attempts to generate less undesirable outputs, as well as achieve higher levels of production and economic growth. This study proposes a novel environmental efficiency data envelopment analysis (DEA) in conjunction with predicting artificial intelligence algorithms. The proposed model –fuzzy undesirable slacks based measure DEA model (FUNSBM) – measures environmental efficiency in terms of the directional distance function and weak disposability, and its combined approaches (Artificial Neural Network (ANN), ANN+ Particle swarm optimization(PSO) and Artificial Immune System (AIS)) predict optimal values of inefficient Decision Making Units (DMUs) so that they become more efficient considering the possible reduction of CO2 emissions in their production process. The FUNSBM model is applied to a dataset of 30 Iranian forest management units. The findings show that almost 47% DMUs are operating at low efficiency levels with a weak efficiency dispersion, however, these inefficient DMUs could improve their efficiency border via following the combined approaches. This analysis shows that the FUNSBM-AIS approach, by 53% reduction of CO2 emission, is the best approach to predict and/or control CO2 emission in optimal way while FUNSBMANN, and FUNSBM - ANN+PSO are reduced CO2 emission by 15%, and 32% respectively. As the major conclusion, the FUNSBM-AIS approach exhibits a high degree of reliability to predict the lowest amount of CO2 emission and can help improve the inefficient DMUs by following their predicted optimal values. Keywords: Artificial intelligence Algorithms (AIAs); Fuzzy data envelopment analysis (DEA); Greenhouse gas emissions; Nondiscretionary factors; Undesirable output; Uncertain environmental efficiency 2 1. Introduction Anthropogenic use of fossil fuels and higher levels of deforestation and forest degradation have resulted in higher levels of greenhouse gas (GHGs) emissions such as carbon dioxide (CO2), increasing global temperatures. The emissions of CO2 and other pollutants– undesirable outputs of industrial economic activities–have become a climate change challenge across the world (Sueyoshi and Goto 2012a). Industries are evolving to aim greater environmental efficiency in their different operational units, by generating less undesirable outputs as they achieve higher levels of production and economic growth. The nonparametric methodologydata envelopment analysis (DEA), initially developed by Charnes et al. (1978), is one well-documented managerial tool in this case. DEA analyzes and benchmarks a set of decision making units (DMUs)’ environmental efficiency considering their multiple inputs and corresponding outputs. In the recent DEA literature, undesirable outputs (i.e. waste and pollution) have been considerably modeled (Seiford and Zhu 2002; Hua et al. 2007; Zhou et al. 2014; Maghbouli et al. 2014). Some DEA approaches treat the undesirable outputs as inputs for processing (Liu and Sharp 1999; Dyckhoff and Allen 2001; Hailu and Veeman 2001); however, this approach does not accurately represent the manufacturing process. To tackle this issue, Färe et al. (1989) and Picazo-Tadeo et al. (2005) proposed to treat the undesirable outputs by using a directional distance function and weak disposability assumption, in order to expand (contract) good (bad) outputs. Färe and Grosskopf (2010) extended the directional distance function approach by including measurement of slacks. Other extensive DEA models that include impacts of undesirable outputs impacts on environmental efficiency can be found in Fujii and Managi (2013); Huang et al. (2014); Tongying et al. (2017); Fan et al. (2017); and Yu et al. (2018). Although DEA has been widely used to analyze environmental efficiency, some limitations of this approach should be recognized when expanding its applications in different benchmarking fields. DEA conventionally is known as a data-oriented approach which may cause homogeneity problems; this implies that the DMU can be changed at the discretion of decision makers. However, in many real cases, there are some factors that cannot be controlled, known as ‘non-discretionary factors, which have a significant impact on the production process and therefore must be considered in any efficiency analysis (Banker and Morey 1986; Ruggiero 1996 and 2004; Rashidi et al. 2015). Another limitation of the DEA application is its sensitivity to data. It means that the values of the decision variable values are almost ambiguous for the calculation to be calculated accurately, in the case of qualitative data and judgment data. As such, uncertainty and noncrispness arise from volatile and imprecise data. One well-known technique to tackle this kind of uncertainty including non-crisp data is the fuzzy set theory (Zadeh 1978). This approach, first addressed by the fuzzy DEA (FDEA) approach (Sengupta 1992), presents data as linguistic variables using different membership functions. There are some other studies that implemented different FDEA models to deal with undesirable environmental efficiency results (Yu and Su 2017; Mu et al. 2018; Khanjarpanah et al. 2019). Recently, a survey was conducted to apply an FDEA model for undesirable outputs with ideal points (Ebrahimnejad and Amani 2021), which proposed a new approach to solving the FDEA model including triangular fuzzy undesirable inputs and outputs. 