Interval number multi-attribute evaluation and decision-making methods of organizational quality-specific immunity of digital technology start-ups based on martin System-TOPSIS

Abstract

In this paper, we take the organizational quality-specific immunity of digital technology start-ups as the starting point, and comprehensively use the martin system-TOPSIS research method to evaluate the organizational quality-specific immunity status of digital technology start-ups. The empirical results show that the martin system-TOPSIS method can effectively solve the evaluation and decision-making problem of organizational quality-specific immunity of digital technology start-ups, and the interval number multi-attribute evaluation and decision-making method based on martin system-TOPSIS is effective and feasible in solving the problem of organizational quality-specific immunity evaluation and decision-making of digital technology start-ups.

Keywords

martin system TOPSIS organizational quality-specific immunity interval number multi-attribute evaluation and decision-making methods digital technology start-ups

Introduction

Nowadays, the development and evolution of digital technology start-ups play a crucial role in the country’s economic development, affecting not only their own competitive advantages, but also the competition between enterprises. If an enterprise wants to have a certain competitive advantage, it must first pay attention to the quality of its products. So far, catastrophic incidents caused by product quality problems have emerged one after another, such as the Sanlu milk powder incident, the dyed steamed bun incident, the clenbuterol incident, and so on. This series of events is similar to that of a biological organism, when there is a fatal disease in the biological organism, the body’s immune system fails to respond effectively, resulting in health problems in the body. Similarly, when the above events occur, the organizational immune system of the enterprise does not respond accordingly, resulting in serious problems with the quality of the company’s products, and ultimately the enterprise is seriously affected.¹ Organizational quality-specific immunity is the embodiment and characterization of organizational-specific immunity at the quality level, and organizational quality-specific immunity is a mirror mapping product between organizational-specific immunity and enterprise quality management.^2–8 Organizational quality-specific immunity is the core dominant architecture of organizational quality immunity, which has acquired, non-innate activity, acquired, adaptive, self-consistent, adaptive, and specific central immune response functions.^9–11 Organizational quality-specific immunization of digital technology start-ups is effectively integrated with digital quality and data quality.^12–16 The six evaluation indicators and components of organizational quality-specific immunity mainly include organizational quality monitoring, organizational quality cognition, organizational quality defense, organizational quality clearance, organizational quality repair, organizational quality memory, and immune self-stability.^2–8 Enterprise quality management departments and quality management personnel jointly govern the enterprise quality management immune system, activate the function of organizational quality-specific immune system, prevent enterprise quality diseases at all times, keep the organizational quality-specific immune system in a healthy state, drive the adaptive evolution and dynamic evolution of organizational quality-specific immunity, improve enterprise quality performance, and enhance organizational dynamic adaptability.^17–19 Finding and removing the inducing factors of quality accidents at the first time is an effective means for the organizational-specific immune system to prevent and resist quality diseases. Organizational dynamic adaptation is the key goal of organizational quality-specific immune adaptation evolution. In this paper, the evaluation indexes and components of tissue quality-specific immunity (tissue quality monitoring, tissue quality cognition, tissue quality defense, tissue quality clearance, tissue quality repair, tissue quality memory and immune self-stability) were comprehensively evaluated and analyzed, and finally the advantages and disadvantages of tissue quality-specific immunity status of digital technology start-ups were compared. According to the Mahalanobis distance, the distance from the distribution set of each digital technology start-up to the distribution set of the positive and negative ideal scheme was further measured, and the signal-to-noise ratio was used to calculate the corresponding closeness, and finally the comprehensive score of tissue quality-specific immunity of digital technology start-ups was ranked, and the best and worst enterprises of tissue quality-specific immunity were mined.

Martin system is a multivariate system quantitative pattern recognition method, which is mostly used in engineering, medical and other fields. In recent years, domestic scholars have produced certain research results in organizational quality-specific immune evaluation and decision-making, which have certain theoretical significance and practical value.^2–9 However, there are relatively few relevant research results that comprehensively adopt the martin system-TOPSIS study method to evaluate and make decisions on the quality of organizational quality-specific immune status. Therefore, this paper takes the tissue quality-specific immunity of digital technology start-ups as the starting point, comprehensively adopts the martin system-TOPSIS research method to evaluate the tissue quality-specific immunity status of digital technology start-ups, combines the martin system and TOPSIS method to rank the interval number decision attributes, and uses the interval number multi-attribute evaluation and decision-making method of the martin system and TOPSIS to evaluate and make decisions on the degree of tissue quality-specific immunity. Compared with Euclidean distance, Mahalanobis distance has stronger decision-making ability, orthogonal table, and signal-to-noise ratio (SNR) system; orthogonal table can reduce the loss of decision-making information; and the signal-to-noise ratio can improve the effectiveness of decision-making information to a certain extent. The research results provide theoretical reference, methodological basis, interval number multi-attribute evaluation, and decision-making methods and practical enlightenment for further evaluation of tissue quality-specific immunity of digital technology start-ups.

