Assessment on Knowledge Network Sharing Capability of Industrial Cluster Based on Dempster-Shafer Theory of Evidence

Based on Theory of Evidence and reviewing research papers concerned, a concept model of knowledge sharing network among industrial cluster firms, which can be applied to assess knowledge sharing capacity, has been built. Next, the authors create a set of assessment index systems including twelve subindexes under four principle indexes. In this study, ten experts in the same field were invited to score all the indexes of knowledge sharing capacity concerning one certain industrial cluster. The research result shows relatively high knowledge network sharing capacity among the certain industrial cluster firms. Another conclusion is that the assessment method with Theory of Evidence is feasible to conduct such a research.


Introduction
In recent years, it has become increasingly apparent that cluster economy, accompanied by industrial cluster boom, is one important form of the world economy development and presents a state that develops quickly. In the study field of industrial cluster, operation of knowledge network is focused on by some researchers.
The relationship of cooperation between enterprises and knowledge exchange attracts more and more attention. In the study of process of knowledge transfer, emphasis is widely put on knowledge characteristic (e.g., recessive, tacit-codified, individual-social, appropriable-exclusive, and divisible-indivisible) [1]. There is also much research, which contributes to knowledge network of industrial cluster. The Framework of Knowledge Networks comprises the following components: actors individuals, groups, and organizations; relationships between actors, which can be categorized by form, content, and intensity; resources which may be used by actors within their relationships, and institutional properties, including structural and cultural dimensions such as control mechanisms, standard operating procedures, norms and rules, and communication patterns [2]. Regional clusters depend on the networks that arise from reciprocal linkages among colocated organizations, while physical proximity among firms can alter the nature of information and resource flows through networks [3]. In all industries, knowledge can flow through the linkage border and the effect of knowledge flow is enhanced by spatial proximity between the actors taking part in the exchange [4]. The focal firms and their organized networks within industrial districts, being the driving force of cluster innovation, play a crucial role in the process of knowledge creation and transfer [5]. Knowledge alliance, one kind of strategic alliance similar to knowledge network, means a group of firms entering into voluntary arrangements that involve knowledge creation, transfer and exchange [6]. Alliances may serve different purposes from knowledge alliance formation. However, rather than using alliances to acquire capabilities, scholars suggest that firms use interfirm collaboration to gain access to other firms' capabilities, supporting more focused, intensive exploitation of existing capabilities [7]. Based on heterogeneity of knowledge acquired from accumulative research, different firms can develop various capabilities [8]. Some researches concerning 2 The Scientific World Journal knowledge transfer and sharing have been done. The study of Ahuja and Giuliani shows the existing relation between structural properties of social networks and learning and innovation output [9,10]. Ahuja's study shows that direct and indirect ties between a firm's partners both have a positive impact on innovation but that the impact of indirect ties is moderated by the number of a firm's direct ties. More brokerage opportunities in network firms relate to better innovative performance, because actors in a network rich in structural holes will be able to access novel information from remote parts of the network and exploit that information to their advantage. Hansen's research argues that indirect ties in network firms are conducive to knowledge transfer and focal firms usually are the bridge of the connections [11]. In the study of the Boston Biotechnology Community innovative activities, Owen-Smith and Powell emphasize that focal firms are the organizer of the network knowledge and fundamentally alter the flow of information through a network [12,13].
Though there are many insights on explaining the process of knowledge transfer and innovation, more emphasis was put on structural character of knowledge network. Because of much uncertainty, many methods have been applied to evaluate the capacity of knowledge networks sharing, for example, Analytic Hierarchy Process, Fuzzy Theory, Grey Theory, Neutral Network Analysis, Data Envelop Analyze, Factor Analysis, and Bayesian Network. In our view, the existing researches on assessing the capacity of knowledge networks sharing have a number of important weaknesses and constraints, especially on assessment methodologies and unclear attribute of the evaluation objects. In this research, to begin with, one new evaluation index system concerning the evaluation object will be established. We attempt to assess the capacity of knowledge networks sharing among cluster industries based on another powerful method-Dempster-Shafer Theory of Evidence.
There are quite a few models concerning knowledge networks sharing among cluster industries. Szulanski argues that knowledge transfer process includes four stages-initiation, implementation, ramp-up, and integration [14]. In Xiao's opinion, there are several categories of Knowledge Flows in Knowledge Networks: technical corporation, talent flow, new technology transfer, transfer of patent right, market research, and informal exchange [15]. Zhang constructs a cluster model of enterprise knowledge networks based on social network tools and argues that knowledge base, recessive knowledge center, knowledge transfer center, knowledge innovation center, and knowledge expansion center exist among cluster enterprises [16]. Above, researches present a reasonable analysis on operation mechanism of knowledge network sharing among cluster industries and draw some valuable conclusions. In authors' view, much efficient discussion on the knowledge sharing process is required. In the knowledge sharing process among cluster industries, knowledge from knowledge source, combined with knowledge transfer carrier, finally transfers to knowledge accepter via certain transfer path. The knowledge source includes universities, institutions, financial institutions, administration consulting company, administration and industry association, upstream firms, downstream firms, and competitive firms as shown in Figure 1.