3 As an extreme point technique, DEA suffers from predictability issues and cannot accurately forecast the efficiency of other DMUs’ efficiency (Wang et al. 2013; Mostafa 2009). This is a challengeable issue for seek innovative approaches that combine measurement and prediction techniques (McAdam et al. 2008). In this regard, artificial neural network (ANN), a branch of artificial intelligence, first introduced by McCulloch and Pitts (1988), predicts multiple output variables in response to multiple input variables. This technique has been implemented for various problems in engineering and management, especially in some cases where traditional modeling have failed. The combination of ANN and DEA (Athanassopoulos and Curram 1996), has been used to predict the performance of DMU’s performance (Kuo et al. 2010; Ching-Hwang et al. 2009; Kwon 2014; Hsiang-His et al. 2013). Few studies have applied the DEA-ANN approach to environmental efficiency assessment (Shokrollahpour et al. 2016; Olanrewaju and Mbohwa 2017). Recently, a DEA Window approach was used to assess the efficiency of GHG emissions and identify efficiency changes in the primary sectors of European Union countries, under common agricultural policies (Vlontzos and Pardalos 2017). The recurrent neural network has been employed to model efficiency and optimization process, but it is long term dependent (Liu et al., 2021). Other studies have addressed this issue, e.g., Liu et al. (2023), by using the long short-term memory neural network and attention mechanism based gated recurrent method and combining them with uniform manual approximation and projection to reduce the nonlinearity and large scale of data, in the scope of predicting gasoline production. Han et al. (2023) proposed a model to optimize energy structure and ethylene production by developing the long short-term memory neural network and combining it with Montecarlo simulation. Han et al. (2023) proposed an improved residual neural network in the context of predicting CO2 emissions to alleviate vanishing gradients due to increasing network depth. However, there are some problems in choosing ANN parameters mainly because of users’ lack of experience and its back-propagation algorithm, causing biased results. To close this gap, particle swarm optimization (PSO), as a new learning algorithm, can be used for optimizing the predictability parameters of ANN model, particularly with non-linear problems. There are few studies that have combined DEA with ANN+PSO algorithm to assess the performance prediction of DMUs, for example, Khaldi et al. (2019) who investigated the feasibility of using DEA in conjunction with PSO and other meta-heuristic algorithms to assess and predict the performance of pharmaceutical suppliers’ performance. More recently, to tackle complex real-life problems, a new field of computational intelligence has been developed, Artificial Immune System-AIS. These systems solve a wide range of complicated problems including mathematics, information technologies, and engineering. The key benefit of this approach is to learn and memorize intelligently. Furthermore, its results are reliable and the learning process is really fast due to its deterministic nature and, therefore, provides stability against missing data (Dudek 2013; Chan et al. 2018). The combination DEA-Artificial Immune network was initially suggested by Yarahmadi et al. (2016). Since then, different combined fuzzy DEA-AIS approaches have been developed to predict the best units’ values of units in various managerial cases (Hasanzadeh et al. 2018; Amirteimoori et al. 2021). One practical weakness of previous studies is the lack of documentation on how to integrate Data Envelopment Analysis (DEA) and Artificial Immune Algorithms (AIAs) to evaluate 4 performance and predict optimal values for real-world scenarios involving complex, multidimensional decision-making. For example, in a multifunctional forest management system, quantitative forest outputs like growing stock and harvesting revenues can be affected by uncertain socioeconomic and climatic indicators (Zadmirzaei et al., 2019). Furthermore, forest harvesting operations can result in undesirable outcomes like CO2 emissions and other greenhouse gases, which cannot be marketed and are considered judgment data. These outputs are often ambiguous and should be treated as non-crisp (fuzzy) numbers. However, the inputs of forest production can be treated as deterministic data since they are nonvolatile. Furthermore, some external non-discretionary inputs cannot be adjusted in the short term as they are beyond the control of decision-making units (DMUs). Thus, it is crucial to develop an environmental efficiency Slacks-Based Measure (SBM)-DEA model that includes both fuzzy outputs and crisp inputs This model, called fuzzy undesirable nondiscretionary SBM (FUNSBM), can be applied for any production systems. Unlike previous studies, we attempt to develop a FUNSBM model that includes both deterministic discretionary and nondiscretionary inputs, and fuzzy desirable and undesirable outputs to mitigate CO2 emissions resulting from forest harvesting operations. We identify