Research on the flexibility evaluation of platform organization based on fuzzy linguistic variables

Abstract

Platformization is an important direction for business in the present and future. Platforms with strong flexibility are able to quickly respond to changes in the internal and external environment. So businesses can effectively avoid all kinds of risks and keep steady and sustainable development. The flexibility evaluation of platform organization is the key point to improve the flexibility of the platform enterprise. Based on the international and domestic related research, this paper constructs an evaluation index system of flexibility for platform organization and puts forward a kind of method to evaluate the flexibility of platform organization based on fuzzy linguistic variables. Finally, the feasibility and practicability of the method are verified by a numerical example.

Keywords

Fuzzy linguistic variables platform organization flexibility

1 Introduction

In the era of the Internet, the platformization is an important direction for the development and transformation of organization forms of enterprises. Platform organization is a new organizational form of modern enterprises in order to adapt to the new trend of the market, technology and talents. While the platform organization provides possibility for the enterprises to adapt to the new competitive advantage, it also puts forward new challenges for the enterprise internal operation and external governance. So it puts forward a new task for the further development of the platform organization. Flexibility is an important indicator to measure the stability and sustainable development of the platform organization. The flexibility of the platform organization refers to the ability of the platform to make corresponding adjustment to the disturbance factors which arise from the causes of internal and external environmental changes of the platform with the minimum time cost, energy cost and cost loss. The platform organization with high flexibility will have high market sensitivity and adaptability which can help it avoid the risks brought about by the changes in the market and technological environment quickly and effectively. Therefore, with the deepening and development of the enterprise platform, the flexibility evaluation of platform organization has become the focus of domestic and foreign scholars. As for the flexibility evaluation of the platform organization, many scholars both at home and abroad have done some research on it. Son and Park evaluated the economic effect of organizational flexibility by using the principle of economics [1]. Chatterjee and Falkner examined the effectiveness of organizational flexibility in performance standards [2, 3]. Gupta done the qualitative evaluation of flexibility by using the multidimensional classification method [4]. Barad carried out quantitative evaluation of organizational flexibility by using the Petri network [5]. Kumar evaluated the organizational flexibility by the information theory [6]. In the field of network platform, Feng Jian applied the complex network theory to the research of P2P network platform, and pointed out the development prospect of P2P network platform [7]. Wu Hualong discussed the remote data audit (RDA) technology to ensure the data reliability of cloud service platform [8]. In addition, Hutchinson studied the evaluation method of flexibility by using decision theory [9]. At home, Wang Wei and Chen Rongqiu used the method of information theory to make quantitative research on the organization structure of enterprise [10]. But it only proved the feasibility and validity of information theory in the study of organizational structure flexibility.

Most of the organization flexibility evaluation indexes are qualitative indexes. How to effectively deal with qualitative indexes and reduce the loss of information which is converted into quantitative indexes is the key to make accurate evaluation. The linguistic variable is the most comfortable method to express the fuzzy information. In order to make a more accurate and clear evaluation to the flexibility of the platform organization, based on the theoretical research of domestic and foreign scholars, a method for evaluating the flexibility of the platform organization based on fuzzy linguistic variables is proposed in this paper.

2 Basic knowledge of fuzzy linguistic variables

The fuzzy linguistic variable method is generated based on the fuzzy theory. In many fields, it is difficult to evaluate the numerical value of many phenomena. Therefore, a practical method is to replace the numerical evaluation with fuzzy linguistic variable evaluation. The difference between a fuzzy linguistic variable and a numeric variable is that it is not a number, but a word or sentence in a natural or artificial language. Although the words or sentences are not as accurate as the numerical values, but the concept of fuzzy linguistic variables provides an approximate solution to solve the problem of overly complicated, unstructured and that is difficult to describe in conventional quantitative methods.

In daily life, people use natural language when they exchange information, and the semantic meaning of natural language is full of fuzziness. In order to formalize and quantify the fuzzy natural language and further distinguish and characterize the degree of fuzzy value, people usually use modifiers in natural language [11] such as “more” “slightly” “a little” “very” and so on, which introduces the concept of fuzzy linguistic variables. Suppose L is a finite discrete set, $\begin{matrix} L & = & {l_{j} | j = - t, - (t - 1), \dots 0, \dots t - 1, t} \\ (t \in Z^{*} and t \geq 1) \end{matrix}$

l_j is called the language variable [12, 13]. Because L ={ l_j|j = - t, - (t - 1) , …0, … t - 1, t } is a discrete set of language, it will cause the loss of information if integrating language information on L. In order to avoid the loss of information in the integration process, this paper extends the discrete set of language L to a continuous set of languag [14]. $\begin{matrix} \bar{L} & = & {{\bar{l}}_{α} = - (t + 1) < α < t + 1, α \in R} \\ (t \in Z^{*} and t \geq 1), L \subset \bar{L} \end{matrix}$