Relevant theoretical foundations of research methods

Martin system

The martin system was proposed by Dr Kenichi Taguchi of Japan as a data analysis technique that integrates Mahalanobis distance, orthogonal table, and signal-to-noise ratio.^20–25

(1) Orthogonal table. Orthogonal tables can generally be used to obtain the most comprehensive information with the least number of trials. Orthogonal tables are usually denoted as $L_{q} (t^{m})$ , where $L$ is the symbol for orthogonal tables, $q$ is the number of trials, $t$ is the number of factor levels, and $m$ is the number of factors participating in the experiment. In general, the commonly used 2-level orthogonal tables are $L_{4} (2^{3})$ , $L_{8} (2^{7})$ , $L_{16} (2^{15})$ , and $L_{32} (2^{31})$ . Figure 1 shows the principle of orthogonal table, and points A, B, C, and D are all test points that are uniformly selected by the $L_{4} (2^{3})$ orthogonal table. As can be seen from Figure 1, a cuboid is formed, see Table 1.

Figure 1.

$L_{4} (2^{3})$ orthogonal table.

Table 1.

$L_{4} (2^{3})$ orthogonal table.

Trial	X1	X2	X3
A	1	1	1
B	1	2	2
C	2	1	2
D	2	2	1

Tests designed according to the $L_{q} (t^{m})$ orthogonal table are called $L_{q} (t^{m})$ orthogonal tests.

If there are m test factors $X = (x_{1}, x_{2}, \dots, x_{m})$ in the $L_{q} (t^{m})$ orthogonal test, then the test factor $x_{j}$ obeys a uniform distribution on $[a_{j}, b_{j}]$ $(j = 1, 2, \dots, m)$ .

(1) Mahalanobis distance. Mahalanobis distance is a method of calculating the population mean distance between two unknown samples, which represents the covariance distance of the data. Unlike Euclidean distance, Mahalanobis distance is scale-independent and takes into account the relationship between individual properties.

Let A and B be the two sample populations in the m-dimensional attribute space, b be any sample in B, and $\bar{a}$ and $S_{A}$ are the mean directivity and covariance matrix of A, respectively, then the squared Mahalanobis distance from b to A (hereinafter referred to as Mahalanobis distance) is equation (1).

d_{M}^{2} (b, A) = {(b - \bar{a})}^{T} S_{A}^{- 1} (b - \bar{a})

(1)

(2) Signal-to-noise ratio. The signal-to-noise ratio is primarily used to measure the output response of each test. It is divided into the signal-to-noise ratio of the eye-looking feature, the signal-to-noise ratio of the small-looking feature, and the signal-to-noise ratio of the large-looking feature. In this paper, the signal-to-noise ratio of the small characteristic is studied, and the formula is equation (2).

η = - 10 \log_{10} [\frac{1}{q} \sum_{k = 1}^{q} d_{M}^{2} (k)]

(2)

The signal-to-noise ratio of the small characteristic is $η = - 10 \log_{10} [\frac{1}{q} \sum_{k = 1}^{q} d_{M}^{2} (k)]$ .

(1) When $0 \leq d_{M}^{2} (k) \leq 1$ , $η \geq 0$ ;

(2) When $η = 0$ , if and only if $d_{M}^{2} (1) = d_{M}^{2} (2) = \dots = d_{M}^{2} (q) = 1$ .

Number of intervals

Let a closed interval $a = [a^{L}, a^{U}] = {x | a^{L} \leq x \leq a^{U}, a^{L}, a^{U} \in R}$ on the real number axis, then a be an interval number.

If $a = {x | 0 \leq a^{L} \leq x \leq a^{U}}$ , then $a$ is a positive interval, and if $a^{L} = a^{U}$ , then a is a real number.

Let $a = [a^{L}, a^{U}], b = [b^{L}, b^{U}], λ \geq 0$ , then the calculation rule for the number of intervals is:

(1) $a \pm b = [a^{L} \pm b^{L}, a^{U} \pm b^{U}]$ ; (2) $a \times b = [a^{L} b^{L}, a^{U} b^{U}]$ ; (3) $a \div b = [a^{L} / b^{L}, a^{U} / b^{U}]$ ; (4) $λ a = [λ a^{L}, λ a^{U}]$ ; (5) $1 / a = [1 / a^{U}, 1 / a^{L}]$ . Let $a = [a^{L}, a^{U}], b = [b^{L}, b^{U}]$ , if $d (a, b) = ‖ a - b ‖ = | b^{L} - a^{L} | + | b^{U} - a^{U} |$ , then $d (a, b)$ is said to be the degree of separation between interval a and interval b.