inefficiencies of forest management units’ actual outputs and apply an improved FUNSBM procedure to conduct a sensitivity test for inefficient DMUs and define their target outputs. Furthermore, we integrate the FUNSBM model with artificial neural network (ANN) and immune system (IS) approaches (“FUNSBM –ANN”, “FUNSBM - ANN+PSO”, and “FUNSBM -AIS”) to identify inefficient DMUS’ optimal values and reduce their CO2 emissions. Finally, we compare the results of the these approaches to demonstrate the distinct advantages of each of the new proposed approaches, and to determine best approach for predicting the optimal values (lowest) of CO2 emissions. The rest of this paper unfolds as follows: Section 2 briefly presents the proposed DEA framework; details how to incorporate crisp inputs and fuzzy outputs in the modified FUNSBM model to calculate the inefficiency and CO2 emissions. Section 3 introduces the above-mentioned AIAs; ANN, ANN+PSO and AIS as well as describes the combined approaches proposed combined approaches, (“FUNSBM –ANN”, “FUNSBMANN + PSO” and “FUNSBM-AIS”) to predict the optimal values of all inefficient DMUs’ optimal values and mitigate their CO2 emissions. Section 4 describes a case study located in Iranian Caspian forests. The results and a discussion of our analysis are presented in Sections 5 and 6, respectively. Finally, we offer concluding remarks in Section 7. 2. Proposed methodology The conventional DEA is a data-driven technique and can encounter methodological issues when dealing with complex problems. For example, external uncertain indicators may lead to significant errors in data measurement. To address this, various DEA models have been modified to account for different production process assumptions, including various types of observational data. In the case of the multifunctional forest management system being proposed, a DEA framework has been adapted accordingly, as illustrated in Figure 1. 5 Figure 1. Proposed framework of applied approaches 6 To analyze the data, various DEA methodologies were used. Firstly, the FUNSBM model was developed to measure environmental efficiency and identify inefficient DMUs and their actual values. Secondly, an improved FUNSBM procedure (illustrated by a dotted circle as an intermediate chain) was applied as a sensitivity test for inefficient DMUs to identify their target values. Thirdly, the FUNSBM model was integrated with ANN, ANN+PSO, and AIS algorithms to find the optimal values (i.e., the closest values to targets) of inefficient DMUs and increase overall environmental efficiency. Finally, the results of the three combined algorithms were analyzed in the context of a multifunctional forest management system to determine the most effective approach for predicting the optimal (i.e., lowest) values of CO2 emissions. 2.1. A modified fuzzy undesirable non-discretionary SBM-DEA model Most recent undesirable output DEA studies have utilized non-radial-oriented models. An extended version of the SBM-DEA has been adapted for undesirable outputs to distinguish between efficiency and inefficiency levels for output and input items (Tone 2004; Zhou et al. 2006). The directional distance function (DDF) is formulated under the weak disposability assumption, enabling the calculation of DMUs’ relative efficiency along a predetermined direction and restricting the expansion of undesirable outputs (Appendix A) (Färe et al. 1989; Chambers et al. 1996; Yang and Zhang 2018). An extended SBM-DEA model, including both fuzzy outputs (consisting of two separate desirable and undesirable products) and deterministic inputs (consisting of two separate discretionary and non-discretionary factors), the so-called FUNSBM model, is proposed. It is assumed that there are a total of m DMUs, {DMUj, j=1, …, m}, where each DMU uses fuzzy outputs and crisp inputs in the production process. The deterministic inputs consist of two categories: discretionary (xij), and nondiscretionary (ND) inputs (zj) for i=1, 2, …n and j=1, …, m. The outputs are triangular fuzzy numbers and are divided into two categories: desirable, ( , , ) l m u rj rj rj rj y y y y= , and undesirable outputs, ( , , ) l m u kj kj kj kj w w w w= and represent the r-th fuzzy desirable output and k-th undesirable fuzzy output of the j-th DMU which are self-contained. Therefore, a fuzzy DEA model is proposed for an under evaluation (DMU0) based on the modified version of an output-oriented SBM (Tone 2001) as follows (Model 1): *11 11 1 KT t r rt o ro to s s Max e K T y w − + ==  = + +  +  (1a) s.t. 1 , 1,2,...., ; 1,2,...., n j ij i io j x s x i n j m  − = + = = =  (1b) 1 , 1,2,....., n j rj r ro j y s y r K  + = − = =  (1c) 7 1 , 1,2,.... n j tj t to j w s w t T  − = + = =  (1d) 0 ( ) j j o if z z z=  +  (1e) 0, 0, 0, 0, ( ) 0 j i r t s s s z  − + −      (1f) , , i i i t t t r r r s e s e s e    − − + = = = (1g) The proposed output-oriented model aims to simultaneously increase desirable outputs and decrease undesirable ones (1a). The SBM model is transformed into a directional distance measure of efficiency (DDM) approach (Färe and Grosskopf 2004 and 2010); adapting the objective function and slacks variables as shown in Eq.