- (t + 1) and t + 1 respectively represent the lower and upper bounds of the linguistic scalar used by decision makers in practical situations. Continuous language variable sets can effectively avoid the loss of information, which can be used to arrange and select the best alternative. Based on the definition and nature of linguistic variables, the operation of linguistic variables can be introduced. The operation of linguistic variables are as follows [15, 16]: $\begin{matrix} \forall \bar{l_{α}}, \bar{l_{β}} \in R, there are : \\ \bar{l_{α}} \oplus \bar{l_{β}} = g^{- 1} (g (\bar{l_{α}}) + g (\bar{l_{β}})) \\ λ \bar{l_{α}} = g^{- 1} (λ g (\bar{l_{α}})) \end{matrix}$

Among the formula: $\begin{matrix} g : \bar{L} \to (- \infty, + \infty) : g (\bar{l_{α}}) = tan (\frac{π α}{2 t + 2}), \bar{l_{α}} \in \bar{L} \\ g^{- 1} : (- \infty, + \infty) \to \bar{L} : g (x) = \bar{l_{β}} \\ β = \frac{(2 t + 2) arctan (x)}{π}, x \in R . \end{matrix}$

Order $f (x) = tan (\frac{π x}{2 t + 2}); x \in (- t - 1, t + 1),$ $f^{- 1} (x) = \frac{(2 t + 2) arctan (x)}{π}, x \in R,$ f^-1 (x) is a monotonic continuous function and it is satisfied the follows: $\begin{matrix} \lim_{x \to - \infty} f^{- 1} (x) = - t - 1; \\ \lim_{x \to + \infty} f^{- 1} (x) = t + 1; \\ f^{- 1} (0) = 0 . \end{matrix}$

Then $\forall \bar{l_{α}}, \bar{l_{β}} \in \bar{L}, λ \in R,$ $\begin{matrix} \bar{l_{α}} \oplus \bar{l_{β}} = {\bar{l}}_{f^{- 1}}; \\ λ \bar{l_{α}} = {\bar{l}}_{f^{- 1} [λ f (α)]} . \end{matrix}$

The expectation, variance and standard deviation of language vector which is constituted by the linguistic variables are defined as follows:

Definition 1. Let ${\bar{l}}_{α} = ({\bar{l}}_{α 1}, {\bar{l}}_{α 2}, \dots {\bar{l}}_{α m})^{T}, {\bar{l}}_{α i} \in \bar{L}$ be a set of linguistic information and the expectation and variance of the linguistic information of the group are as follows: $\begin{array}{l} E ({\bar{l}}_{α}) = \frac{1}{m} ({\bar{l}}_{α_{1}} \oplus {\bar{l}}_{α_{2}} \oplus \dots \oplus {\bar{l}}_{α_{m}}) \\ = \frac{1}{m} {\bar{l}}_{f^{- 1} [\sum_{i = 1}^{m} f (α_{i})]} = {\bar{l}}_{f^{- 1} [\frac{1}{m} \sum_{i = 1}^{m} f (α_{i})]} \\ D ({\bar{l}}_{α}) = \frac{1}{m} \sum_{i = 1}^{m} [g ({\bar{l}}_{α_{i}}) - g ({\bar{l}}_{_{\bar{α}}})]^{2} \\ = \frac{1}{m} \sum_{i = 1}^{m} [f (α_{i}) - f (\bar{α})]^{2} \\ = \frac{1}{m} \sum_{i = 1}^{m} [f (α_{i}) - \frac{1}{m} \sum_{i = 1}^{m} f (α_{i})]^{2} \end{array}$

Then the standard deviation is $σ ({\bar{l}}_{α}) = \sqrt{D ({\bar{l}}_{α})}$ .

3 Flexibility evaluation of the platform organization

3.1 Construction of the flexibility evaluation index system of the platform organization

The systematicness of existing organization flexibility evaluation index system is not strong. Many index systems are aimed at a certain aspect, a certain stage or a certain level of organization flexibility. In addition, the number of evaluation indexes are either too many and lack of maneuverability, or indexes are too small to contain the main aspects of the platform organizational flexibility. The establishment of index system should be based on the systematic, hierarchical and operational. Gawer pointed out in the process of platform research that there are obvious differences in the three aspects of the interface openness, innovation ability and governance mechanism for different platform organizations [17]. In this paper, a large number of research literature is consulted from the three dimensions proposed by Gawer and get the factor set of flexibility evaluation for platform organization which is shown in Table 1.

