Exploring mobile banking services for user behavior in intention adoption: using new hybrid MADM model

Abstract

Mobile banking services are one of the most promising recent technological innovations. In this study, we developed a conceptual model to explore mobile banking services for user behavior in the financial banking industry in intention adoption. The aim of this study is to explore the effect of user behavior and guidance on the mobile banking services intention adoption structure model among customers based on decomposed theory of planned behavior and trust-related behaviors based on the knowledge of experts. In this study, we use a new hybrid model, the multiple attribute decision making (MADM) model, which combines decision making trial and evaluation laboratory (DEMATEL) for building an influential network relationship map (INRM), DANP (DEMATEL-based ANP) for determining the influential weights of criteria, and the VIKOR method using the influential weights to evaluate and integrate the criteria in the gaps and reduce the gaps to satisfy the users’ behavior needs based on INRM. An empirical case of Taiwan’s financial banking industry is used as an example to demonstrate the application of the proposed hybrid MADM model and its efficiency. In the results, we find that the proposed user behavior framework can offer a deeper understanding of the variables/criteria that influence the interrelationship for the intention adoption of mobile banking services by DEMATEL technique. We can also combine the influential weights of DANP with weighting gaps using the VIKOR method to evaluate how to reduce these gaps and provide the best improvement strategies to satisfy the mobile banking services for users’ behavior needs.

Appendices

Appendix 1: DEMATEL technique

DEMATEL technique is used to build an influence relationship matrix for dimensions/criteria to measure the cause and effect on each element. This technique is widely used in various types of complex studies to understand the intricacies of the problem structure. The DEMATEL technique contains five steps.

The first step confirms the number of elements in a system, n, and develops scales for measuring the influential relationship in each element, comparing contexts/criteria by pair-wise comparison, using a scale of 0–4 to represent a complete lack of influence (0), low influence (1), medium influence (2), high influence (3), and extremely high influence (4) by natural language.

The second step identifies an initial influence matrix, comparing influence interaction degree pairs to directly obtain the influence matrix $\varvec{Z} = [z_{ij} ]_{n \times n}$, where z _ij represents the degree that criterion i affects criterion j. If the ith criterion directly affects the jth criterion, then z _ij  ≠ 0; otherwise, z _ij  = 0.

The third step normalizes the direct influence matrix to obtain the matrix $\varvec{A}$ from Eqs. (1) and (2). The diagonal term of matrix $\varvec{A}$ is zero, and the maximum sum of any row or column is 1.

$$ \varvec{A} = s\,\varvec{Z}, $$

(1)

where

$$ s = \mathop {\hbox{min} }\limits_{i,j} \left\{ {\frac{1}{{\max_{i} \sum\nolimits_{j = 1}^{n} {|z_{ij} |} }},\frac{1}{{\max_{j} \sum\nolimits_{i = 1}^{n} {|z_{ij} |} }}} \right\},\quad i ,j = 1 , 2 ,\ldots , { }n. $$

(2)

The fourth step obtains the total influence matrix $\varvec{T}$ from Eq. (3):

$$\varvec{T} = \varvec{A} + \varvec{A}^{2} + \cdots + \varvec{A}^{h} = \varvec{A}(\varvec{I} - \varvec{A})^{ - 1}, \hbox{when} \lim_{h \to \infty } \varvec{A}^{h} = [0]_{n \times n} , $$

(3)

where $\varvec{A} = [a_{ij} ]_{n \times n}$, $0 \le a_{{ij}} < 1,0 < \sum\limits_{{j = 1}}^{n} {a_{{ij}} \le 1} ,\;0 < \sum\limits_{{i = 1}}^{n} {a_{{ij}} \le 1} .$If the total of at least one row or column is equal to 1 (but not all) in ∑  ⁿ _j=1 a _ij and ∑  ⁿ _i=1 a _ij , then we can guarantee $\lim_{h \to \infty } \varvec{A}^{h} = [0]_{n \times n}$, and $\varvec{I}$ is the identity matrix.

