Analyzing blockchain adoption barriers in manufacturing supply chains by the neutrosophic analytic hierarchy process

Abstract

Tools established for managing information flow in supply chain management and logistics should match digital transformations. This issue is particularly salient for develo** nations that hope to achieve sustainable development goals in a globalized era. Modern technologies are required to ensure a secure, transparent, and traceable path of information flow in global supply chains; however, it is not always straightforward for businesses in develo** economies to adopt new digital technologies while sustaining productivity. One of the foundational technologies that can be used to create a basis for economic and social systems and to affect manufacturing supply chains in develo** economies is blockchain. In this study, we analyze the barriers to blockchain technology adoption in manufacturing supply chains using the neutrosophic analytic hierarchy process (N-AHP). We propose an action plan framework for the validation of blockchain technology in a develo** economy. The findings demonstrate that “transaction-level uncertainties” comprise the most critical barrier and have the highest weight in the final ranking followed by “usage in the underground economy”, “managerial commitment”, “challenges in scalability”, and “privacy risks”. This paper can assist industrial managers and experts in emerging economies to more clearly identify barriers to the implementation of blockchain technology and show them how to successfully employ blockchain technology in their supply chains.

Appendix: Neutrosophic set theory (NST)

Some basic definitions of NST are provided in this section to aid in understanding the implementation of N-AHP.

Definition 1

Neutrosophic set (NS) (Vafadarnikjoo, 2020). Let $U$ be a finite set of objects, and let $x$ signify a generic element in $U$. The NS $A$ in $U$ is characterized by a truth-membership function ${T}_{A}(x)$, an indeterminacy-membership function ${I}_{A}(x)$, and a falsity-membership function ${F}_{A}(x)$. ${T}_{A}(x)$, ${I}_{A}(x)$, and ${F}_{A}(x)$ are the elements of $\left]{0}^{-},{1}^{+}\right[$. It can be shown as Eq. (5):

$$ A = \left\{ {\left\langle {x, \left( {T_{A} \left( x \right), I_{A} \left( x \right), F_{A} \left( x \right)} \right)} \right\rangle :x \in U, T_{A} \left( x \right), I_{A} \left( x \right), F_{A} \left( x \right) \in \left] {0^{ - } ,1^{ + } } \right[ } \right\} $$

(5)

Note that ${0}^{-}\le {T}_{A}\left(x\right)+{I}_{A}\left(x\right)+{F}_{A}(x)\le {3}^{+}$.

Definition 2

Single-valued neutrosophic set (SVNS) (Vafadarnikjoo, 2020). Let $U$ be a finite set of elements, and let $x$ signify a generic element in $U$. An SVNS $A$ in $U$ is defined by a truth-membership function ${T}_{A}(x)$, an indeterminacy-membership function ${I}_{A}(x)$, and a falsity-membership function ${F}_{A}(x)$. ${T}_{A}(x)$, ${I}_{A}(x)$, and ${F}_{A}(x)$ are the elements of $\left[{0,1}\right]$. It can be shown as Eq. (6):

$$ A = \left\{ {\left\langle {x, \left( {T_{A} \left( x \right), I_{A} \left( x \right), F_{A} \left( x \right)} \right)} \right\rangle :x \in U, T_{A} \left( x \right), I_{A} \left( x \right), F_{A} \left( x \right) \in \left[ {0,1} \right] } \right\} $$

(6)

Note that $0\le {T}_{A}\left(x\right)+{I}_{A}\left(x\right)+{F}_{A}(x)\le 3$.

For convenience, an SVNS $A=\left\{<x, \left({T}_{A}\left(x\right), {I}_{A}\left(x\right), {F}_{A}(x)\right)>:x\in U\right\}$ is sometimes shown as a $A=\left\{<{T}_{A}\left(x\right), {I}_{A}\left(x\right), {F}_{A}(x)>:x\in U\right\}$ in simplified form.

Definition 3

Single-valued trapezoidal neutrosophic number (SVTNN) (Deli & Subas, 2014). An SVTNN $\stackrel{\sim }{a}=<\left({a}_{1},{b}_{1},{c}_{1},{d}_{1}\right);{w}_{\stackrel{\sim }{a}},{u}_{\stackrel{\sim }{a}},{y}_{\stackrel{\sim }{a}}>$, ${a}_{1},{b}_{1},{c}_{1},{d}_{1}\in R$, ${a}_{1}\le {b}_{1}\le {c}_{1}\le {d}_{1}$, and ${w}_{\stackrel{\sim }{a}},{u}_{\stackrel{\sim }{a}},{y}_{\stackrel{\sim }{a}}\in \left[\mathrm{0,1}\right]$ is a particular single-valued neutrosophic number (SVNN) whose ${T}_{\stackrel{\sim }{a}}\left(x\right)$, ${I}_{\stackrel{\sim }{a}}\left(x\right)$, and ${F}_{\stackrel{\sim }{a}}\left(x\right)$ are presented as Equations (7) to (9), respectively.