Table 1
Factor set of flexibility evaluation factors for platform organization

Sequence Factors Sequence Factors Sequence Factors

number number number

1 Open range of interface 14 Available resources and distribution capabilities 27 Innovative execution ability

2 Transparency of interface 15 Ability to understand the competitors 28 Organizational structure and cultural conditions

3 Availability of interface 16 Ability to understand the development of the industry 29 Cultural mechanism

4 Transparency of distribution channel 17 Ability to understand the development of the technology 30 Trust mechanism

5 Availability of distribution channel 18 Ability to interpret the market environment 31 Reputation mechanism

6 Product innovation 19 Pioneering strategic management ability 32 Distribution mechanism

7 Technological innovation 20 Information analysis ability 33 Decision mechanism

8 Market innovation 21 Innovation management ability 34 Learning mechanism

9 Management innovation 22 Innovative input capability 35 Coordinating mechanism

10 Information acquisition ability 23 Technology innovation ability 36 Incentive mechanism

11 Opportunity recognition ability 24 Technology innovation performance capability 37 Restraint mechanisms

12 Rapid organizational capability 25 Innovation risk control ability

13 Workhorse spirit 26 Innovative decision ability

Sequence	Factors	Sequence	Factors	Sequence	Factors
1	Open range of interface	14	Available resources and distribution capabilities	27	Innovative execution ability
2	Transparency of interface	15	Ability to understand the competitors	28	Organizational structure and cultural conditions
3	Availability of interface	16	Ability to understand the development of the industry	29	Cultural mechanism
4	Transparency of distribution channel	17	Ability to understand the development of the technology	30	Trust mechanism
5	Availability of distribution channel	18	Ability to interpret the market environment	31	Reputation mechanism
6	Product innovation	19	Pioneering strategic management ability	32	Distribution mechanism
7	Technological innovation	20	Information analysis ability	33	Decision mechanism
8	Market innovation	21	Innovation management ability	34	Learning mechanism
9	Management innovation	22	Innovative input capability	35	Coordinating mechanism
10	Information acquisition ability	23	Technology innovation ability	36	Incentive mechanism
11	Opportunity recognition ability	24	Technology innovation performance capability	37	Restraint mechanisms
12	Rapid organizational capability	25	Innovation risk control ability
13	Workhorse spirit	26	Innovative decision ability

According to the factor set, this paper uses the expert scoring method to consult to the experts who research on platform. Through two rounds of screening, the following indicators are selected as the basis for the flexibility evaluation of the platform organization as shown in Table 2 which respectively belong to the three dimensions of interface openness, innovation capability, and governance mechanism.

Table 2

Flexibility evaluation index system of the platform organization

Dimension	Indictor code	Specific indicator
Interface openness (I)	I1	Open range ofinterface
	I2	Availability of interface
	I3	Transparency of interface
Innovation capability (C)	C1	Innovative execution ability
	C2	Risk preference
	C3	Information acquisition and analysis Ability
Governance mechanism (G)	G1	Distribution
	G2	Incentive and restraint
	G3	Decision making and coordination
	G4	Trust and reputation

3.2 Deviation method of platform flexibility index based on fuzzy language information

Let U = {u₁, u₂, …, u_n} be a flexibility evaluation index set of platform organization and S = {s₁, s₂, …, s_m} be a collection of the reviewers. Valuators make language evaluation to each evaluation index and the evaluation language matrix ${\bar{l}}_{A} = ({\bar{l}}_{a_{ij}})_{m \times n}$ is as shown in Table 3.

Table 3
Evaluation language matrix

u ₁ u ₂ ⋯ u _n

s ₁ ${\bar{l}}_{a_{11}}$ ${\bar{l}}_{a_{12}}$ ⋯ ${\bar{l}}_{a_{1 n}}$

s ₂ ${\bar{l}}_{a_{21}}$ ${\bar{l}}_{a_{22}}$ ⋯ ${\bar{l}}_{a_{2 n}}$

⋮ ⋮ ⋮ ⋱

s _m ${\bar{l}}_{a_{m 1}}$ ${\bar{l}}_{a_{m 2}}$ ⋯ ${\bar{l}}_{a_{mn}}$

	u ₁	u ₂	⋯	u _n
s ₁	${\bar{l}}_{a_{11}}$	${\bar{l}}_{a_{12}}$	⋯	${\bar{l}}_{a_{1 n}}$
s ₂	${\bar{l}}_{a_{21}}$	${\bar{l}}_{a_{22}}$	⋯	${\bar{l}}_{a_{2 n}}$
⋮	⋮	⋮	⋱
s _m	${\bar{l}}_{a_{m 1}}$	${\bar{l}}_{a_{m 2}}$	⋯	${\bar{l}}_{a_{mn}}$

Among the Table 3, the value of ${\bar{l}}_{a_{ij}}$ is taken in L, which indicates the language evaluation that the valuator s_i makes to the evaluation index u_j. In this paper, the weight of each index is determined by the deviation method of linguistic variables. Firstly, the expectation, variance and standard deviation of the language information of each column arecalculated: $\begin{matrix} E ({\bar{l}}_{a_{ij}}) = \frac{1}{m} \sum_{i = 1}^{m} {\bar{l}}_{a_{ij}}, j = 1, 2, \dots, n \\ D ({\bar{l}}_{a_{i j}}) = \frac{1}{m} \sum_{i = 1}^{m} [g ({\bar{l}}_{a_{ij}}) - g (E (u_{j}))]^{2}, \\ j = 1, 2, \dots, n \\ σ ({\bar{l}}_{a_{ij}}) = \sqrt{D ({\bar{l}}_{a_{i j}}}), j = 1, 2, \dots, n \end{matrix}$