(1g); i s− , r s+ , t s− , are replaced by predetermined direction vectors ( ii e  , rr e  , tt e  ) and represents the slacks of inputs, undesirable and desirable outputs, respectively. Constraint (1d) is designated for undesirable output under the DDF and weak disposability assumption. Constraint (1e), based on the Ruggiero model (Ruggiero, 2004), evaluates the performance of DMU0 when dealing with external ND inputs ( o z ). In this regard, if the difference between the external nondiscretionary levels is less than or equal to the “correlation factor” -δ(z), a DMU with a higher external nondiscretionary input level could be included in the reference. Various parametric approaches, such as fractional equations, regression analyzes can be used to calculate the value of δ(z) (Amirteimoori et al. 2014; Zadmirzaei et al. 2017). The optimal * o e represents the efficiency based on output slacks─ if *1e= indicates that DMUo is overall output efficient. Furthermore, model (1) is a modified fuzzy undesirable nondiscretionary SBM-DEA, therefore the objective function and constraints (1a and 1c-1d) indicate the triangular fuzzy numbers of the output, which must be converted to crisp values to facilitate a feasible solution for solving model (1). In the fuzzy DEA literature, the α-level approach is the most widespread approach (Khodabakhshi et al. 2016; Mugera 2013; Saati and Memariani 2005; Zadeh 1978). Desirable and undesirable outputs could be reformulated by applying the α-cut technique, 01  , (Esmaeili et al. 2014): ˆ[ (1 ) , (1 ) ] m l m u rj rj rj rj rj y y y y y  = − − + − (2) ˆ[ (1 ) , (1 ) ] m l m u tj tj tj tj tj w w w w w  = − − + − (3) In addition, the crisp distance, dα, can be integrated in the equation. (4) and Eq. (5) and, therefore, the crisp data can be generated for any output as follows: 1 0 1 1/ 2 [ (1 ) , (1 ) ] ( 2 ) 4 m l m u l m u rj rj rj rj rj rj rj rj y y y y y d y y y    = − − + − = + +  (4) 1 0 1 1/ 2 [ (1 ) , (1 ) ] ( 2 ) 4 m l m u l m u tj tj tj tj tj tj tj tj w w w w w d w w w    = − − + − = + +  (5) 8 The FUNSBM model can then be reformulated as α-model (6): *11 11 1 KT t r rt o ro to s s Max e K T y w − + ==  = + +  +  (6a) s.t. 1 , 1,2,...., ; 1,2,...., n j ij i io j x s x i n j m  − = + = = =  (6b) 1 , 1,2,....., n j rj r ro j y s y r K  + = − = =  (6c) 1 , 1,2,.... n j tj t to j w s w t T  − = + = =  (6d) 0 ( ) j j o if z z z=  +  (6e) 0, 0, 0, 0, ( ) 0 j i r t s s s z  − + −      (6f) , , i i i t t t r r r s e s e s e    − − + = = = (6g) 2.2. Improved FUNSBM Procedure In this section, we implement an improved FUNSBM procedure to rectify the outcomes of the preceding Model (6) by adding a certain number of points for inefficient DMUs. The procedure defines the extra improvement needed to increase desirable outputs and decrease undesirable ones until all inefficient DMUs can be fully efficient, as follows: An ()  - inefficient o DMU becomes ()  -efficient if * ˆ() o o r y y s  + =+ and * ˆ() o o t w w s  − =− , in which *() r s  + and *() t s  − are the optimal solutions of the model (6). Currently, we use an improved FUNSBM procedure to calculate the inefficient DMUs’ target values. However, we are aware that achieving accurate target values in real-world applications is a challenge. To overcome this, a combination of the three approaches (FUNSBM-ANN, FUNSBM– ANN+PSO and FUN FUNSBM -AIS) is applied to find the value of the closets value to targets, which called them ‘optimal values’. 3. Integrated FUNSBM model and artificial intelligence algorithms 3.1. The proposed FUNSBM-ANN approach ANNs, which are inspired by the biological complex neural structures, have been applied to predict a variety of economic activities, such as engineering, supplier selection, and ecoefficiency problems (Kuo et al. 2010). Since the 1980s, many different ANN models have been proposed, with the multilayer perceptron (MLP) network being one of the most commonly employed, especially in forecasting (Appendix B). ANN is a data imitation technique that attempts to predict the relationship between the provided input and its corresponding output for a specific data set. It plays a key role in dealing with cases where the relationships between variables are not clearly defined. 9 Furthermore, ANN can correlate a series of independent variables with several dependent variables. Therefore, when DMUs are faced with multiple inputs and their corresponding outputs (parameters), ANN can correspond to DEA models (Karamali et al. 2013). The parameters of the estimated ANN according to the FUNSBM-ANN approach are shown in Table 1. Table 1. Estimated parameters of an Artificial Neural Network * The Levenberg-Marquardt algorithm (LMA) is a numerical optimization technique that falls under the category of trust region algorithms. LMA iteratively adjusts the parameter values, taking into account both the gradient and the curvature of the function, until a local minimum is reached. A two-layer MLP network, consisting of the hidden layer (sigmoid function) and the output layer (linear transfer function), is considered by the FUNSBM-ANN approach (Vlontzos and Pardalos 2017). The Levenberg-Marquardt algorithm is implemented to train the network because it requires more memory, but takes less time, and when the mean square error (MSE) of the validation data set increases, the training