The traditional concept of the internet as an infrastructure network seeks to diminish end-user terminals and move to the idea of “smart” interconnected objects to shape pervasive computing environments. A new paradigm called “Internet of Things” (Atzori et al., 2010; Noje et al., 2020; Perera et al., 2014) has been formed to refer to:

Identifying the challenges to the implementation of IoT can help researchers and PMs in planning to develop its applications. Table 2 highlights the most critical challenges facing the development of IoT from the technological, security, business, legal, and cultural aspects.

Since IoT applications are widespread and evolving (Kim and Kim, 2016) and have a variety of applications in the agricultural sector (Elijah et al., 2018), the Sandelowski and Barroso’s Meta-Synthesis Method is used to identify applications of the IoT in the agriculture sector (Sandelowski and Barroso, 2006). Figure 1 summarises the research process, including the criteria for accepting and rejecting articles, keywords used in searching for research articles, research timeframe, and the search of databases, journals, and various search engines. In the final step, policy-makers out of 862 items were identified, and 403 articles were analysed.

The identified IoT applications fall into eight areas: open-field agriculture, greenhouses, hydroponics and aquaponics, open-air horticulture, livestock farming, fishery and aquaculture, forestry, and distribution and supply networks. Table 3 presents the IoT applications identified based on different agriculture areas.

On the one hand, the applications of IoT in various agricultural areas are ubiquitous. On the other hand, the implementation of IoT has many challenges due to its evolutionary nature. However, no framework has been provided to assist PMs in making decisions regarding implementing IoT in different agriculture areas. To be transparent, a framework for selecting the agriculture areas that are more appropriate for implementing IoT that must be considered both SD goals and IoT challenges simultaneously is necessary. Of course, as previously shown in Tables 1 and 2, measuring each of these two objectives need to take into account several criteria that are sometimes inconsistent. MADM approaches offer a variety of methods for obtaining expert opinions and making the right decisions on a particular issue by considering multiple criteria (Shen and Tzeng, 2018). A review of applications of MADM methods in similar domains (Kim and Kim, 2016; Luthra et al., 2018; Quaddus and Siddique, 2001; Vinodh et al., 2013; Zarei et al., 2016) indicates the potential of these methods in establishing decision-making frameworks in the field of study.

In this study, the fuzzy Delphi method (FDM) is used to adapt the experts’ views on the determination of essential criteria (Lin, 2013) in evaluating IoT applications in the agriculture sector. The Delphi method, first used in technology prediction in 1950, was rapidly developed in various fields (Mullen, 2003). Then, in 1985, Murray et al. improved its ambiguity and uncertainty by applying fuzzy theory (Dahooie et al., 2018; Kuo and Chen, 2008). Since various techniques have been proposed for FDM calculations, this study uses the approach proposed Kuo and Chen (2008). Each fuzzy number ( T A ) is defined as follows: (1) T A = ( L A , M A , U A ) , L A = min ( X A i ) , U A = max ( X A i ) , M A = ∏ i = 1 n X A i n , where X A i is the proposed value of the decision-maker i in terms of the critical factor A, ( i = 1 , 2 , … ). L A , U A , and M A are the lower limit values, the upper limit values, and the geometric mean of the essential factor A, respectively. In the next step, the defuzzification process is performed using the following model (Dahooie et al., 2018): (2) D F k = ( U k − L k ) + ( M k − L k ) 3 + L k , where L k , U k , and M k are the lower limit values, the upper limit values, and the geometric mean of the vital factor k, respectively.

The last step is to set a threshold to accept or reject the criteria (Dahooie et al., 2018). For this purpose, according to experts’ opinions, the value 4 and 3.5 was set as the threshold for the SD criteria and IoT challenge criteria, respectively. Finally, the criteria with the values lower than the threshold were removed from the list, and the final list of measures necessary for evaluation was created (Tables 3 and 4).