$$ T_{{\tilde{a}}} \left( x \right) = \left\{ {\begin{array}{*{20}c} {\begin{array}{*{20}c} {\left( {x - a_{1} } \right)w_{{\tilde{a}}} /\left( {b_{1} - a_{1} } \right)} & {a_{1} \le x < b_{1} } \\ \end{array} } \\ {\begin{array}{*{20}c} {w_{{\tilde{a}}} } & {b_{1} \le x \le c_{1} } \\ \end{array} } \\ {\begin{array}{*{20}c} {\begin{array}{*{20}c} {\left( {d_{1} - x} \right)w_{{\tilde{a}}} /\left( {d_{1} - c_{1} } \right) } & {c_{1} < x \le d_{1} } \\ \end{array} } \\ {\begin{array}{*{20}c} {0 } & {otherwise} \\ \end{array} } \\ \end{array} } \\ \end{array} } \right. $$

(7)

$$ I_{{\tilde{a}}} \left( x \right) = \left\{ {\begin{array}{*{20}c} {\begin{array}{*{20}c} {\left( {b_{1} - x + u_{{\tilde{a}}} \left( {x - a_{1} } \right)} \right)/\left( {b_{1} - a_{1} } \right)} & {a_{1} \le x < b_{1} } \\ \end{array} } \\ {\begin{array}{*{20}c} {u_{{\tilde{a}}} } & {b_{1} \le x \le c_{1} } \\ \end{array} } \\ {\begin{array}{*{20}c} {\begin{array}{*{20}c} {\left( {x - c_{1} + u_{{\tilde{a}}} \left( {d_{1} - x} \right)} \right)/\left( {d_{1} - c_{1} } \right) } & {c_{1} < x \le d_{1} } \\ \end{array} } \\ {\begin{array}{*{20}c} {1 } & {otherwise} \\ \end{array} } \\ \end{array} } \\ \end{array} } \right. $$

(8)

$$ F_{{\tilde{a}}} \left( x \right) = \left\{ {\begin{array}{*{20}c} {\begin{array}{*{20}c} {\left( {b_{1} - x + y_{{\tilde{a}}} \left( {x - a_{1} } \right)} \right)/\left( {b_{1} - a_{1} } \right)} & {a_{1} \le x < b_{1} } \\ \end{array} } \\ {\begin{array}{*{20}c} {y_{{\tilde{a}}} } & {b_{1} \le x \le c_{1} } \\ \end{array} } \\ {\begin{array}{*{20}c} {\begin{array}{*{20}c} {\left( {x - c_{1} + y_{{\tilde{a}}} \left( {d_{1} - x} \right)} \right)/\left( {d_{1} - c_{1} } \right) } & {c_{1} < x \le d_{1} } \\ \end{array} } \\ {\begin{array}{*{20}c} {1 } & {otherwise} \\ \end{array} } \\ \end{array} } \\ \end{array} } \right. $$

(9)

Definition 4

Addition of two SVTNNs (Vafadarnikjoo, 2020). Given $\stackrel{\sim }{a}=<\left({a}_{1},{b}_{1},{c}_{1},{d}_{1}\right);{w}_{\stackrel{\sim }{a}},{u}_{\stackrel{\sim }{a}},{y}_{\stackrel{\sim }{a}}>$ and $\stackrel{\sim }{b}=<\left({a}_{2},{b}_{2},{c}_{2},{d}_{2}\right);{w}_{\stackrel{\sim }{b}},{u}_{\stackrel{\sim }{b}},{y}_{\stackrel{\sim }{b}}>$, ${w}_{\stackrel{\sim }{a}},{u}_{\stackrel{\sim }{a}},{y}_{\stackrel{\sim }{a}}, {w}_{\stackrel{\sim }{b}},{u}_{\stackrel{\sim }{b}},{y}_{\stackrel{\sim }{b}} \in \left[\mathrm{0,1}\right]$, ${a}_{1},{b}_{1},{c}_{1},{d}_{1},{a}_{2},{b}_{2},{c}_{2},{d}_{2}\in {\mathbb{R}}$, ${a}_{1}\le {b}_{1}\le {c}_{1}\le {d}_{1}$, and ${a}_{2}\le {b}_{2}\le {c}_{2}\le {d}_{2}$, Eq. (10) is true.