The fifth step obtains prominence and relation. By totaling each row and column of the total influence matrix $\varvec{T = }[t_{ij} ]$, we obtain the sum of all row and column vectors as follows:

$$ \varvec{d} = [d_{i} ]_{n \times 1} = \left[ {\sum\nolimits_{j = 1}^{n} {t_{ij} } } \right]_{n \times 1} = (d_{1} , \ldots ,d_{i} , \ldots ,d_{n} )^{\prime}, $$

$$ \varvec{s} = [s_{j} ]^{\prime}_{1 \times n} = \left[ {\sum\nolimits_{i = 1}^{n} {t_{ij} } } \right]^{\prime }_{1 \times n} = (s_{1} , \ldots ,s_{j} , \ldots ,s_{n} )^{\prime}. $$

The value d _i , the sum of all rows in the total influence matrix T, represents the degree that the criterion directly or indirectly affects all other criteria. The value s _j , the sum of all columns in T, represents the degree that the criterion is affected by all other criteria. According to the definition, when j = i, then d _i  + s _i represents the degree of the total influence relationship of i criterion which denotes to include i criterion affects all other criteria and is affected by all other criteria, meaning “prominence”; d _i  − s _i represents the degree of the effect on and from other criteria, showing the “net influence relationship”. If (d _i  − s _i ) is positive, then criterion i affects other criteria, and if (d _i  − s _i ) is negative, then criterion i is influenced by other criteria.

Appendix 2: influential weights of DANP

We can use the DEMATEL technique to not only build the interacting relationships among the factors/criteria but also obtain the most accurate influential weights. We improve the traditional ANP to solve the interrelationship of dependence and feedback problems among factors/criteria. Therefore, we use the basic concept of ANP (Saaty 1996) as a basis with total influence matrix of DEMATEL technique to solve the influential weights. Thus, DANP (DEMATEL-based ANP) contains the following steps.

The first step develops the expert influence questionnaire structure of DEMATEL technique. The questionnaires are clearly described and broken down into components.

The second step develops an unweighted supermatrix $W = \text{(}\varvec{T}_{c}^{\alpha } )^{\prime}$, transposing each normalized dimension (or called context/cluster) with the total degree of influence $\varvec{T}_{c}^{\alpha }$ obtained from the total influence matrix T _c using the DEMATEL technique, as shown in Eq. (4) from Eq. (3).

(4)

The normalized T _c , with a total degree of influence, provides $\varvec{T}_{c}^{\alpha }$ from the dimensions (contexts/clusters) shown in Eq. (5).

(5)

We use $\varvec{T}_{c}^{\alpha 11}$ to demonstrate the basic concept as example in Eqs. (6) and (7).

$$ d_{i}^{11} = \sum\nolimits_{j = 1}^{{m_{1} }} {t_{{_{C} ij}}^{11} } ,i = 1,2, \ldots ,m_{1} , $$

(6)

$$ {\varvec{T}}_{{{}_{C}}}^{\alpha 11} = \left[ {\begin{array}{*{20}c} {t_{{_{C} 11}}^{11} /d_{1}^{11} } & \cdots & {t_{{_{C} 1j}}^{11} /d_{1}^{11} } & \cdots & {t_{{_{C}^{{1m_{1} }} }}^{11} /d_{1}^{11} } \\ \vdots & {} & \vdots & {} & \vdots \\ {t_{{_{C} i1}}^{11} /d_{i}^{11} } & \cdots & {t_{{_{C} ij}}^{11} /d_{i}^{11} } & \cdots & {t_{{_{C}^{{im_{1} }} }}^{11} /d_{i}^{11} } \\ \vdots & {} & \vdots & {} & \vdots \\ {t_{{_{C}^{{m_{1} 1}} }}^{11} /d_{{m_{1} }}^{11} } & \cdots & {t_{{_{C}^{{m_{1} j}} }}^{11} /d_{{m_{1} }}^{11} } & \cdots & {t_{{_{C}^{{m_{1} m_{1} }} }}^{11} /d_{{m_{1} }}^{11} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {t_{{_{C} 11}}^{\alpha 11} } & \cdots & {t_{{_{C} 1j}}^{\alpha 11} } & \cdots & {t_{{_{C}^{1m} }}^{\alpha 11} } \\ \vdots & {} & \vdots & {} & \vdots \\ {t_{{_{C} i1}}^{\alpha 11} } & \cdots & {t_{{_{C} ij}}^{\alpha 11} } & \cdots & {t_{{_{C}^{{im_{1} }} }}^{\alpha 11} } \\ \vdots & {} & \vdots & {} & \vdots \\ {t_{{_{C}^{{m_{1} 1}} }}^{\alpha 11} } & \cdots & {t_{{_{C}^{{m_{1} 1}} }}^{\alpha 11} } & \cdots & {t_{{_{C}^{{m_{1} m_{1} }} }}^{\alpha 11} } \\ \end{array} } \right]. $$

(7)

We normalize the total influence matrix T _c into the normalized total influence matrix $\varvec{T}_{c}^{\alpha }$ using its contexts; then, the unweighted supermatrix $\varvec{W}$ is obtained by transposing $\varvec{T}_{c}^{\alpha }$, i.e., $W = \text{(}\varvec{T}_{c}^{\alpha } )^{\prime}$, according to the basic concept of ANP in an unweighted supermatrix $\varvec{W}$, as shown in Eq. (8).