One of the applications of the fuzzy number set theory proposed by Zadeh (1965, 1975) is to use it in the process of making decisions based on ambiguous and uncertain information like decision-makers’ opinions (Lima Junior et al., 2014). In this theory, the membership of an element in the fuzzy number can only have a definite value between zero and one. However, in reality, the degree of non-membership of an element in the fuzzy number is not equal to one minus the degree of membership. It means that there may be some degree of hesitance. Thus, Atanassov introduced intuitive fuzzy sets by generalising the fuzzy number set (Atanassov, 1986; Zeng et al., 2019). The intuitive fuzzy number has the features of membership degree, non-membership degree, and degree of hesitance. Atanassov and Gargov (1989) presented the interval-valued intuitive fuzzy numbers set by generalising the fuzzy number (Wang et al., 2019b; Ye, 2010). As with generalised fuzzy numbers, the interval-valued fuzzy numbers can be trapezoidal (interval-valued trapezoidal fuzzy numbers) or triangular (IVTFN). As shown in Fig. 4, Yao and Lin (2002) presented an IVTFN as follows Stanujkic (2015): (3) A ˜ = [ A ˜ L , A ˜ U ] = [ ( a l ′ , a m ′ , a u ′ ; ω A ′ ) , ( a l , a m , a u ; ω A ) ] , where A ˜ L and A ˜ U represent low and high triangular fuzzy numbers, respectively. A ˜ L ⊂ A ˜ U ; μ A ˜ ( x ) is the membership function and denotes the degree to which an event may be a member of A ˜. μ A ˜ L ( x ) = ω A ′ Besides, μ A ˜ U ( x ) = ω A are the lower and upper membership functions, respectively.

Besides, a particular case of IVTFN is the normalised IVTFN in which ω A ′ = ω A = 1 has the same state. The normalised IVTFN shown in Fig. 4 can be represented in Fig. 5 (Stanujkic, 2016). (4) A ˜ = [ A ˜ L , A ˜ U ] = [ ( a l , a l ′ ) , a m , ( a u ′ , a u ) ] .

If A ˜ = [ A ˜ L , A ˜ U ] = [ ( a l , a l ′ ) , a m , ( a u ′ , a u ) ] and B ˜ = [ B ˜ L , B ˜ U ] = [ ( b l , b l ′ ) , b m , ( b u ′ , b u ) ] are two IVTFN, the main algebraic operation can be defined as follows Stanujkic (2016). (5) A ˜ ⊕ B ˜ = [ ( a l + b l , a l ′ + b l ′ ) , a m + b m , ( a u ′ + b u ′ , a u + b u ) ] , (6) A ˜ ⊝ B ˜ = [ ( a l − b l , a l ′ − b l ′ ) , a m − b m , ( a u ′ − b u ′ , a u − b u ) ] (7) A ˜ ⊗ B ˜ = [ ( a l × b l , a l ′ × b l ′ ) , a m × b m , ( a u ′ × b u ′ , a u × b u ) ] , (8) A ˜ ◯ ÷ B ˜ = [ ( a l ÷ b u , a l ′ ÷ b u ′ ) , a m ÷ b m , ( a u ′ ÷ b l ′ , a u ÷ b l ) ] , (9) 1 k ⊗ A ˜ = [ ( 1 k × a l , 1 k × a l ′ ) , 1 k × a m , ( 1 k × a u ′ , 1 k × a u ) ] , k > 0 . 0.\end{aligned}\]]]>

Decision-makers cannot quantitatively evaluate many aspects of various activities in the real world but can qualitatively evaluate, i.e. by ambiguous or inaccurate knowledge. In this case, using linguistic variables instead of numerical values could be a better approach (Keršulienė and Turskis, 2014). Therefore, the variables used in such problems are evaluated through linguistic terms (Herrera and Martínez, 2000). In the researches done by several authors, different linguistic variables based on triangular or trapezoidal fuzzy numbers have been proposed (Stanujkic et al., 2015). Table 4 presents linguistic variables for weighting criteria and ranking alternatives based on IVTFN (Stanujkic et al., 2015).