The size of variance and standard deviation reflects the concentration degree of linguistic assessment information. The larger standard deviation means the greater deviation. It shows that the conclusions of the evaluation are dispersed and the evaluation object is more controversial. Therefore, it can provide more information and play a more significant role in the comprehensive evaluation. So the weight of the index is greater. On the contrary, the smaller standard deviation means the smaller deviation. It shows that the conclusions of the evaluation are centralized. Therefore, it can provide less information and play a limited role in the comprehensive evaluation. So the weight of the index is smaller. Accordingly, the weight of each index which is determined through the controversy degree of valuators is as Equation (1): $w_{j} = σ ({\bar{l}}_{a_{. j}}) / - \sum_{j = 1}^{n} σ ({\bar{l}}_{a_{. j}}), j = 1, 2, \dots, n$ (1)

3.3 The deviation method of calculating the valuators’ credibility

In the evaluation problem, the evaluation subject can be an expert in the field of the platform, or it can be the public. Therefore, the professional background and the knowledge structure of the evaluation subject are diverse. For the evaluation of the same problem, the credibility of different evaluation subjects is different. In this paper, the weight of the evaluation subject is determined from its gender, age and educational level. Assuming the weight of gender is v₁, so the male is v₁₁ and the female is v₁₂. Assuming that the weight of age is v₂, then the age less than 20 is v₂₁, 21 to 30 years old is v₂₂, and so on. The weight of education level is v₃, high school and the following degree is v₃₁, college degree is v₃₂, bachelor degree is v₃₃ and the graduate degree is v₃₄. Then the weight of the evaluation subject is given by Equation (2). $w^{k} = v_{1} v_{2} v_{3}$ (2)

Among the Equation (2), v₁, v₂, v₃ can be determined according to the deviation method. Take v₁ for example. According to the different gender of the valuators, all the evaluation subjects are divided into two categories. The linguistic assessment matrix which is composed by the evaluation language information of the male evaluation subject is as shown in Table 4.

Table 4

Linguistic assessment matrix of male evaluation subjects

	u ₁	u ₂	⋯	u _n
s ₁₁	${\bar{l}}_{b_{11}}$	${\bar{l}}_{b_{12}}$	⋯	${\bar{l}}_{b_{1 n}}$
s ₁₂	${\bar{l}}_{b_{21}}$	${\bar{l}}_{b_{22}}$	⋯	${\bar{l}}_{b_{2 n}}$
⋯	⋯	⋮	⋱
s _1m	${\bar{l}}_{b_{m 1}}$	${\bar{l}}_{b_{m 2}}$	⋯	${\bar{l}}_{b_{mn}}$

The variance and standard deviation of each column in Table 4 can be calculated according to the calculation method of expectation, variance and standard deviation of the language vector: $\begin{matrix} D ({\bar{l}}_{b_{. j}}) = \frac{1}{m_{1}} \sum_{i = 1}^{m 1} {[f (b_{ij}) - \frac{1}{m_{1}} \sum_{i = 1}^{m 1} f (b_{ij})]}^{2}, \\ j = 1, 2, \dots, n \\ σ ({\bar{l}}_{b_{. j}}) = \sqrt{D ({\bar{l}}_{b_{. j}}}), j = 1, 2, \dots, n \end{matrix}$

Sum the standard deviation of each column and then it can get the standard deviation of linguistic evaluation information of the male subject: $σ (male) = \sum_{j = 1}^{n} σ ({\bar{l}}_{b_{. j}}), j = 1, 2, \dots, n$ . Similarly, it can be deduced that the standard deviation of the linguistic evaluation information of all female subjects: $σ (female) = \sum_{j = 1}^{n} σ ({\bar{l}}_{c_{. j}}), j = 1, 2, \dots, n$ . The weight of the male and the female can be calculated by the following formulas: $V_{11} = \frac{σ (male)}{σ (male) + σ (female)};$ (3) $V_{12} = \frac{σ (female)}{σ (male) + σ (female)} .$ (4)

3.4 Language information integration

Definition 2. If ${{\bar{l}}_{β_{1}}, {\bar{l}}_{β_{2}}, \dots, {\bar{l}}_{β_{n}}}$ is the language in formation group to be integrated and W = (w₁, w₂, w₃, …, w_n) ^T is the corresponding weight of the language information, the operator of integrated linguistic information in Equation (3) is called language weighted arithmetic average operator (LWAA). $\begin{matrix} LWAA ({\bar{l}}_{β_{1}}, {\bar{l}}_{β_{2}}, \dots, {\bar{l}}_{β_{n}}) \\ = w_{1} {\bar{l}}_{β_{1}} \oplus w_{2} {\bar{l}}_{β_{2}} \oplus \dots \oplus w_{n} {\bar{l}}_{β_{n}} = {\bar{l}}_{β} \end{matrix}$ (5) $β = f^{- 1} [\sum_{i = 1}^{n} w_{j} f (β_{j})]$ (6)