$$ \tilde{a} + \tilde{b} = \left\langle {\left( {a_{1} + a_{2} , b_{1} + b_{2} , c_{1} + c_{2} , d_{1} + d_{2} } \right);w_{{\tilde{a}}} + w_{{\tilde{b}}} - w_{{\tilde{a}}} w_{{\tilde{b}}} , u_{{\tilde{a}}} u_{{\tilde{b}}} , y_{{\tilde{a}}} y_{{\tilde{b}}} } \right\rangle $$

(10)

Definition 5

Subtraction of two SVTNNs (Smarandache, 2016). Let $\stackrel{\sim }{a}=<\left({a}_{1},{b}_{1},{c}_{1},{d}_{1}\right);{w}_{\stackrel{\sim }{a}},{u}_{\stackrel{\sim }{a}},{y}_{\stackrel{\sim }{a}}>$ and $\stackrel{\sim }{b}=<\left({a}_{2},{b}_{2},{c}_{2},{d}_{2}\right);{w}_{\stackrel{\sim }{b}},{u}_{\stackrel{\sim }{b}},{y}_{\stackrel{\sim }{b}}>$ be two SVTNNs and ${w}_{\stackrel{\sim }{a}},{u}_{\stackrel{\sim }{a}},{y}_{\stackrel{\sim }{a}}, {w}_{\stackrel{\sim }{b}},{u}_{\stackrel{\sim }{b}},{y}_{\stackrel{\sim }{b}} \in \left[\mathrm{0,1}\right]$ with the restrictions that ${w}_{\stackrel{\sim }{b}}\ne 1$, ${u}_{\stackrel{\sim }{b}}\ne 0$, ${y}_{\stackrel{\sim }{b}}\ne 0$, and ${a}_{1},{b}_{1},{c}_{1},{d}_{1},{a}_{2},{b}_{2},{c}_{2},{d}_{2}\in {\mathbb{R}}$, ${a}_{1}\le {b}_{1}\le {c}_{1}\le {d}_{1}$, and ${a}_{2}\le {b}_{2}\le {c}_{2}\le {d}_{2}$; then, the subtraction of the two SVTNNs is shown in Eq. (11):

$$ \tilde{a} - \tilde{b} = \left\langle {\left( {a_{1} - d_{2} , b_{1} - c_{2} , c_{1} - b_{2} , d_{1} - a_{2} } \right);\frac{{w_{{\tilde{a}}} - w_{{\tilde{b}}} }}{{1 - w_{{\tilde{b}}} }}, \frac{{u_{{\tilde{a}}} }}{{u_{{\tilde{b}}} }}, \frac{{y_{{\tilde{a}}} }}{{y_{{\tilde{b}}} }}} \right\rangle $$

(11)

Remark: If a component result is less than zero, it is replaced with zero; if a component result is greater than one, it is replaced with one.

Definition 6

Division of two SVTNNs (Smarandache, 2016). Let $\stackrel{\sim }{a}=<\left({a}_{1},{b}_{1},{c}_{1},{d}_{1}\right);{w}_{\stackrel{\sim }{a}},{u}_{\stackrel{\sim }{a}},{y}_{\stackrel{\sim }{a}}>$, and $\stackrel{\sim }{b}=<\left({a}_{2},{b}_{2},{c}_{2},{d}_{2}\right);{w}_{\stackrel{\sim }{b}},{u}_{\stackrel{\sim }{b}},{y}_{\stackrel{\sim }{b}}>$ be two SVTNNs, where ${a}_{1},{b}_{1},{c}_{1},{d}_{1},{a}_{2},{b}_{2},{c}_{2},{d}_{2}>0$, ${a}_{1}\le {b}_{1}\le {c}_{1}\le {d}_{1}$, ${a}_{2}\le {b}_{2}\le {c}_{2}\le {d}_{2}$, and ${w}_{\stackrel{\sim }{a}},{u}_{\stackrel{\sim }{a}},{y}_{\stackrel{\sim }{a}}, {w}_{\stackrel{\sim }{b}},{u}_{\stackrel{\sim }{b}},{y}_{\stackrel{\sim }{b}} \in \left[\mathrm{0,1}\right]$ with the restrictions that ${w}_{\stackrel{\sim }{b}}\ne 1$, ${u}_{\stackrel{\sim }{b}}\ne 0$, ${y}_{\stackrel{\sim }{b}}\ne 0$; then, the division of the two SVTNNs is shown in Eq. (12):

$$ \tilde{a} \div \tilde{b} = \left\langle {\left( {\frac{{a_{1} }}{{d_{2} }}, \frac{{b_{1} }}{{c_{2} }}, \frac{{c_{1} }}{{b_{2} }}, \frac{{d_{1} }}{{a_{2} }}} \right);\frac{{w_{{\tilde{a}}} }}{{w_{{\tilde{b}}} }}, \frac{{u_{{\tilde{a} - }} u_{{\tilde{b}}} }}{{1 - u_{{\tilde{b}}} }}, \frac{{y_{{\tilde{a}}} - y_{{\tilde{b}}} }}{{1 - y_{{\tilde{b}}} }}} \right\rangle $$

(12)

Remark: If a component result is less than zero, it is replaced with zero; if a component result is greater than one, it is replaced with one.