(8)

In addition, Eq. (9) produces matrix ${\varvec{W}}^{11}$. If the groups or criteria are independent, then the corresponding entry in the matrix is blank or zero. Matrix ${\varvec{W}}^{nn}$ is obtained in a similar manner.

$$ {\varvec{W}}^{11} = (\varvec{T}^{11} )^{'} = \begin{array}{*{20}c} {c_{11} } \\ \vdots \\ {c_{1j} } \\ \vdots \\ {c_{{1m_{1} }} } \\ \end{array} \left[ {\begin{array}{*{20}c} {t_{{c^{11} }}^{\alpha 11} } & \cdots & {t_{{_{c} i1}}^{\alpha 11} } & \cdots & {t_{{_{c} m_{1} 1}}^{\alpha 11} } \\ \vdots & {} & \vdots & {} & \vdots \\ {t_{{c^{1j} }}^{\alpha 11} } & \cdots & {t_{{_{c} ij}}^{\alpha 11} } & \cdots & {t_{{_{c} m_{1} j}}^{\alpha 11} } \\ \vdots & {} & \vdots & {} & \vdots \\ {t_{{c^{{1m_{1} }} }}^{\alpha 11} } & \cdots & {t_{{_{c} im_{1} }}^{\alpha 11} } & \cdots & {t_{{_{C} m_{1} m_{1} }}^{\alpha 11} } \\ \end{array} } \right]. $$

(9)

The third step obtains the weighting supermatrix, contextualizing the total influence relationship matrix ${\varvec{T}}_{D}$, as in Eq. (10). Let each context of matrix ${\varvec{T}}_{D}$ be normalized with the total degree of influence to obtain ${\varvec{T}}_{D}^{\alpha }$. Eq. (11) shows the following result:

$$ d_{i} = \sum _{j = 1}^{n} t_{D}^{ij} , i = 1, 2, \ldots ,n\quad {\text{and}}\;t_{D}^{\alpha ij} = t_{D}^{ij} /d_{i} , i = 1, 2, \ldots ,n $$

$$ {\varvec{T}}_{D} { = }\left[ {\begin{array}{*{20}c} {t_{D}^{11} } & \cdots & {t_{D}^{1j} } & \cdots & {t_{{_{D} }}^{1n} } \\ \vdots & {} & \vdots & {} & \vdots \\ {t_{D}^{i1} } & \cdots & {t_{D}^{ij} } & \cdots & {t_{D}^{in} } \\ \vdots & {} & \vdots & {} & \vdots \\ {t_{D}^{n1} } & \cdots & {t_{D}^{nj} } & \cdots & {t_{{_{D} }}^{nn} } \\ \end{array} } \right]. $$

(10)

$$ {\varvec{T}}_{D}^{\alpha } = \left[ {\begin{array}{*{20}c} {t_{D}^{11} /d_{1} } & \cdots & {t_{D}^{1j} /d_{1} } & \cdots & {t_{D}^{1n} /d_{1} } \\ \vdots & {} & \vdots & {} & \vdots \\ {t_{D}^{i1} /d_{i} } & \cdots & {t_{D}^{ij} /d_{i} } & \cdots & {t_{D}^{in} /d_{i} } \\ \vdots & {} & \vdots & {} & \vdots \\ {t_{D}^{n1} /d_{n} } & \cdots & {t_{D}^{nj} /d_{n} } & \cdots & {t_{D}^{nn} /d_{n} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {t_{D}^{\alpha 11} } & \cdots & {t_{D}^{\alpha 1j} } & \cdots & {t_{D}^{\alpha 1n} } \\ \vdots & {} & \vdots & {} & \vdots \\ {t_{D}^{\alpha i1} } & \cdots & {t_{D}^{\alpha ij} } & \cdots & {t_{D}^{\alpha in} } \\ \vdots & {} & \vdots & {} & \vdots \\ {t_{D}^{\alpha n1} } & \cdots & {t_{D}^{\alpha nj} } & \cdots & {t_{D}^{\alpha nn} } \\ \end{array} } \right]\; $$

(11)