There are a variety of methods for assessing the importance of criteria that researchers have used or modified when solving complex problems, e.g. eigenvector method, SWARA (Keršuliene et al., 2010), expert judgement method, Eckenrode’s rating technique (Turskis et al., 2019a), Analytic Hierarchy Process (AHP) (Saaty, 1977, 1980; Turskis et al., 2012; Zavadskas et al., 2020) and Entropy method. Keršuliene et al. (2010) developed the Step-wise Weight Assessment Ratio Analysis (SWARA) method to weight the criteria based on the opinions and judgments of decision-makers and experts (Keršuliene et al., 2010; Keršulienė and Turskis, 2011). This method is a subjective method with low complexity, low time, and the ability to estimate the opinions of experts or stakeholders on the importance of criteria in the weighting process (Karabasevic et al., 2016; Stanujkic et al., 2017). On the other hand, the inaccuracy and inadequacy of candidates’ information in many situations lead to the inefficiency of using methods that consider input parameters accurately and conclusively (Ye, 2010). Among sets that consider uncertainty in decision-making, interval-valued fuzzy numbers have received special attention from researchers. However, despite numerous developments of the SWARA method, this method has not yet been developed to take advantage of these numbers. Therefore, the authors develop an IVTFN SWARA extension and present it below. 1.

Prioritise the criteria: At this stage, the final criteria for evaluating the alternatives are sorted based on their importance in a descending order. The most important and the least essential criteria are ranked highest and lowest in the ranking process, respectively.

The ARAS method is one of the newest MADM approaches introduced by Zavadskas and Turskis in 2010 (Zavadskas and Turskis, 2010). This method is useful to solve various decision-making problems. According to the literature, the fuzzy (Turskis and Zavadskas, 2010a), grey (Turskis and Zavadskas, 2010b; Mardani et al., 2018), and IVTFN (Dahooie et al., 2018) extensions of this method are proposed. The steps of the IVTFN ARAS are as follows (Dahooie et al., 2018).

1. Formulate the decision matrix and determine the optimal performance rating for each criterion (14) X ˜ = x ˜ 01 ⋯ x ˜ 0 j ⋯ x ˜ 0 n ⋮ ⋱ ⋮ ⋱ ⋮ x ˜ i 1 ⋯ x ˜ i j ⋯ x ˜ i n ⋮ ⋱ ⋮ ⋱ ⋮ x ˜ m 1 ⋯ x ˜ m j ⋯ x ˜ m n , i = 0 , 1 , … , m ; j = 1 , 2 , … , n , where m is the number of alternatives, n is the number of criteria describing each choice, x ˜ i j is the interval-valued fuzzy number that denotes the performance value of the option i in criterion j, and x ˜ 0 j is the optimal value of criterion j. The mark ‘∼’ at the top of each symbol indicates an interval-valued triangular fuzzy set.

The optimal performance rank for each criterion with the interval values is calculated using equation (15). (15) x ˜ 0 j = [ ( l 0 j , l 0 j ′ ) , m 0 j , ( u 0 j ′ , u 0 j ) ] , where x ˜ 0 j denotes the optimal fuzzy performance rank with interval values for criterion j. Besides, the other criteria are defined as follows. (16) l 0 j = max i l i j , j ∈ Ω max , min i l i j , j ∈ Ω min , (17) l 0 j ′ = max i l i j ′ , j ∈ Ω max , min i l i j ′ , j ∈ Ω min , (18) m 0 j = max i m i j , j ∈ Ω max , min i m i j , j ∈ Ω min , (19) u 0 j ′ = max i u i j ′ , j ∈ Ω max , min i u i j ′ , j ∈ Ω min (20) u 0 j = max i u i j , j ∈ Ω max , min i u i j , j ∈ Ω min , where Ω max denotes the benefit-type criteria (where the higher value is preferable), and Ω min denotes the cost-type criteria (where the lower value is preferable).