Evaluation and decision-making methods

Let $I = {I_{1}, I_{2}, \dots, I_{n}}$ be n decision schemes, $X = {x_{1}, x_{2}, \dots, x_{m}}$ be m decision attributes, and $z_{i j}$ be the number of intervals of $I_{i} (i = 1, 2, \dots, n)$ under the decision attribute $X_{j} (j = 1, 2, \dots, m)$ of the decision scheme, and finally form the decision matrix $Z = {(z_{i j})}_{n \times m}$ where the number of intervals is $z_{i j} = [z_{i j}^{L}, z_{i j}^{U}]$ .^26–29

If you want to normalize the decision matrix Z, you need to process the corresponding benefit-based decision attribute value and cost-based decision attribute value according to equations (3) and (4), and finally obtain the processed decision matrix $R = {(r_{i j})}_{n \times m}$ , where $r_{i j} = [r_{i j}^{L}, r_{i j}^{U}]$ .

(1) The results of the processing of benefit-based decision-making attribute values, see equation (3).

r_{i j}^{L} = z_{i j}^{L} / \sum_{i = 1}^{n} z_{i j}^{U}, r_{i j}^{U} = z_{i j}^{U} / \sum_{i = 1}^{n} z_{i j}^{L}

(3)

(2) The processing result of the attribute value of the cost-based decision, see equation (4).

r_{i j}^{L} = \frac{1}{z_{i j}^{U}} / \sum_{i = 1}^{n} \frac{1}{z_{i j}^{L}}, r_{i j}^{U} = \frac{1}{z_{i j}^{L}} / \sum_{i = 1}^{n} \frac{1}{z_{i j}^{U}}

(4)

At the same time, the normalized decision matrix R needs to be weighted, and the processed decision matrix $A = {(a_{i j})}_{n \times m} = {(r_{i j} w_{j})}_{n \times m}$ , where the weight $w_{j}$ is equation (5).¹⁰

w_{j} = \frac{\sum_{i = 1}^{n} \sum_{k = 1}^{n} d (r_{i j}, r_{k j})}{\sum_{j = 1}^{m} \sum_{i = 1}^{n} \sum_{k = 1}^{n} d (r_{i j}, r_{k j})}, j = 1, 2, \dots, m

(5)

Let $I_{+}$ and $I_{-}$ be positive and negative ideal schemes, respectively, then the formula is equations (6) and (7).

I_{+} = ([\max_{1 \leq i \leq n} a_{i 1}^{L}, \max_{1 \leq i \leq n} a_{i 1}^{U}], [\max_{1 \leq i \leq n} a_{i 2}^{L}, \max_{1 \leq i \leq n} a_{i 2}^{U}], \dots, [\max_{1 \leq i \leq n} a_{i m}^{L}, \max_{1 \leq i \leq n} a_{i m}^{U}])

(6)

I_{-} = ([\min_{1 \leq i \leq n} a_{i 1}^{L}, \min_{1 \leq i \leq n} a_{i 1}^{U}], [\min_{1 \leq i \leq n} a_{i 2}^{L}, \min_{1 \leq i \leq n} a_{i 2}^{U}], \dots, [\min_{1 \leq i \leq n} a_{i m}^{L}, \min_{1 \leq i \leq n} a_{i m}^{U}])

(7)

When the TOPSIS method is used to deal with the multi-decision attribute of interval number, each decision scheme in I should be regarded as n super boxes of the m-dimensional attribute space.

Let

a_{i} = (a_{i 1}, a_{i 2}, \dots, a_{i m})

be the decision vector of the number of intervals corresponding to

I_{i}

. In order to comprehensively obtain the decision vector information of the interval number, it is necessary to introduce the idea of orthogonal experiment, use the two horizontal orthogonal table to extract q distribution points on the ultra-cuboid to represent the decision scheme, take

a = ([a_{1}^{L}, a_{1}^{U}], [a_{2}^{L}, a_{2}^{U}], [a_{3}^{L}, a_{3}^{U}])

as an example, select the

L_{4} (2^{3})

orthogonal table, and the “1″ and “2″ in Table 1 correspond to the lower bound

a^{L}

and upper limit

a^{U}

of the interval number, respectively, and finally obtain the distribution points in Table 2.