3.5 The evaluation process of platform organization flexibility based on language integration operator

Step 1. Getting the flexibility evaluation data through questionnaire and further obtaining the language flexibility vector of the platform organization ${\bar{L}}_{α} = ({\bar{l}}_{α 1}, {\bar{l}}_{α 2}, \dots {\bar{l}}_{α m})^{T}$ .

Step 2. According to the Equation (2) to determine the weight of each evaluation subject with different personal information.

Step 3. According to the weight of each evaluation subject, the Equations (3) and (4) are used to integrate the linguistic evaluation information of the flexibility index.

Step 4. According to the Equation (1), the weight of each flexibility index is determined by deviation method.

Step 5. Integrate all the linguistic evaluation information in Step 3 and Step 4 according to Equations (3) and (4). Integrate the language information of the second level indexes under the first level evaluation indexes. According to the result, the language information of the first level evaluation index is then integrated to form the overall evaluation result.

Step 6. Based on the results of the overall integration evaluation, the flexibility of the platform organizational is discussed and analyzed.

4 Empirical research

L company is a chain retail enterprise in China which is well-known in pregnancy baby industry. Through the continuous development of the trinity marketing pattern for chain store, online shopping mall and direct purchase catalog, now L company has become an industry platform with profound impact on the industry. In this part, the L enterprise platform is selected as an example to illustrate the implementation steps and feasibility of the platform organization flexibility evaluation method based on fuzzy linguistic variables.

First of all, a questionnaire survey to the L company’s internal staff was conducted from the 10 aspects of the flexibility evaluation indexes. A total of 150 questionnaires were issued in L company and 141 questionnaires were recovered which contained 138 valid questionnaires. The effective rate reached 97.87%. According to the evaluation process based on language integration operator, the flexibility state of L company is evaluated by using the language information integration evaluation method, as follows:

According to the characteristics of each option in questionnaire, it can use linguistic variables to represent the evaluation results of the investigators. Let t = 2, the definition of language variables are respectively the follows: ${\bar{l}}_{3}$ indicates very strong, ${\bar{l}}_{2}$ indicates strong, ${\bar{l}}_{1}$ indicates relatively strong, ${\bar{l}}_{0}$ indicates general, ${\bar{l}}_{- 1}$ indicates relatively weak, ${\bar{l}}_{- 2}$ indicates weak, ${\bar{l}}_{- 3}$ indicates very weak.

Calculate the weight of each evaluation subject according to the Equation (2). First, on the basis of the gender, age, education information,determine the gender weight v₁, age weight v₂ and education weight v₃.

Taking sex as an example, there are 81 men and 57 women in the respondents. According to the different gender of the respondents, all the questionnaires are divided into two categories. Based on the data of the linguistic information in male questionnaire, the variance of the evaluation index I1 is calculated as follows: $\begin{matrix} E (I 1) \\ = \frac{1}{81} \sum_{i = 1}^{81} {\bar{l}}_{a_{i 1}} \\ = \frac{1}{81} ({\bar{l}}_{1} \oplus {\bar{l}}_{1} \oplus {\bar{l}}_{3} \oplus {\bar{l}}_{1} \oplus {\bar{l}}_{0} \oplus {\bar{l}}_{1} \oplus {\bar{l}}_{0} \oplus {\bar{l}}_{1} \oplus \dots \\ \oplus {\bar{l}}_{3} \oplus {\bar{l}}_{2} \oplus {\bar{l}}_{- 1} \oplus {\bar{l}}_{0} \oplus {\bar{l}}_{- 1} \oplus {\bar{l}}_{1} \oplus {\bar{l}}_{1} \oplus {\bar{l}}_{0} \oplus {\bar{l}}_{0}) \\ = {\bar{l}}_{0.8603} \end{matrix}$ $\begin{matrix} D (I 1) & = & \frac{1}{81} \sum_{i = 1}^{81} [g ({\bar{l}}_{a_{i 1}}) - g ({\bar{l}}_{0.8603})]^{2} \\ = & \frac{1}{81} ([g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.8603})]^{2} + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.8603})]^{2} + [g ({\bar{l}}_{3}) - g ({\bar{l}}_{0.8603})]^{2} \\ + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.8603})]^{2} + [g ({\bar{l}}_{0}) - g ({\bar{l}}_{0.8603})]^{2} + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.8603})]^{2} \\ + [g ({\bar{l}}_{0}) - g ({\bar{l}}_{0.8603})]^{2} + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.8603})]^{2} + . . . + [g ({\bar{l}}_{0}) - g ({\bar{l}}_{0.8603})]^{2} \\ + [g ({\bar{l}}_{- 1}) - g ({\bar{l}}_{0.8603})]^{2} + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.8603})]^{2} + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.8603})]^{2} \\ + [g ({\bar{l}}_{0}) - g ({\bar{l}}_{0.8603})]^{2} + [g ({\bar{l}}_{0}) - g ({\bar{l}}_{0.8603})]^{2} \\ = & 0.5825 \\ σ (I 1) & = & \sqrt{D (I 1)} = 0.7632 \end{matrix}$