and generalization process will be stopped to automatically improve. The proposed FUNSBM-ANN algorithm is applied to find the optimal values of inefficient DMUs as follows: Step 1. Assess the performance of DMUs. Evaluate the efficiency scores by FUNSBM model (6) and determine the inefficient DMUs with their actual values. Step 2. Estimate the target values of the inefficient units. The values of inefficient units (score < 1) can be recalculated to become α-efficient ones by applying the improved FUNSBM procedure. Step 3. Train ANN. ANNs trained by different architectures provide an estimate of relations between inputs (actual values of inefficient DMU calculated by Step 1) and the targets (values of inefficient DMU calculated by Step 2). Step 4. Assess the accuracy of the mathematical modeling by applying the well-tested analysis. The best parameterization for the ANN has been determined after several Parameters Value Data Set 112 Learning rate 0.54 Neurons in hidden layer 10 Optimizer Levenberg- Marquardt* Epochs (max) 2,000 Error tolerance 0.05 16 10; Liyashi-Sara district 8; Chofroud district 4; Fiyab district 5; Astarachai forest company; Rashestan forest company; and Barangostar forest research and extension company. Notice, also, that the forest management unit monitors each district or our studied DMU and includes a 10-year operational management period known as the "forest management planning horizon”, furthermore, the consumer price index (CPI) of Iran for the base year 2016 was used to adjust the monetary data (Central Bank of Iran 2018). 5. Results Some of the fuzzy DEA extensions are implemented in the output-oriented version to estimate the efficiency and/or inefficiency scores of the studied DMUs based on the foregoing framework. 5.1. Environmental efficiency using FUNSBM model The results of the modified FUNSBM model, initially utilized to evaluate the uncertain environmental efficiency of forest management units, are presented in (Table 5). Table 5. FUNSBM efficiency score and actual defuzzified actual output DMUs O1 O2 O3 UO4 Efficiency score DMU01 363.22 53814.33 16.59 1888.84 0.16 DMU02 379.46 80914.55 21.51 2837.32 1.00* DMU03 344.30 121251.66 25.83 4242.92 1.00 DMU04 308.19 70275.12 15.47 2463.97 0.18 DMU05 447.54 311292.36 3.47 43.96 1.00 DMU06 234.08 255692.29 10.42 131.18 1.00 DMU07 377.23 1199507.12 15.27 188.50 1.00 DMU08 300.63 881470.20 10.29 127.66 1.00 DMU09 304.96 600798.42 18.03 241.46 0.61 DMU10 247.63 103757.01 16.50 211.87 0.34 DMU11 295.41 338358.88 9.81 65.53 1.00 DMU12 344.41 468658.38 12.13 298.64 0.62 DMU13 346.30 174741.64 18.79 160.97 1.00 DMU14 214.59 244767.14 16.19 602.79 0.54 DMU15 172.01 489407.77 26.23 77.89 1.00 DMU16 255.23 17105.22 13.58 175.19 0.06 DMU17 298.43 288949.15 24.29 290.73 0.60 17 Note: *Efficient DMUs are shown in bold. DMU18 355.53 231322.20 8.70 108.57 0.61 DMU19 202.88 257454.79 34.07 435.66 0.69 DMU20 220.93 13975.18 12.82 163.50 1.00 DMU21 277.59 222846.09 21.06 275.65 0.87 DMU22 339.83 1015489.79 75.25 1125.47 1.00 DMU23 277.69 219903.82 30.10 361.44 1.00 DMU24 301.02 278794.53 11.43 160.43 1.00 DMU25 295.15 44331.31 18.87 244.48 0.46 DMU26 290.99 62662.58 16.81 218.65 0.24 DMU27 336.29 119830.04 9.19 119.39 0.39 DMU28 327.80 29247.20 28.56 1024.91 1.00 DMU29 275.91 81306.69 19.82 2825.51 1.00 DMU30 491.45 56780.23 18.12 1890.63 1.00 18 DMUs, in the forest value chain industry, who achieve an efficiency score of 1.00 are fully efficient. They accomplish this by maximizing the production of desirable outputs (O1, O2 and O3) while minimizing the production of undesirable outputs, such as UO4 or CO2 emissions. This leads to improved productivity and environmental efficiency simultaneously, which can benefit their overall performance. The results show that 53% of the observations are efficient and the average efficiency is moderately high (0.74) with a weak efficiency dispersion (0.32) 1 . On the other hand, the utilization of the improved FUNSBM procedure, in conjunction with artificial intelligence approaches, holds the potential to substantially enhance the environmental performance of approximately 47% of the inefficient DMUs in subsequent stages. 5.2. Environmental efficiency using an improved FUNSBM procedure An improved FUNSBM procedure is applied using the weak disposability approach to improve the outcomes of the previous model’s results. Table 6 shows the results of the defuzzified target outputs results. Table 6. Defuzzified target output results using improved FUNSBM procedure DMUs O1 O2 O3 UO4 DMU01 363.23 1061758.14 17.35 212.82 DMU02 379.46 80914.55 21.51 2837.32 DMU03 344.30 121251.66 25.83 4242.92 DMU04 370.89 1168343.18 25.43 347.18 DMU05 447.54 311292.36 3.47 43.96 DMU06 234.08 255692.29 10.42 131.18 DMU07 377.23 1199507.12 15.27 188.50 DMU08 300.63 881470.20 10.29 127.66 DMU09 343.29 858235.20 18.03 212.92 DMU10 263.43 805760.95 21.34 127.17 DMU11 295.41 338358.88 9.81 65.53 DMU12 372.83 1177877.03 22.32 298.64 DMU13 346.30 174741.64 18.79 160.97 DMU14 239.56 723142.06 22.62 114.30 DMU15 172.01 489407.77 26.23 77.89 DMU16 330.76 1014363.37 13.58 154.47 1 It should be noted that this result is in terms of FUNSBM (α=0.4) because its discriminating power is higher than the other FUNSBM models with different α levels to identify inefficiency (Appendix F). 