Table 2.

$L_{4} (2^{3})$ orthogonal test.

Trial	$x_{1}$	$x_{2}$	$x_{3}$	Distribution
Trial	$[a_{1}^{L}, a_{1}^{U}]$	$[a_{2}^{L}, a_{2}^{U}]$	$[a_{3}^{L}, a_{3}^{U}]$	Distribution
1	$a_{1}^{L}$	$a_{2}^{L}$	$a_{3}^{L}$	$t_{1} = (a_{1}^{L}, a_{2}^{L}, a_{3}^{L})$
2	$a_{1}^{L}$	$a_{2}^{U}$	$a_{3}^{U}$	$t_{2} = (a_{1}^{L}, a_{2}^{U}, a_{3}^{U})$
3	$a_{1}^{U}$	$a_{2}^{L}$	$a_{3}^{U}$	$t_{3} = (a_{1}^{U}, a_{2}^{L}, a_{3}^{U})$
4	$a_{1}^{U}$	$a_{2}^{U}$	$a_{3}^{L}$	$t_{4} = (a_{1}^{U}, a_{2}^{U}, a_{3}^{L})$

Let the interval number decision vector of the decision scheme $I_{i}$ be $a_{i} = (a_{i 1}, a_{i 2}, \dots, a_{i m})$ , where $a_{i j} = [a_{i j}^{L}, a_{i j}^{U}]$ , then the set of distribution points under the orthogonal experiment $L_{q} (2^{m})$ is $T_{i} = {t_{1}^{(i)}, t_{2}^{(i)}, \dots, t_{q}^{(i)}}$ , where $t_{k}^{(i)} = (t_{k 1}^{(i)}, t_{k 2}^{(i)}, \dots, t_{k m}^{(i)})$ , $t_{k j}^{(i)} \in {a_{i j}^{L}, a_{i j}^{U}}$ , $i = 1, 2, \dots, n, j = 1, 2, \dots, m, k = 1, 2, \dots, q$ .

Let $T_{a} = {t_{1}^{(a)}, t_{2}^{(a)}, \dots, t_{q}^{(a)}}, T_{b} = {t_{1}^{(b)}, t_{2}^{(b)}, \dots, t_{q}^{(b)}}$ be the two distribution sets under the $L_{q} (2^{m})$ orthogonal experiment, then the signal-to-noise ratio of the m-dimensional interval number decision vectors a and b is equation (8).

η = - 10 \log_{10} [\frac{1}{q} \sum_{k = 1}^{q} {\bar{d}}_{M}^{2} (t_{k}^{(b)}, T_{a})]

(8)

The range of ${\bar{d}}_{M}^{2} (t_{k}^{(b)}, T_{a})$ in the above equation is [0, 1], which is the distance from $t_{k}^{(b)}$ to $T_{a}$ , and the formula is equation (9).

{\bar{d}}_{M}^{2} (t_{k}^{(b)}, T_{a}) = \frac{d_{M}^{2} (t_{k}^{(b)}, T_{a}) - \min_{1 \leq k \leq q} d_{M}^{2} (t_{k}^{(b)}, T_{a})}{\max_{1 \leq k \leq q} d_{M}^{2} (t_{k}^{(b)}, T_{a}) - \min_{1 \leq k \leq q} d_{M}^{2} (t_{k}^{(b)}, T_{a})}, k = 1, 2, \dots, q

(9)

The smaller $η$ in the above equation indicates the stronger the output response between a and b.

Let the signal-to-noise ratios of the decision-making scheme $I_{i} (i = 1, 2, \dots, n)$ and the positive and negative ideal schemes $I_{+}$ and $I_{-}$ be $η_{i}^{+}$ and $η_{i}^{-}$ , respectively, see equation (10).

η_{i}^{+} = - 10 \log_{10} [\frac{1}{q} \sum_{k = 1}^{q} {\bar{d}}_{M}^{2} (t_{k}^{(i)}, T_{+})], η_{i}^{-} = - 10 \log_{10} [\frac{1}{q} \sum_{k = 1}^{q} {\bar{d}}_{M}^{2} (t_{k}^{(i)}, T_{-})]

(10)

T_{+}

and

T_{-}

in the above equation are the distribution sets of positive and negative ideal schemes, respectively.

Let the proximity of the decision scheme $I_{i} (i = 1, 2, \dots, n)$ to the positive ideal scheme $I_{+}$ be $γ_{i}$ , and the formula is equation (11).