Multiplying the normalized matrix ${\varvec{T}}_{D}^{\alpha }$ by the unweighted supermatrix $\varvec{W}$ gives the normalized supermatrix $\varvec{W}^{\alpha }$, as shown in Eq. (12).

$$ \varvec{W}^{\alpha } = \varvec{T}_{D}^{\alpha } \varvec{W} = \left[ {\begin{array}{*{20}c} {t_{D}^{{\alpha \text{11}}} \times \varvec{W}^{{\text{11}}} } & \cdots & {t_{D}^{{\alpha i\text{1}}} \times \varvec{W}^{i1} } & \cdots & {t_{D}^{\alpha n1} \times \varvec{W}^{n1} } \\ \vdots & {} & \vdots & {} & \vdots \\ {t_{D}^{\alpha 1j} \times \varvec{W}^{1j} } & \cdots & {t_{D}^{\alpha ij} \times \varvec{W}^{ij} } & \cdots & {t_{D}^{\alpha nj} \times \varvec{W}^{nj} } \\ \vdots & {} & \vdots & {} & \vdots \\ {t_{D}^{\alpha 1n} \times \varvec{W}^{1n} } & \cdots & {t_{D}^{\alpha in} \times \varvec{W}^{in} } & \cdots & {t_{D}^{\alpha nn} \times \varvec{W}^{nn} } \\ \end{array} } \right]. $$

(12)

The fourth step obtains the normalized supermatrix $\varvec{W}^{\alpha }$. We can obtain the supermatrix limit by multiplying the normalized spuermatrix $\varvec{W}^{\alpha }$ by itself several times until the supermatrix has converged and become a long-term stable supermatrix to a sufficiently large power g. Therefore, the weights of the influence of each criterion are obtained by $\mathop {\lim }\limits_{g \to \infty } ({\varvec{W}}^{\alpha } )^{g}$, where g represents any number for the power/exponent. We use these processes to obtain the weights of influence.

Appendix 3: VIKOR method

The VIKOR method, developed by Opricovic and Tzeng (2003, 2004, 2007), solves the issues of conflicting criteria experienced by MADM. This method is based on the positive-ideal (or the desired level) and negative-ideal (or the least-desired) solutions, with a preference for staying close to the positive-ideal point. This is basic concept according to traditional thinking. The gap concept measures the proximity to the positive-ideal point. We describe the VIKOR method below.

The first step determines the values x ^* _j and x ⁻ _j in the quality criterion assessment criteria. The value x ^* _j represents the positive-ideal point (desired levels or aspiration level in each criterion), which is the best score in criterion j. The value x ⁻ _j represents the negative-ideal point, which is the worst score in criterion j. The development of the VIKOR method began with the following form of the L _p metric:

$$ L_{k}^{p} = \left\{ {\sum\limits_{j = 1}^{n} {\left[ {w_{j} {{\left( {\left| {x_{j}^{*} - x_{kj} } \right|} \right)} \mathord{\left/ {\vphantom {{\left( {\left| {x_{j}^{*} - x_{kj} } \right|} \right)} {\left( {\left| {x_{j}^{*} - x_{j}^{ - } } \right|} \right)}}} \right. \kern-0pt} {\left( {\left| {x_{j}^{*} - x_{j}^{ - } } \right|} \right)}}} \right]^{p} } } \right\}^{1/p} , $$

(13)

where 1 ≤ p ≤ ∞; k = 1, 2, …, m, and the influential weight w _j is derived from DANP. In the article, we use the new concepts of Eqs. (14) and (15) to obtain the following results for the improvement gaps of each context/criterion based on interdependence and feedback problems:

$$ \begin{gathered} x_{j}^{*} = { \hbox{max} } _{k} x_{kj} ,\quad j = 1, 2, \ldots , n\;\left( {\text{traditional approach}} \right), \hfill \\ {\text{We set the aspiration levels }}\left( {\text{new approach}} \right),{\text{ vector}}\;\varvec{x}^{ * } = (x_{1}^{*} ,x_{2}^{*} , \cdots ,x_{n}^{*} ), \hfill \\ \end{gathered} $$

(14)

$$ \begin{gathered} x_{j}^{ - } = { \hbox{min} } _{k} x_{kj} ,\quad j = 1, 2, \ldots , n\;\left( {\text{traditional approach}} \right), \hfill \\ {\text{We set the worst values }}\left( {\text{new approach}} \right),{\text{ vector }}\varvec{x}^{ - } = (x_{1}^{ - } ,x_{2}^{ - } , \cdots ,x_{n}^{ - } ). \hfill \\ \end{gathered} $$

(15)