19 DMU17 313.70 974400.51 24.29 247.20 DMU18 355.53 701184.93 13.42 108.57 DMU19 206.75 600463.69 34.07 256.72 DMU20 220.93 13975.18 12.82 163.50 DMU21 279.26 314153.22 21.06 234.67 DMU22 339.83 1015489.79 75.25 1125.47 DMU23 277.69 219903.82 30.10 361.44 DMU24 301.02 278794.53 11.43 160.43 DMU25 330.17 237263.90 20.25 244.48 DMU26 290.99 826646.43 16.81 129.14 DMU27 336.29 766089.60 34.75 119.39 DMU28 327.80 29247.20 28.56 1024.91 DMU29 275.91 81306.69 19.82 2825.51 DMU30 491.45 56780.23 18.12 1890.63 Average of improvement changes (%)* (+) 3.61 (+) 438 (+) 18.72 (-) 14.37 Note:*AIC=   (target output-actual output)/(actual output) 100 Our approach is used to estimate the additional improvement for all outputs of 14 inefficient DMUs and to determine their target values, with a specific focus on UO4 (CO2 emission). The improved FUNSBM model is an output-oriented version, in which some desirable outputs are increased while the studied undesirable outputs (CO2 emission) are stabilized and/or significantly decreased for inefficient units to make them fully efficient. Our analysis indicates that the average improvement changes for desirable outputs (O1-O3) are 3.61%, 438%, and 18.72%, respectively, while the undesirable output (UO4-CO2 emission) must be reduced by 14.37%. As a result, the inefficient DMUs may be approaching their efficiency frontier and becoming fully efficient. 5.3. Environmental efficiency using FUNSBM -artificial intelligence integrated approach Based on the FUNSBM model, 14 DMUs (47%) are inefficient. Therefore, to predict their optimal values and identify the best structure of the output dataset, approximately 70% of the dataset is chosen for algorithms’ training, while the remaining 30% is reserved for testing the network's dataset and validating the algorithms' predictive power with different iterations. The validation of various approaches is conducted by comparing the predicted results from the regression analysis. 5.3.1. Performance evaluation of FUNSBM -artificial intelligence approaches 20 The performance metrics of each approach (FUNSBM-ANN, FUNSBM-ANN + PSO, and FUNSBM-AIS) are summarized in Table 7. It shows the performance metrics for both training and testing datasets of the 14 inefficient DMUs. In this case, a comparison of common error measures used in the model evaluation (i.e., determination coefficient, average absolute error, and mean square error) on training and test DMUs is shown. Table 7. Performance metrics of FUNSBM-ANN, FUNSBM-ANN+PSO and FUNSBMAIS approaches Approaches Operations MSE AAE R2 DMUs FUNSBM –ANN All 0.0098 0.00892 0.9085 14 Train 0.009 0.00825 0.9116 10 Test 0.010 0.016896 0.8832 4 FUNSBM -ANN+PSO All 0.007 0.00789 0.933 14 Train 0.006 0.007433 0.9156 10 Test 0.009 0.0191098 0.9482 4 FUNSBM –AIS All 0.00035 0.00030 0.9999 14 Train 0.0004 0.000425 0.9999 10 Test 0.00024 0.0002 1.0000 4 Note: Mean square error (MSE) = ( ) 2 1 ˆ/ n ii i y y n = −  ; Average absolute error (AAE) = 1 ˆ/ n ii i y y n = −  ; Determination coefficient (R2) = ( ) ( ) 22 11 ˆ 1/ nn i i i ii y y y y ==  − − −    . This table displays the results of the MSE and AEA values for the different approaches in the training and test datasets. It reveals that the MSE and AEA values are generally similar or slightly worse in the test dataset than in the training dataset for FUNSBM-ANN and FUNSBM-ANN+PSO, whereas they are better in the test dataset for FUNSBM-AIS. This indicates the higher accuracy of the FUNSBM-AIS approach in minimizing errors achieved from FUNSBM-ANN and FUNSBM-ANN+PSO. Moreover, the R2 coefficient, which measures the variation in the optimal value explained by the target value, shows that FUNSBM-AIS and FUNSBM-ANN+PSO fit better in the test dataset than in the training dataset, while FUNSBM-ANN performs poorly. Overall, these results demonstrate the high predictive power of the FUNSBM-AIS approach, achieving the lowest error rates and the best-fit estimates for both the training and test datasets. Conversely, FUNSBM-ANN approaches have weak predictive accuracy, and their error rates vary between low and high for both datasets. 21 Figure 2 presents a scatterplot of optimal values versus target values (normalized between 0 and 1) for the different approaches in the training and test datasets. It shows that FUNSBMAIS outperforms the other approaches in terms of fitting the data. The R2 values for the test dataset indicate that FUNSBM-AIS has the highest prediction similarity index (R2=1) and FUNSBM-ANN has the lowest (R2=0.8832), resulting in a 13.22% improvement for FUNSBM-ANN versus FUNSBM-AIS and a 5.46% improvement for FUNSBM-ANN+PSO versus FUNSBM-AIS. Figure -Regression result of FUNSBM - ANN+PSO model Data Fit Y=T ANN ANN+PSO AIS 22 Figure 2. Regression plots of FUNSBM-ANN, FUNSBM –ANN+PSO, and FUNSBM-.AIS during training and testing Notes: Solid line: difference between the target values of the final FUNSBM procedure and the optimal values of FUNSBM –ANN, FUNSBM –ANN+PSO, FUNSBM -AIS approaches. Dashed line: best fit linear regression between the optimal values of the foregoing approaches and the targets values of improved FUNSBM procedure. Hence, it indicates that the FUNSBM-AIS network is well trained to perform the prediction with a high level of similarity for the obtained optimal values, confirming the better accuracy/predictive power of the FUNSBM-AIS approach. The results of the comparison between the predicted optimum and target values of each inefficient DMU using improved FUNSBM procedure and three integrated algorithms (FUNSBM-ANN, FUNSBM -ANN + PSO, and FUNSBM -AIS) are depicted in Figure 3. This analysis is only used for fourteen inefficient DMUs in order to increase their desirable outputs (a-c) and decrease their undesirable output-CO2 emission (d) simultaneously. 