γ_{i} = \frac{η_{i}^{-}}{η_{i}^{-} + η_{i}^{+}}

(11)

When $η_{i}^{+} \to 0$ , $γ_{i} \to 1$ is $I_{i} \to I_{+}$ ;

When $η_{i}^{-} \to 0$ , $γ_{i} \to 0$ , is $I_{i} \to I_{-}$ .

According to the relevant theorem, the larger the $γ_{i}$ , the better the scheme $I_{i}$ .

In summary, the decision-making steps for interval number multi-attribute evaluation and decision-making scheme are as follows^30,31:

Step 1 Uses equations (3) and (4) to process the interval number decision matrix, and finally obtains the processed normalized decision matrix R.

Step 2 Uses equation (5) to obtain the weights, and finally obtains the weighted decision matrix A.

Step 3 Use equations (6) and (7) to obtain the decision vectors of positive and negative ideal schemes.

Step 4 The two horizontal orthogonal tables are used to determine the distribution set of the decision-making scheme and the ideal scheme of the government.

Step 5 Use equation (1) to calculate the Mahalanobis distance from the distribution point of the decision scheme to the distribution point of the positive and negative ideal scheme, and use equation (9) to standardize it.

Step 6 Using equation (10) to calculate the signal-to-noise ratio $η_{i}^{+}$ and $η_{i}^{-}$ of the decision-making scheme and the positive and negative ideal schemes, respectively.

Step 7 Uses equation (11) to obtain the closeness, and the decision-making scheme is ranked, and finally the optimal decision-making scheme is selected.

Empirical analysis

There are four digital technology start-ups

I_{1}

I_{2}

I_{3}

, and

I_{4}

, and now it is time to compare the advantages and disadvantages of the organizational quality-specific immunity of the four digital technology start-ups, which are the four decision scenarios. In the eastern region of China, four large-scale digital technology start-up enterprises (enterprise age of more than 10 years, enterprise scale of large enterprises, and enterprise nature of state-owned enterprises, private enterprises, and foreign-funded enterprises) are representative and typical in terms of enterprise age, enterprise output value, total enterprise profit, total enterprise assets, enterprise scale, etc. They attach great importance to organizational quality-specific immunization and organizational quality management practices, and are committed to reasonable planning and management of enterprise quality defects, so as to improve enterprise quality management capabilities and enterprise quality-specific immunity efficiency. Among the survey respondents, private enterprises, state-owned enterprises, Hong Kong, Macao and Taiwan and foreign-funded enterprises accounted for 50.0%, 25.0%, and 25.0%, respectively. 52% of the sample were males and 48% were females. 16.7% were under 25 years old, 59.8% were 26∼35 years old, 18.3% were 36∼45 years old, and 5.2% were over 46 years old. A large proportion (84.5%) have a master’s degree, and a small proportion (15.5%) have a master’s degree or above. The respondents were all senior managers of enterprises (100%). Regarding the length of service, 10∼12 years accounted for more (35.7%), followed by 12–13 years (29.9%) and 13∼15 years (24.3%), and 15 years and above was the least, at 10.1%. The positions of the respondents were mainly from the technology research and development (43.3%) and general management (41.7%), while the production (11.4%) and other subjects such as marketing (3.6%) were relatively small. Through on-site interviews and on-site questionnaires, the senior management of large digital technology start-ups was surveyed and the relevant questionnaire survey data was obtained, and the senior management personnel all had a master’s degree or above, and the senior management personnel had more than 10 years of working experience. The questionnaire was designed using the Likert 1–7 point scale, in which the scores of 1–7 represented “very dissatisfied, dissatisfied, somewhat dissatisfied, average, relatively satisfied, satisfied, and very satisfied.” The questionnaire is mainly distributed through online and offline channels. Offline channels include on-site interviews, face-to-face communication and research, on-site distribution of questionnaires, and other processes and links. Online channels include QQ links, network connections, emails, and WeChat links. A total of 500 questionnaires were distributed and 500 questionnaires were recovered, with a questionnaire recovery rate of 100% and a questionnaire validity rate of 100%. The basic needs and necessary requirements for data processing have been met. Furthermore, in the process of empirical analysis, this paper selects six decision-making attributes, namely, organizational quality monitoring (

x_{1}

), organizational quality cognition (

x_{2}

), organizational quality defense (

x_{3}

), organizational quality purge (

x_{4}

), organizational quality repair (

x_{5}

), and organizational quality memory and immune self-stability (

x_{6}

). Among them,

x_{1}

x_{2}

x_{3}

x_{4}

, and

x_{5}

are cost type,

x_{6}

is benefit type, the interval number decision matrix of these four enterprises is shown in Table 3, Table 4 shows the normalized decision matrix, and the weight vector is

w = (0.0237, 0.2419, 0.3096, 0.1750, 0.1890, 0.0608)

by using equation (5). Table 5 is the weighted decision matrix. Table 6 is the decision vector of positive and negative ideal schemes, because there are 6 decision attributes, so

L_{8} (2^{7})

orthogonal table is selected, as shown in Table 7, the 6 decision attributes can be arranged in six columns of Table 7 at will, and the first six columns are selected in this paper.