In the same way, the standard deviation of I2, I3, C1, C2, C3, G1, G2, G3 and G4 can be calculated as follows:

$\begin{matrix} σ (I 2) & = & 0.8533; σ (I 3) = 0.6709; \\ σ (C 1) & = & 0.8880; σ (C 2) = 0.8590; \\ σ (C 3) & = & 0.8177; σ (G 1) = 1.1443; \\ σ (G 2) & = & 0.8512; σ (G 3) = 0.8526; \\ σ (G 4) & = & 0.9239 . \end{matrix}$

The sum of standard deviation of the male linguistic evaluation is σ(male) = 7.8690. The result of female samples is obtained by the same method: σ(female) = 7.1685. According to the calculation data, the weights of the male subjects and female subjects are determined respectively:

$\begin{matrix} V_{11} & = & \frac{σ (male)}{σ (male) + σ (female)} \\ = & \frac{7.8690}{7.8690 + 7.1685} = 0.5233; \\ V_{12} & = & \frac{σ (female)}{σ (male) + σ (female)} \\ = & \frac{7.1685}{7.8690 + 7.1685} = 0.4767 . \end{matrix}$

Similarly, the weight of age and education can be calculated separately through the above calculation method. The summary weight matrix based on personal background information (statistical features) is as shown in Table 5.

Table 5
Weight matrix based on statistical features

Statistic feature Weight distribution

v_1h (h = 1, 2) 0.5233 0.4767

v_2i (i = 1, 2, 3, 4) 0.3546 0.3401 0.3053

v_3j (j = 1, 2, 3, 4) 0.0000 0.0000 0.4876 0.5124

Statistic feature	Weight distribution
v_1h (h = 1, 2)	0.5233	0.4767
v_2i (i = 1, 2, 3, 4)		0.3546	0.3401	0.3053
v_3j (j = 1, 2, 3, 4)	0.0000	0.0000	0.4876	0.5124

According to the background information, the evaluation subjects can be divided into 2×3×2 = 12 categories. Taking the evaluation subject K = 1 (male, 21– 30 years old, undergraduate) as an example, the weight of it is as follows: $\begin{matrix} w^{k} & = & w^{1} = v_{11} \times v_{22} \times v_{33} \\ = & 0.5233 \times 0.3546 \times 0.4876 \\ = & 0.09048 \end{matrix}$

Calculate the weight of evaluation subjects belong to different types in turn w^k (k = 1, 2, …, 12), as shown in Table 6. And according to the value of w^k and the corresponding number of evaluation subjects, the weight of each evaluation subject is calculated wⁿ (n = 1, 2, …, 138).

Table 6

Weight of evaluation subjects of various types

Types of evaluation subjects			Weight
Gender	Age	Education
male	21– 30	Undergraduate	0.090480
male	31– 40	Undergraduate	0.086780
male	>40	Undergraduate	0.077901
male	21– 30	Graduate	0.095082
male	31– 40	Graduate	0.091194
male	>40	Graduate	0.081863
female	21– 30	Undergraduate	0.082423
female	31– 40	Undergraduate	0.079052
female	>40	Undergraduate	0.070964
female	21– 30	Graduate	0.086615
female	31– 40	Graduate	0.083073
female	>40	Graduate	0.074573

(3) Integrate the corresponding linguistic evaluation information of the evaluation index. According to the weight of each evaluation subject wⁿ (n = 1, 2, …, 138), the evaluation information of evaluation elements (I1, I2, I3, C1, C2, C3, G1, G2, G3 and G4) are integrated by the Equations (3 and 4) respectively. Taking I1 as an example, the integrated linguistic evaluation information is as follows: $\begin{matrix} LWAA (I 1) = w^{n} {\bar{l}}_{a_{i 1}} \\ = w^{1} {\bar{l}}_{- 1} \oplus w^{2} {\bar{l}}_{1} \oplus w^{3} {\bar{l}}_{1} \oplus w^{4} {\bar{l}}_{- 1} \oplus w^{5} {\bar{l}}_{1} \\ \oplus w^{6} {\bar{l}}_{1} \oplus w^{7} {\bar{l}}_{1} \oplus w^{8} {\bar{l}}_{1} \oplus \dots \oplus w^{129} {\bar{l}}_{0} \\ \oplus w^{130} {\bar{l}}_{1} \oplus w^{131} {\bar{l}}_{- 1} \oplus w^{132} {\bar{l}}_{1} \oplus w^{133} {\bar{l}}_{1} \oplus \\ w^{134} {\bar{l}}_{0} \oplus w^{135} {\bar{l}}_{2} \oplus w^{136} {\bar{l}}_{1} \oplus w^{137} {\bar{l}}_{0} \oplus w^{138} {\bar{l}}_{1} \\ = {\bar{l}}_{0.9617} \end{matrix}$

In the same way, the integrated linguistic evaluation information of all flexibility evaluation indexes are obtained, as shown in Table 7.