23 Figure 3. Comparison of ANN, ANN-PSO and AIS approaches according optimal versus target values by DMU level and by desirable (a-c) and undesirable output (d) This analysis reveals that the most significant difference in applied approaches for desirable output1 (a) is found in DMU18, where the target value is nearly 355.53 (m3/ha), but its optimal value predicted by FUNSBM-ANN, FUNSBM-ANN+PSO, and FUNSBM-AIS is 250.53, 303.67, and 355.53 (m3/ha), respectively. Additionally, for the undesirable output of CO2 emission (d), the observed DMU18 has a target value of approximately 108.57 (kg/ha), while its optimal value predicted by FUNSBM-ANN, FUNSBM-ANN+PSO, and FUNSBMAIS is 75.57, 101.57, and 108.57 (kg/ha), respectively. As a result, the FUNSBM-AIS approach approximates the target values for all inefficient DMUs in a similar manner. 24 Box plots of the difference between target values and predecited optimal values for AIS, ANN+PSO and ANN by the output (O1, O2, O3 and UO4) are shown in Figure 4. Figure 4. Target values-Simulated values (differences) for AIS, ANN+PSO and ANN by the output (O1, O2, O3 and UO4) Notes: Boxplots display the first quantile, median and third quartile of differences data. Lower and upper whiskers extend from the hinges by first quantile -1.5·interquartile range and third quantile +1.5·interquartile range, respectively. Dots represent corresponding differences. P-values correspond to significant differences between the simulated approaches according Kruskal-Wallis test. The differences between the target and predicted optimal values of the outputs were in the ranges 0-4.13 m3/ha, 0-880.84 Iranian millionRials /ha, 0-0.32 tons/ha and 0-0.93 kg/ ha for the AIS approach, 1.76 -51.86 m3/ha, 4999.99-118000 Iranian millionRials /ha, 0.3-2.0 tons/ha and 4-31 kg/ha for the ANN + PSO approach and 28.86-105 m3/ha, 77000-214000 Iranian millionRials /ha, 1-3 tons/ha and 22-52 kg/ha for the ANN approach. The Kruskal- Wallis test is used for comparison across the different approaches by output. The results of the tests confirm that all the differences were significant between the approaches (all, pvalue<0.01). Post hoc analysis for each output, using the Jonckheere-Terpstra test for ordered alternatives, revealed that the AIS approach had significantly smaller distance to the target than ANN+PSO and ANN for each output, in turn, ANN + PSO had significantly smaller distance to the target than ANN approach (Z statistic; p-value<0.01(***): ZO1=6.32***; ZO2=6.56***; ZO3=6.57*** ZUO4=6.14***). The percentage of reduction in CO2 emission using three applied approaches for all inefficient DMUs is illustrated in Figure 5. 25 Figure 5. Reduction percent of CO2 emission through FUNSBM -ANN, FUNSBM - ANN + PSO, and FUNSBM -AIS approaches This analysis shows that the FUNSBM-AIS approach, by 53% reduction of CO2 emission, is the best approach to predict and/or control CO2 emission in optimal way while FUNSBMANN, and FUNSBM - ANN+PSO are able to reduce CO2 emissions by only 15% and 32%, respectively. The trained FUNSBM-ANN, FUNSBM-ANN+PSO, and FUNSBM-AIS are evaluated based on their performance in predicting the optimum values of the fourteenth inefficient DMUs. The analysis focused on the errors between the predicted and the target values (Figure 6). 15% 32% 53% ANN ANN+PSO AIS 32 Appendix A. Directional Distance Function (DDF) and weak disposability DDF lets decision makers have more flexibility in choosing either a general directional vector for all DMUs or a specific vector for each. The concept of weak disposability is of great significance in environmental management to change proportionally both good and bad outputs, exposing therefore the potential efficiency improvement along different directions (Long et al. 2015; Aparicio et al. 2016). The proposed approach suppose that the regulated model is based on null-joint production hypothesis which imply both desirable and undesirable outputs are jointly produced in real production systems as follows: ( ) ( ) , ; 0 0y w p x w y =  = (A.1) Where the vectors of input, desirable output, undesirable output, and means of output sets through a given technology are denoted by , , ,x y w and ( ) px . The DDF approach defined is based on Shephard’s distance functions (Shephard 1970), which could be formally defined for undesirable outputs into a given technology set (T) as follows: ( ) ( ) ( ) , , ; , , : , T i r t r t i D x y w e e e Sup y e w e p x e     − − = + −  −   (A.2) where ( ) ,, i r t e e e e= − − is the direction vector. Eq. (A.2) tries to maximize the desirable output amounts in the r e , and search for the largest feasible contraction of undesirables and inputs in the t e− and i e− directions, respectively. The negative signs indicated (-) in ( ) ,, i r t e e e e= − − reflect undesirable outputs and inputs are being reduced. Appendix B. Multilayer Perceptron (MLP) network Each neuron, which is organized into one of the three basic layers: input, output, and (one or more) hidden layers, is linked with other neurons in other layers via weighted connections in the MLP network; also each neuron’s weighted inputs and bias unit are calculated using the mathematical expressions such as the Back Propagation (BP) method (Shahin et al. 2008; Dang et al. 2021) (Figure B). 