In basic concept of this new approach, we use the performance scores from 0 to 10 (complete dissatisfaction (0), ← 0, 1, 2, 3,…, 7, 8, 9, 10 → extreme satisfaction (10)) in questionnaires; therefore, that aspiration level can be set at 10 score and the worst value at zero score. Therefore, in this study, we set x ^* _j  = 10, j = 1, 2,…, n as the aspiration level and x ⁻ _j  = 0, j = 1,2,…,n as the worst value, which differs from traditional approach. In this approach, we set x ^* _j as the aspiration level and x ⁻ _j as the worst value because this approach allow us to avoid “Choose the best among inferior choices/options/alternatives (i.e., pick the best apple among a barrel of rotten apples).”

The second step calculates the minimal mean of the group utility F _k (minimal average gap) and maximal regret Q _k (maximal gap for all criteria or for each context of criteria to give improvement priority).

$$ L_{k}^{p = 1} = F_{k} = \sum\limits_{j = 1}^{n} {w_{j} r_{kj} } = \sum\limits_{j = 1}^{n} {w_{j} } {{\left( {\left| {x_{j}^{*} - x_{kj} } \right|} \right)} \mathord{\left/ {\vphantom {{\left( {\left| {x_{j}^{*} - x_{kj} } \right|} \right)} {\left( {\left| {x_{j}^{*} - x_{j}^{ - } } \right|} \right)}}} \right. \kern-0pt} {\left( {\left| {x_{j}^{*} - x_{j}^{ - } } \right|} \right)}}, $$

(16)

$$ L_{k}^{p = \infty } = Q_{k} = \mathop {\hbox{max} }\limits_{j} \left\{ {r_{kj} |j = 1,2, \ldots ,n} \right\}, $$

(17)

where r _kj  = (|x ^* _j  − x _kj |)/(|x ^* _j  − x _kj |)(|x ^* _j  − x ⁻ _j |)(|x ^* _j  − x ⁻ _j |) represents the gap ratio (on a normalization scale) and F _k represents the ratios of the average gap from the aspiration level x ^* _j to the performance value x _kj in criterion j of alternative k. In this article, we focus on minimizing the gap r _kj for all criteria j = 1, 2,…,n. Then, w _j represents the relative influential weight of criterion j; w _j can be obtained from DANP based on the DEMATEL technique. Q _k represents the maximum gap in all criteria (or the context of each criterion of the k-th alternative) for prioritizing improvement.

The third step provides the comprehensive indicator R _k and its ranked results. Equation (17) computes these values. From Eq. (17), we observe how mobile banking for user behavior implementation can be improved to reduce the gaps for achieving the aspiration level based on the influential network relation map.

$$ R_{k} = v{{\left( {F_{k} - F^{*} } \right)} \mathord{\left/ {\vphantom {{\left( {F_{k} - F^{*} } \right)} {\left( {F^{ - } - F^{*} } \right) + \left( {1 - v} \right)}}} \right. \kern-0pt} {\left( {F^{ - } - F^{*} } \right) + \left( {1 - v} \right)}}{{\left( {Q_{k} - Q^{*} } \right)} \mathord{\left/ {\vphantom {{\left( {Q_{k} - Q^{*} } \right)} {\left( {Q^{ - } - Q^{*} } \right)}}} \right. \kern-0pt} {\left( {Q^{ - } - Q^{*} } \right)}}. $$

(18)

Using the values derived from S ^* = min _k S _k (traditional approach) or F ^* = 0 (achieving the aspiration level where the gap is zero, our approach), F ⁻ = max _k F _k (traditional approach) or F ⁻ = 1 (the worst situation, our approach); Q ^* = min _k Q _k (traditional approach) or Q ^* = 0 (achieving the desired level, our approach), Q ⁻ = max _k Q _k (traditional approach) or Q ⁻ = 1 (the worst situation, our approach). Thus, in our approach, the gap for S ^* = 0 and F ⁻ = 1, and Q ^* = 0, and Q ⁻ = 1, we can re-write Eq. (17) as R _k  = vF _k  + (1 − v)Q _k (i.e., weighting two objectives F _k and Q _k ). The weight v = 1 only considers how we can minimize the average gap (average regret), and the weight v = 0 only determines how to select the maximum gap for improvement. In general, v = 0.5, but this value can be adjusted depending on the situation.

Based on the above concepts, we can easily determine how to improve the gaps r _kj (k = 1, 2,…, m; j = 1, 2,…, n) and the improvement priority according to the influential network relationship map for the achieving aspiration level.