Table 3.

Interval number decision matrix Z of the four firms.

	$x_{1}$	$x_{2}$	$x_{3}$	$x_{4}$	$x_{5}$	$x_{6}$
$I_{1}$	[5, 7]	[3, 5]	[4, 7]	[2, 5]	[2, 7]	[6, 7]
$I_{2}$	[5, 7]	[2, 7]	[5, 6]	[2, 6]	[4, 6]	[2, 6]
$I_{3}$	[4, 6]	[1, 6]	[1, 5]	[3, 5]	[1, 7]	[3, 5]
$I_{4}$	[4, 7]	[1, 8]	[1, 7]	[1, 6]	[2, 3]	[1, 5]

Table 4.

Normalized decision matrix R for the number of intervals of the four firms.

	$x_{1}$	$x_{2}$	$x_{3}$	$x_{4}$	$x_{5}$	$x_{6}$
$I_{1}$	[0.1587, 0.3360]	[0.0707, 0.5253]	[0.0583, 0.3832]	[0.0857, 0.6818]	[0.0635, 0.6364]	[0.2609, 0.5833]
$I_{2}$	[0.1587, 0.3360]	[0.0504, 0.9518]	[0.0680, 0.3066]	[0.0714, 0.6818]	[0.0741, 0.3182]	[0.0870, 0.5000]
$I_{3}$	[0.1852, 0.4200]	[0.0588, 1.5760]	[0.0816, 1.5328]	[0.0857, 0.4546]	[0.0635, 1.2728]	[0.1304, 0.4167]
$I_{4}$	[0.1587, 0.4200]	[0.0441, 1.5760]	[0.0583, 1.5328]	[0.0714, 1.3637]	[0.1481, 0.6364]	[0.0435, 0.4167]

Table 5.

Interval number-weighted normalized decision matrix A for the four firms.

	$x_{1}$	$x_{2}$	$x_{3}$	$x_{4}$	$x_{5}$	$x_{6}$
$I_{1}$	[0.0038, 0.0080]	[0.0171, 0.1271]	[0.0180, 0.1186]	[0.0150, 0.1193]	[0.0120, 0.1203]	[0.0159, 0.0355]
$I_{2}$	[0.0038, 0.0080]	[0.0122, 0.2302]	[0.0211, 0.0949]	[0.0125, 0.1193]	[0.0140, 0.0601]	[0.0053, 0.0304]
$I_{3}$	[0.0044, 0.0100]	[0.0142, 0.3812]	[0.0253, 0.4746]	[0.0150, 0.0796]	[0.0120, 0.2406]	[0.0079, 0.0253]
$I_{4}$	[0.0038, 0.0100]	[0.0107, 0.3812]	[0.0180, 0.4746]	[0.0125, 0.2386]	[0.0280, 0.1203]	[0.0026, 0.0253]

Table 6.

Interval number decision vectors for positive and negative ideal schemes.

	$x_{1}$	$x_{2}$	$x_{3}$	$x_{4}$	$x_{5}$	$x_{6}$
$I_{+}$	[0.0044, 0.0100]	[0.0171, 0.3812]	[0.0253, 0.4746]	[0.0150, 0.2386]	[0.0280, 0.2406]	[0.0159, 0.0355]
$I_{-}$	[0.0038, 0.0080]	[0.0107, 0.1271]	[0.0180, 0.0949]	[0.0125, 0.0796]	[0.0120, 0.0601]	[0.0026, 0.0253]

Table 7.

$L_{8} (2^{7})$ orthogonal table.

Trial	$x_{1}$	$x_{2}$	$x_{3}$	$x_{4}$	$x_{5}$	$x_{6}$
1	1	1	1	1	1	1	1
2	1	1	1	2	2	2	2
3	1	2	2	1	1	2	2
4	1	2	2	2	2	1	1
5	2	1	2	1	2	1	2
6	2	1	2	2	1	2	1
7	2	2	1	1	2	2	1
8	2	2	1	1	1	1	2

Table 7 distributes the decision-making scheme and the positive and negative ideal schemes to obtain the corresponding distribution set. Table 8 and Table 9 calculate the Mahalanobis distance from each distribution set to the distribution set

T_{+}

and

T_{-}

of the positive and negative ideal scheme, respectively, and use equation (9) to normalize the Mahalanobis distance, Table 10 uses equation (10) to calculate the signal-to-noise ratio of the decision-making scheme and the positive and negative ideal scheme, and uses equation (11) to calculate the proximity, and the specific calculation result is

γ_{1} = 0.4312, γ_{2} = 0.2767, γ_{3} = 0.5724, γ_{4} = 0.6184

Table 8.