Table 7

Integrated linguistic evaluation information

Flexibility evaluation index	I1	I2	I3	C1	C2
Integrated language information	${\bar{l}}_{0.9617}$	${\bar{l}}_{1.8677}$	${\bar{l}}_{1.7318}$	${\bar{l}}_{2.1939}$	${\bar{l}}_{1.7286}$
Flexibility evaluation index	C3	G1	G2	G3	G4
Integrated language information	${\bar{l}}_{2.5002}$	${\bar{l}}_{2.5200}$	${\bar{l}}_{2.5918}$	${\bar{l}}_{2.9245}$	${\bar{l}}_{2.6660}$

(4) Determine the weight of each evaluation index. According to the Equation (1), the weight is determined by the deviation method. The expectation, variance and standard deviation of the evaluation index I1 are as follows: $\begin{matrix} E (I 1) & = & \frac{1}{138} \sum_{i = 1}^{138} {\bar{l}}_{a_{i 1}} \\ = & \frac{1}{138} ({\bar{l}}_{- 1} \oplus {\bar{l}}_{1} \oplus {\bar{l}}_{1} \oplus {\bar{l}}_{- 1} \oplus {\bar{l}}_{1} \oplus {\bar{l}}_{1} \oplus {\bar{l}}_{1} \\ \oplus {\bar{l}}_{1} \oplus \dots \oplus {\bar{l}}_{0} \oplus {\bar{l}}_{1} \oplus {\bar{l}}_{- 1} \oplus {\bar{l}}_{1} \oplus {\bar{l}}_{1} \\ \oplus {\bar{l}}_{0} \oplus {\bar{l}}_{2} \oplus {\bar{l}}_{1} \oplus {\bar{l}}_{0} \oplus {\bar{l}}_{1}) \\ = & {\bar{l}}_{0.7631} \end{matrix}$ $\begin{matrix} D (I 1) & = & \frac{1}{138} \sum_{i = 1}^{138} [g ({\bar{l}}_{a_{i 1}}) - g ({\bar{l}}_{0.7631})]^{2} \\ = & \frac{1}{138} ([g ({\bar{l}}_{- 1}) - g ({\bar{l}}_{0.7631})]^{2} \\ + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.7631})]^{2} + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.7631})]^{2} \\ + [g ({\bar{l}}_{- 1}) - g ({\bar{l}}_{0.5560})]^{2} + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.7631})]^{2} \\ + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.7631})]^{2} + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.7631})]^{2} \\ + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.7631})]^{2} + . . . \\ + [g ({\bar{l}}_{0}) - g ({\bar{l}}_{0.7631})]^{2} + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.7631})]^{2} \\ + [g ({\bar{l}}_{- 1}) - g ({\bar{l}}_{0.7631})]^{2} + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.7631})]^{2} \\ + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.7631})]^{2} + [g ({\bar{l}}_{0}) - g ({\bar{l}}_{0.7631})]^{2} \\ + [g ({\bar{l}}_{2}) - g ({\bar{l}}_{0.7631})]^{2} + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.7631})]^{2} \\ + [g ({\bar{l}}_{0}) - g ({\bar{l}}_{0.7631})]^{2} + [g ({\bar{l}}_{1}) - g ({\bar{l}}_{0.7631})]^{2} \\ = & 0.2233 \\ σ (I 1) & = & \sqrt{D (I 1}) = \sqrt{0.2233} = 0.4725 \end{matrix}$

In the same way, the standard deviations of other evaluation indexes are obtained: $\begin{matrix} σ (I 2) & = & 0.6146; σ (I 3) = 0.5495; \\ σ (C 1) & = & 0.6265; σ (C 2) = 0.8196; \\ σ (C 3) & = & 0.5634; σ (G 1) = 0.7969; \\ σ (G 2) & = & 0.5918; σ (G 3) = 0.6692; \\ σ (G 4) & = & 0.6730 . \end{matrix}$

After standardizing the above data, the weight of each evaluation index can be obtained as follows: $\begin{matrix} w (I 1) & = & \frac{σ (I 1)}{(σ (I 1) + . . + σ (I 3) + σ (C 1) + . . + σ (C 3) + σ (G 1) + . . + σ (G 4))} \\ = & 0.0741 \end{matrix}$

Similarly, the weights of other evaluation indexes are obtained as shown in Table 8.