33 Figure B. Basic structure of a MLPANN network and BP method Note: i x = the input from node i, i = 0, 1, …, n; j y = the output of node j; ji w = the connection weight between nodes j and i; j I = the activation level of node j; and ( ) f = the transfer function. Appendix C. PSO algorithm Assuming that the dimensions of the number of particles and the searching space are denoted by N and D, respectively. In this d-dimensional search space, each particle (ith) is associated with a k-dimensional position vector ( k i x ) and a k-dimensional velocity vector ( k i v ) which indicate where the particle is travelling, hence the population can move to a new optimal point (at time t+1) using the following updating Eq. (C.1) and Eq. (C.2) (Sharaf et al. 2018; Guo et al. 2018): ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 12 1 . (#) . (#) k k k k k k i i i i i i v t w v t c rand p t x t c rand g t x t+ =  + − + − (C.1) ( 1) ( ) ( 1), 1 , 1 k k k i i i x t x t v t i N k D+ = + +     (C.2) Where w is the inertia factor which use to evaluate the performance and convergence rate. c1 and c2 denote different acceleration coefficients, i.e., cognitive component and social component which are the best situation that a member and entire group could gain, respectively, “rand(#)” random numbers in a standard normal distribution, U(0; 1), t stands for the iteration number, k i p and k i g are the best position of the ith particle in the search stage called personal experience (Pbest), and the global best position found in the population called overall experience (Gbest), respectively. Appendix D. Hybrid ANN+PSO procedure D.1. ANN+PSO fitness function In hybrid ANN+PSO model, the trainable ANN parameters (weights and biases) are considered as the particles (decision variables) and the problem’s feasible space is specified 34 by the range of these variables variations. Therefore, the cost/fitness function of these particles can be defined as the RMSE (Chau 2007; Shariati et al. 2019): ( )   2 11 1( , ) O S k i i kl i l kl fw T P w b S==  −=    (D.1) Where f is the cost function, Pkl and Tkl stand for the predicted output (based on wi (weights) and bi (biases)) and the target value, S and O denote the number of training samples and neurons, respectively. D.2. Diagram of the ANN+PSO program Figure D.2. Flow diagram for training ANN using PSO algorithm 35 Appendix E. AIS algorithm Figure E. The network structural of AIS approach The antigen is processed and transformed into the competitive layer by a pre-processing layer. One TH cell that gets the most input stimuli is just activated in the TH cell layer. Mathematically, the weights between the APC layer and the TH layer are represented by ij W for i=1, 2, …, N and j=1, 2, …. M, whereas the weights between the competitive layer and stimulation–inhibition layer are determined by ( , 1,2,..., , 1,2,..., ) ji V v j M i N= = = (Dai et al. 2010). 36 Appendix F. Table F. Performance results of the FUNSBM model with different α levels DMUs FUNSBM (α=0.2) FUNSBM (α=0.6) FUNSBM (α=0.8) DMU01 0.55 0.77 0.81 DMU02 1.00 1.00 1.00 DMU03 1.00 1.00 1.00 DMU04 1.00 1.00 1.00 DMU05 1.00 1.00 1.00 DMU06 1.00 1.00 1.00 DMU07 1.00 1.00 1.00 DMU08 1.00 1.00 1.00 DMU09 0.82 1.00 1.00 DMU10 0.34 0.63 0.68 DMU11 1.00 1.00 1.00 DMU12 0.69 0.72 0.82 DMU13 1.00 1.00 1.00 DMU14 0.54 0.74 0.79 DMU15 1.00 1.00 1.00 DMU16 0.26 0.44 0.47 DMU17 0.68 0.70 0.73 DMU18 0.71 0.74 0.81 DMU19 0.76 0.79 1.00 DMU20 1.00 1.00 1.00 DMU21 0.89 0.91 0.93 DMU22 1.00 1.00 1.00 DMU23 1.00 1.00 1.00 DMU24 1.00 1.00 1.00 DMU25 0.46 0.66 0.69 DMU26 0.35 0.37 0.39 DMU27 1.00 1.00 1.00 DMU28 1.00 1.00 1.00 DMU29 1.00 1.00 1.00 DMU30 1.00 1.00 1.00 37 Ethics declarations Conflict of interest: Authors declare that they have no conflict of interest. Ethical approval: This manuscript does not contain any studies with human participants or animals performed by any of the authors and they approve the final version of this manuscript. Informed consent: Informed consent was obtained from all individual participants included in the study. Authorship contributions Majid Zadmirzaei: Conceptualization, Methodology, Resources, Software, Writing – original draft. Fahimeh Hasanzadeh: Software, Formal analysis, Data curation, Visualization. Andres Susaeta: Methodology, Validation, Writing – review & editing, Supervision. Ester Gutiérrez: Visualization, Formal analysis, Writing – review & editing, Supervision. Data availability Due to some limitations, the datasets analyzed during the current study are not publicly available, but may be requested from the corresponding author. 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