The distance from each distribution point to $T_{+}$ in each enterprise distribution center.

Dotted set	$d_{M}^{2 +} (t_{1})$	$d_{M}^{2 +} (t_{2})$	$d_{M}^{2 +} (t_{3})$	$d_{M}^{2 +} (t_{4})$	$d_{M}^{2 +} (t_{5})$	$d_{M}^{2 +} (t_{6})$	$d_{M}^{2 +} (t_{7})$	$d_{M}^{2 +} (t_{8})$
$T_{1}$	0.0028	0.2015	0.3667	0.8434	0.3127	0.3696	0.1225	0.0828
$T_{2}$	0.0027	0.1439	0.3165	0.8120	0.3121	0.3956	0.1854	0.1010
$T_{3}$	0.0023	0.2490	0.3037	0.4215	0.5971	0.4469	0.2919	0.2375
$T_{4}$	0.0036	0.2778	0.2457	0.5262	0.5038	0.4435	0.2337	0.2341

Table 9.

The distance from each distribution point to $T_{-}$ in each enterprise distribution center.

Dotted set	$d_{M}^{2 -} (t_{1})$	$d_{M}^{2 -} (t_{2})$	$d_{M}^{2 -} (t_{3})$	$d_{M}^{2 -} (t_{4})$	$d_{M}^{2 -} (t_{5})$	$d_{M}^{2 -} (t_{6})$	$d_{M}^{2 -} (t_{7})$	$d_{M}^{2 -} (t_{8})$
$T_{1}$	0.0002	0.0341	0.0196	0.0177	0.0511	0.0270	0.0232	0.0080
$T_{2}$	0.0030	0.0257	0.0189	0.0199	0.0236	0.0223	0.0286	0.0309
$T_{3}$	0.0005	0.1045	0.4234	0.4175	0.7222	0.5367	0.1830	0.0969
$T_{4}$	0.0010	0.1355	0.4249	0.2773	0.6407	0.4570	0.1098	0.0996

Table 10.

Signal-to-noise ratios of each enterprise and positive and negative ideal schemes.

$η_{1}^{+}$	$η_{2}^{+}$	$η_{3}^{+}$	$η_{4}^{+}$	$η_{1}^{-}$	$η_{2}^{-}$	$η_{3}^{-}$	$η_{4}^{-}$
4.6982	4.5948	2.7408	2.3394	3.5623	1.7580	3.6687	3.7910

And the companies were ranked, that is, $I_{4} > I_{3} > I_{1} > I_{2}$ , so the company with the best organizational quality-specific immunity was the fourth company.

According to a series of calculations, it can be seen that the fourth enterprise has the best organizational quality-specific immunity, followed by the third enterprise, and the second enterprise has the worst organizational quality-specific immunity, so it is necessary to take organizational quality monitoring ( $x_{1}$ ), organizational quality cognition ( $x_{2}$ ), organizational quality defense ( $x_{3}$ ), organizational quality clearance ( $x_{4}$ ), organizational quality repair ( $x_{5}$ ), organizational quality memory and immune self-stability ( $x_{6}$ ) as the entry points, and take measures for continuous quality improvement and quality innovation.

In this paper, the conventional factor analysis method, tomographic analysis method and fuzzy comprehensive evaluation method are further adopted to evaluate and make decisions on the organizational quality-specific immune status of typical and representative digital technology start-ups. There is consistency between the empirical research results obtained by the tomographic analysis method and the fuzzy comprehensive evaluation method and the empirical research results obtained by using the martin system-TOPSIS research method in this paper, which further indicates that the research method in this paper is robust and can effectively avoid the drawbacks and shortcomings of the conventional factor analysis method, tomographic analysis method and fuzzy comprehensive evaluation method.