Table 8

Weights of different evaluation indexes

Evaluation	Weight w	Evaluation	Weight w
Index		Index
I1	0.0741	C3	0.0884
I2	0.0964	G1	0.1250
I3	0.0862	G2	0.0928
C1	0.0982	G3	0.1049
C2	0.1285	G4	0.1055

According to the weight of each evaluation index, the weight of interface openness, innovation ability and governance mechanism in L company can be determined. $\begin{matrix} w (I) & = & w (I 1) + w (I 2) + w (I 3) = 0.2567; \\ w (C) & = & w (C 1) + w (C 2) + w (C 3) = 0.3151; \\ w (G) & = & w (G 1) + w (G 2) + w (G 3) + w (G 4) \\ = & 0.4282 \end{matrix}$

The weight of I1 is w (I1|I) = w (I1)/ - w (I) = 0.2887, and so on, getting the weight of each index is shown in Table 9.

Table 9

Weight of each hierarchy evaluation index

Hierarchy	Weight	Evaluation Index	Weight w (\|)
I	0.2567	I1	0.2887
		I2	0.3755
		I3	0.3358
C	0.3151	C1	0.3118
		C2	0.4079
		C3	0.2803
G	0.4282	G1	0.2918
		G2	0.2167
		G3	0.2450
		G4	0.2465

(5) Integrate the linguistic evaluation information. Firstly, according to the integrated linguistic evaluation information in Table 7, the weight of each hierarchy evaluation index in Table 9 and the Equations (3 and 4), the language information of the layer I can be integrated: $\begin{matrix} LWAA (I) \\ = w (I 1 | I) LWAA (I 1) \oplus w (I 2 | I) LWAA (I 2) \\ \oplus w (I 3 | I) LWAA (I 3) \\ = 0.2887 {\bar{l}}_{0.9617} \oplus 0.3755 {\bar{l}}_{1.8677} \oplus 0.3358 {\bar{l}}_{1.7318} \\ = {\bar{l}}_{1.2680} \end{matrix}$

In the same way, it is calculated that $LWAA (C) = {\bar{l}}_{2.1348}$ and $LWAA (G) = {\bar{l}}_{2.3518}$ . Through the aggregation approach of “bottom-up”, the overall integrated linguistic evaluation information is obtained:

$\begin{matrix} LWAA (ICG) \\ = w (I) LWAA (I) \oplus w (C) LWAA (C) \\ \oplus w (G) LWAA (G) \\ = 0.2567 {\bar{l}}_{1.2680} \oplus 0.3151 {\bar{l}}_{2.1348} \\ \oplus 0.4282 {\bar{l}}_{2.3518} = {\bar{l}}_{2.0698} \end{matrix}$

(6) From the calculation and analysis of the platform flexibility of L company by means of language integration operator, lots of valid information about the company’s flexibility can be obtained. From the perspective of L company’s internal staff, L company as a platform organization has a strong flexibility in general. It can respond quickly to various risks arising from the changes in the market environment. It has reached a very high level especially in the innovation ability and governance mechanism while there is also a great room for improvement in the interface openness. Therefore, L company can further improve the flexibility of the platform through the expansion of the interface open level, so that the company will have a stronger ability to respond torisks.

5 Conclusions

In view of the flexibility evaluation of the platform organization, this paper constructs an evaluation index system of flexibility for platform organization and puts forward a kind of method to evaluate the flexibility of platform based on fuzzy linguistic variables. Firstly, based on the platform research of Gawer and a large amount of literature review, this paper concludes the flexibility evaluation factors set of platform organization from the three dimensions of the interface openness, innovation capability and governance mechanism that he proposed in his research. And through the expert scoring method, 10 secondary indexes of the platform flexibility evaluation are screened out, which constitutes a flexibility evaluation index system; Secondly, through the questionnaires or interviews to the evaluation subjects, it uses the language terminology to describe the state of the platform organization in these ten indexes, thus completes the collection of the language flexibility data; Then, according to the language flexibility data obtained, the weight of each evaluation subject with different information background is determined by the deviation method, and the linguistic evaluation information of the flexibility index is integrated according to the weight; next, it uses the deviation method to determine the weight of each flexibility index and integrates the language information of the secondary indexes. According to the results, the language information of the primary evaluation index is integrated again. The flexibility state of the platform organization is discussed on the basis of the overall integrated evaluation results obtained; Finally, the paper takes L company as an example to illustrate the feasibility and practicality of the whole process, and puts forward the feasible direction for L company in order to improve the organizational flexibility based on the evaluation results. It has practical guiding significance for the development of platform organizations.

Footnotes

Acknowledgments

The authors thank the anonymous referees for their constructive suggestions. We appreciate the support provided for this paper by the Fundamental Research Funds for the Central Universities of Sichuan University (skqy201739).

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