2. Equation (22) helps to normalise the values (21) X ‾ ˜ = x ‾ ˜ 01 ⋯ x ‾ ˜ 0 j ⋯ x ‾ ˜ 0 n ⋮ ⋱ ⋮ ⋱ ⋮ x ‾ ˜ i 1 ⋯ x ‾ ˜ i j ⋯ x ‾ ˜ i n ⋮ ⋱ ⋮ ⋱ ⋮ x ‾ ˜ m 1 ⋯ x ‾ ˜ m j ⋯ x ‾ ˜ m n , i = 0 , 1 , … , m ; j = 1 , 2 , … , n , (22) x ‾ ˜ i j = [ ( a i j c j + , a i j ′ c j + ) , b i j c j + , ( c i j ′ c j + , c i j c j + ) ] , j ∈ Ω max , [ ( 1 a i j a j − , 1 a i j ′ a j − ) , 1 b i j a j − , ( 1 c i j ′ a j − , 1 c i j a j − ) ] , j ∈ Ω min , where x ‾ ˜ i j denotes the optimal fuzzy performance rank with interval values for alternative i in criterion j: a j − = ∑ i = 0 m 1 a i j , c j + = ∑ i = 0 m c i j , i = 0 , 1 , … , m .

3. Calculation of weighted normalized decision matrix with interval values

At this stage, using the normalized weights obtained by the IVTFN SWARA method and the normalized decision matrix, the weighted normalized decision matrix X ˆ ˜ is defined. (23) X ˆ ˜ = x ˆ ˜ 01 ⋯ x ˆ ˜ 0 j ⋯ x ˆ ˜ 0 n ⋮ ⋱ ⋮ ⋱ ⋮ x ˆ ˜ i 1 ⋯ x ˆ ˜ i j ⋯ x ˆ ˜ i n ⋮ ⋱ ⋮ ⋱ ⋮ x ˆ ˜ m 1 ⋯ x ˆ ˜ m j ⋯ x ˆ ˜ m n , i = 0 , 1 , … , m ; j = 1 , 2 , … , n . The following equation determines the weighted normalised values of all criteria. (24) x ˆ ˜ i j = w ˜ j . x ˜ i j , i = 0 , 1 , … , m .

4. Calculate the overall performance index for each alternative

The overall performance index for each alternative is calculated by equation (25) (25) S ˜ i = ∑ j = 1 n x ˆ ˜ i j , i = 0 , 1 , … , m , where S ˜ i denotes the overall performance index for alternative i.

5. Calculate the degree of utility for each alternative

The fuzzy decision result for each alternative is in the form of IVTFN. There exist different defuzzification processes. They may affect the problem solution results. The defuzzification of S ˜ i is performed using equation (26) (26) S i = ( 1 − λ ) S i l + λ S i l ′ + S i m + λ S i u ′ + ( 1 − λ ) S i u 5 , λ ∈ [ 0 , 1 ] . There λ is a coefficient in the interval [ 0 , 1 ]. The PMs can give more importance to S i l ′ and S i u ′ than S i l and S i u , and vice versa by changing λ coefficient. The utility degree of each alternative is obtained by comparing its value with the ideal value of S 0 .

Equation (27) represents the utility degree of alternative A i (27) K i = S i S 0 , i = 0 , 1 , … , m , where S 0 and S i are the defuzzified optimal index values obtained from equation (26), and values of K i are in the interval [ 0 , 1 ].

6. Alternative ranking and choosing the most effective alternative

At this point, the decision-makers ranked the alternatives based on K i values.

IoT development in Iran is in its infancy. Besides, IoT related technologies and enablers have not yet evolved and are facing many challenges. Therefore, the scores associated with each of the two dimensions of Sustainability and Challenges of IoT Development were first calculated using a combination of IVTFN SWARA and IVTFN ARAS methods. Then, the scores are normalised into the interval [ 0 , 1 ] using equation (28) (Zeleny, 1973). (28) s i = x i − min ( x i ) max ( x i ) − min ( x i ) , where x i is the score of application i ( i = 1 , 2 , 3 , … , 8 ) in the associated dimension and max / min ( x i ) are the most significant and smallest values.