Computational Methods for Evidence Theory
Dempster-Shafer theory of evidence was put forward on early 1976 by Dempster and developed by Shafer [17]. Generally, evidences are conclusions of one specific research and observation, which is one part of experience and knowledge. Based on evidences, initial allocations are created, which means to calculate the degrees of support on each proposition. In actual study, evidences available can be used to calculate collective contribution to every proposition and this method can effectively solve the problem of uncertainty in knowledge network sharing assessment. Generally, suppose that one sampling space is called a frame of discernment , one proposition ( = 1, 2, . . . , ) is subset of set , and is individually independent. In the study, some definitions of belief allocation, belief function, and focal elements are brought forward. Evidence combination rules are introduced and knowledge network sharing capability of cluster industries is assessed.
Given a question of interest, let be a finite set of possible answers to the question, called a frame of discernment, and let 2 be the set of all subsets of : The subset includes as special cases the empty set and the full set . It represents a statement or proposition that the truth lies in . A real function over the subsets Bel: 2 → [0, 1] is called a belief function if and only if it satisfies the following three axioms: where is defined as basic probability on frame of discernment and ( ) is called Proposition A's basic probability number. The vacuous belief function is a simple support function with focus . If Bel is a simple support function with focus = , then ( ) = , ( ) = 1− , and is 0 elsewhere. Thus, a simple support function invests all of our committed belief on the disjunction represented by its focus, , and all our uncommitted belief on . Consider The subsets of such that ( ) > 0 are called the focal elements of the belief function, and their union is called its core. Based on the definitions above, evidence combination rules can be derived. Let 1 and 2 be basic probability assignments on the same frame . The function is defined as where 12 is a set function over the frame of discernment and = (1/(1 − )) ∑ ∩ = 1 ( ) 2 ( ) is conflict factor. This formulation (4), called Dempster's rule of combination, namely, 12 = 1 ⋅ 2 , represents the degrees of support by two independent evidences.
In the assessment process, firstly, hierarchy factors' values of model are scored by experts and decision makers and basic probabilities are obtained. Secondly, the assessment is completed based on the combination rules of evidence. There are five steps to assess knowledge network sharing capability among cluster industries via Evidence Theory. Consider the following.
(a) Based on analytic hierarchy process (AHP), the numerical weight is derived for each element of any hierarchy. Corresponding basic probability ( ( ) ) of the lowest hierarchy elements ( ) over set ( = 1, 2, . . . , ) is acquired by experts and decision makers.
(b) Basic probability of each element of each hierarchy is computed. The elements with greatest weight is called core element and their probability over set is ( | ) = ( ), while probability of the lowest elements over set is ( ) , where is preference coefficient reflecting experts' attitude to core elements. 's value ranges over 0.9 ≤ ≤ 1. The greater is the 's value, the more important is the core element. As to noncore elements, their

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The Scientific World Journal (e) Finally, formulation = ∑ =1 ( ) is used to compute knowledge network sharing capability among cluster industries. The output is the result of evidential reasoning [18].

Construction of Assessment Indicator
In authors' view, there are several direct factors that affect the capability of knowledge network sharing among cluster industries. According to the model in the flowchart above, knowledge source, the pathway of knowledge transfer, carrier of knowledge transfer, and knowledge recipient are four prominent factors upon the capability of knowledge network sharing among cluster industries. Generally, the knowledge sharing capability of knowledge source is affected by vigor of knowledge, knowledge quantity, interest motive of knowledge sharing, and knowledge compatibility. The pathway of knowledge transfer is affected by remunerative transfer of new technology, talent flow, and technical corporation. Carrier of knowledge transfer is affected by competency of staff and knowledge sharing technology. Knowledge recipient is affected by knowledge deficiency, knowledge absorptive capacity, and willingness of receiving knowledge. Based on the factors above, the assessment index system is built. represents the indicator and represents the corresponding indicator's weight. Ten experts are invited to score each indicator and scores are listed in Table 1.

Weight of Assessment Indicator
In the aspect of weight, fuzzy clustering analysis is applied to avoid experts' subjective factors. Essentially, fuzzy clustering analysis is one classification method, which divides data elements into classes or clusters so that items in the same class are as similar as possible, and items in different classes are as dissimilar as possible. Under different supposed thresholds , different weights can be calculated as below. And the matrix of normalized data ( ) is derived, is normalization data of and is the simple value of the variable measured in the level .

Computation of Fuzzy Similar Matrix.
Angle cosine method is applied to obtain fuzzy similar matrix = ( ), where represents relation coefficient between any two observed variables, where and , respectively, represent the average scores assessed by ten experts, which range over 0 ≤ ≤ 1.

Construction of Fuzzy Equivalence Matrix.
Convolution computation on fuzzy similar matrix is conducted after iterations until = and = 2 appear, and then fuzzy classification matrix is obtained.

Clustering.
Given different threshold values, Boolean matrixes, which relate to the significance of the indictor, are obtained by computation of fuzzy classification matrix. Generally, the classification categories rise with the increase of value. In order to distinguish the significance of the assessment indicators, greater value should be chosen so that sequence and classification can be well done. Based on the different grades of values, weights of the assessment indicators are determined after data normalization.

Empirical Study
As described above, ten experts anticipate to score each assessment indicator and scores are listed in Table 1 Complex mass matrix about knowledge source 1 is derived from evidence combination computation by following computational steps (c) and (d). In the same way, mass matrix about 2 , 3 , and 4 over the fuzzy set can create a new mass matrix as ] .

Conclusion
Due to asymmetric information, less objective data, and cognitive biases of experts, systematic assessment methods have not dealt with uncertain matters. Evidence Theory is an effective mathematical tool to solve inaccurate and uncertain problems while distinguishing uncertain and unknown facts. Under Dempster's evidence combination rules, experts' opinions with different probability distribution can be operatively synthesized, which bring a new insight to carry out specific assessment.