Conclusions and prospects

Conclusion

In view of the fierce competition in the current society, digital technology start-ups need to pay more attention to their own product quality issues through organizational quality-specific immunity. In order to expand the application scope and scope of the martin system, this paper effectively integrates and integrates the martin system and TOPSIS, and introduces the martin system-TOPSIS research method into the field of interval number multi-attribute evaluation and decision-making, analyzes in detail the processing advantages and processing efficiency of the martin system and TOPSIS research method in the evaluation and decision-making of interval number multi-attribute problems, and expounds in detail the basic principles, basic modeling steps, main advantages of the martin system-TOPSIS research method, and The key processes and specific links, and the martin system-TOPSIS research method is applied to the evaluation and decision-making of the organizational quality-specific immunity status of digital technology start-ups, and the status of organizational quality-specific immunity of typical and representative digital technology start-ups is compared and analyzed, and the advantages and disadvantages of the organizational quality-specific immunity status of typical and representative digital technology start-ups are analyzed in depth through the empirical analysis program, and the organizational quality-specific immunity status and advantages and disadvantages of typical and representative digital technology start-ups are ranked in a directional manner. Specifically, the martin system and TOPSIS were used to process and sort the interval number data, and the distance from the distribution set of each digital technology start-up to the distribution set of the positive and negative ideal scheme was further measured according to the Mahalanobis distance, and the signal-to-noise ratio was used to calculate the corresponding proximity, and finally the comprehensive score of organizational quality-specific immunity of digital technology start-ups was ranked, and the best and worst enterprises of organizational quality-specific immunity were mined.

The empirical results show that the martin system-TOPSIS method is effective, robust and feasible in the evaluation and decision-making of organizational quality-specific immunity of digital technology start-ups, and the interval number multi-attribute evaluation and decision-making method based on martin system-TOPSIS has matching, adaptability, rationality and operability in solving the evaluation and decision-making of organizational quality-specific immunity of digital technology start-ups. The empirical results are helpful to summarize and explore the enterprises with the best organizational quality-specific immunity and the enterprises with the worst organizational quality-specific immunity. Enterprises with the worst organizational quality-specific immunity should take continuous quality improvement and quality innovation with organizational quality monitoring ( $x_{1}$ ), organizational quality cognition ( $x_{2}$ ), organizational quality defense ( $x_{3}$ ), organizational quality clearance ( $x_{4}$ ), organizational quality repair ( $x_{5}$ ), and organizational quality memory and immune self-stability ( $x_{6}$ ) as the starting points. The enterprises with the best organizational quality-specific immunity are the annotated learning objectives for the enterprises with the worst organizational quality-specific immunity, and point out the improvement direction for the enterprises with the worst organizational quality-specific immunity, so that the enterprises with the worst organizational quality can actively enhance the ability of organizational quality-specific immunity, integrate and summarize the weak processes and bottlenecks of organizational quality-specific immunity, and continuously improve quality performance.

Research limitations and prospects

This paper has certain shortcomings, and there are many steps to hoard research methods, and this paper only takes four typical and representative digital technology start-ups as the empirical analysis objects, which has certain limitations. In the future, a large sample size will be adopted to further verify the effectiveness, feasibility and operability of the research method, and enhance the robustness of the research method and the universality of the research results. Integrate and integrate other research methods, jointly refine and collaborate to summarize the weak links and bottlenecks in the process of substantive organizational quality-specific immune evaluation and decision-making, and improve the depth, breadth and breadth of research.

Footnotes

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is supported by Social Science Planning Fund Project of Liaoning Province (L24AGL014).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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Trial	$x_{1}$	$x_{2}$	$x_{3}$	$x_{4}$	$x_{5}$	$x_{6}$
1	1	1	1	1	1	1	1
2	1	1	1	2	2	2	2
3	1	2	2	1	1	2	2
4	1	2	2	2	2	1	1
5	2	1	2	1	2	1	2
6	2	1	2	2	1	2	1
7	2	2	1	1	2	2	1
8	2	2	1	1	1	1	2

Trial	$x_{1}$	$x_{2}$	$x_{3}$	$x_{4}$	$x_{5}$	$x_{6}$
1	1	1	1	1	1	1	1
2	1	1	1	2	2	2	2
3	1	2	2	1	1	2	2
4	1	2	2	2	2	1	1
5	2	1	2	1	2	1	2
6	2	1	2	2	1	2	1
7	2	2	1	1	2	2	1
8	2	2	1	1	1	1	2

Trial	$x_{1}$	$x_{2}$	$x_{3}$	$x_{4}$	$x_{5}$	$x_{6}$
1	1	1	1	1	1	1	1
2	1	1	1	2	2	2	2
3	1	2	2	1	1	2	2
4	1	2	2	2	2	1	1
5	2	1	2	1	2	1	2
6	2	1	2	2	1	2	1
7	2	2	1	1	2	2	1
8	2	2	1	1	1	1	2