Definition 7

Inverse of an SVTNN Let $\stackrel{\sim }{a}=<\left({a}_{1},{b}_{1},{c}_{1},{d}_{1}\right);{w}_{\stackrel{\sim }{a}},{u}_{\stackrel{\sim }{a}},{y}_{\stackrel{\sim }{a}}>$ be an SVTNN where ${a}_{1},{b}_{1},{c}_{1},{d}_{1}>0$, ${a}_{1}\le {b}_{1}\le {c}_{1}\le {d}_{1}$, and ${w}_{\stackrel{\sim }{a}},{u}_{\stackrel{\sim }{a}},{y}_{\stackrel{\sim }{a}}, \in \left[\mathrm{0,1}\right]$ then the inverse of $\stackrel{\sim }{a}$ is represented in Eq. (13):

$$ \tilde{a}^{ - 1} = \frac{1}{{ \tilde{a}}} = \left\langle {\left( {\frac{1}{{d_{1} }},\frac{1}{{c_{1} }},\frac{1}{{b_{1} }},\frac{1}{{a_{1} }}} \right);\frac{1}{{w_{{\tilde{a}}} }},\frac{{u_{{\tilde{a}}} }}{{u_{{\tilde{a}}} - 1}},\frac{{y_{{\tilde{a}}} }}{{y_{{\tilde{a}}} - 1}}} \right\rangle $$

(13)

Remark: If a component result is less than zero, it is replaced with zero; if a component result is greater than one, it is replaced with one.

Definition 8

The TNWAA operator (Vafadarnikjoo et al., 2018). Let ${\stackrel{\sim }{a}}_{j}=<\left({a}_{j},{b}_{j},{c}_{j},{d}_{j}\right);{w}_{{\stackrel{\sim }{a}}_{j}},{u}_{{\stackrel{\sim }{a}}_{j}},{y}_{{\stackrel{\sim }{a}}_{j}}>\left(j=\mathrm{1,2},\dots ,n\right)$ be a set of SVTNNs; then, a TNWAA operator is computed based on Eq. (14):

$$ TNWAA\left( {\tilde{a}_{1} ,\tilde{a}_{2} , \ldots ,\tilde{a}_{n} } \right) = \mathop \sum \limits_{j = 1}^{n} p_{j} \tilde{a}_{j} = \left\langle {\left( {\mathop \sum \limits_{j = 1}^{n} p_{j} a_{j} ,\mathop \sum \limits_{j = 1}^{n} p_{j} b_{j} ,\mathop \sum \limits_{j = 1}^{n} p_{j} c_{j} ,\mathop \sum \limits_{j = 1}^{n} p_{j} d_{j} } \right);1 - \mathop \prod \limits_{j = 1}^{n} \left( {1 - w_{{\tilde{a}_{j} }} } \right)^{{p_{j} }} ,\mathop \prod \limits_{j = 1}^{n} u_{{\tilde{a}_{j} }}^{{p_{j} }} ,\mathop \prod \limits_{j = 1}^{n} y_{{\tilde{a}_{j} }}^{{p_{j} }} } \right\rangle $$

(14)

Here, ${p}_{j}$ is the weight of ${\stackrel{\sim }{a}}_{j}$ $\left(j=\mathrm{1,2},\dots ,n\right)$ while ${p}_{j}>0$, and $\sum_{j=1}^{n}{p}_{j}=1$.

Definition 9: Score function of a SVTNN

(Vafadarnikjoo, 2020). Given $\stackrel{\sim }{a}=<\left(a,b,c,d\right);{w}_{\stackrel{\sim }{a}},{u}_{\stackrel{\sim }{a}},{y}_{\stackrel{\sim }{a}}>$ and $a,b,c,d>0$. Then, the score function of $\stackrel{\sim }{a}$ can be calculated in accordance with Eq. (15):

$$ S\left( {\tilde{a}} \right) = \frac{1}{12}\left( {a + b + c + d} \right)\left( {2 + w_{{\tilde{a}}} - u_{{\tilde{a}}} - y_{{\tilde{a}}} } \right) S\left( {\tilde{a}} \right) \in \left[ {0,1} \right] $$

(15)