**3.1 Documents' crystallisation process**

The Knowledge Crystallisation mechanism takes into account the users' opinions about the documents and the evolution of its received opinions in order to determinate which documents have enough acceptation during a determinate period of time. They will then crystallise.

Each document has a value called "crystallisation degree" or "social acceptation degree"–or acceptation degree, for short–, which is a value between 0-1. A document "crystallise" when his acceptation degree stay for a period of time called "time for crystallising", e.g. 2 weeks, over a determinate "crystallisation point" , e.g. 0.65.

The acceptation degree of a document takes into account:


The acceptation degree, which is called as *AcceptationDegree*, of each document, *doci*, in a concrete moment ,*tj*, is calculated from the mentioned elements in the following way:

It is considered that the explicit opinions are more useful in order to determinate the acceptation of a document, because they are more elaborated opinions that implicit opinions, so the *coefE* is higher than *coefI* (e.g. *coefE* = 0.9; *coefI* = 0.1).

Knowledge Crystallisation Supported by the KnowCat System 193

*d i*

*d i*

*d i*

a lot of votes but close to *ti* it doesn't receive new votes.

*percentageVotes doc ,t normalPercentageVotes doc ,t* 

*j numberVotes doc , t t percentageVotes doc ,t numberVotes doc , t t* 

*evolutionVotes* is a value in the rank 0.95-1.10 when *docd* has a good evolution of the number of the received votes in time, e.g. *docd* receives constantly votes. However, *evolutionVotes* is a value in the rank 0.80-0.95 when *docd* has a bad evolution, e.g. *docd* received at the beginning

*ExplicitAcceptationDegree\_Notes* of *docd* is calculated taking into account on the one hand the received "support" annotations and on the other hand the received "review" annotations.

*normalPercentageSupportNotes(docd,ti)* is the normalised percentage of the received "support"

*normalPercentageReviewNotes(docd,ti)* is the normalised percentage of the received "review"

It is proposed that *coefSA*=1 and the following function is used in order to calculate the coefficient *coefRA.*. With this function the following two cases are distinguished: if a document receives few "review" notes means that this document has social interest and *coefRA* is close to value 1; if it receives a lot of "review" notes means that the document needs

*ExplicitAcceptationDegree\_Assessments* of *docd* is calculated taking into account the normalised

*d i*

*d i*

*averageValueAssessments doc ,t numberAssessments doc , t t*

*averageValueAssessments doc ,t ExplicitAcceptationDegree Assessments doc ,t averageValueAssessments doc ,t* (10)

*j*

*normalPercertageSupportNotes doc ,t coef ExplicitAcceptationDegree Notes(doc ,t ) normalPercertage viewNotes doc ,t coef*

where,

where,

where,

notes by *docd* until the moment *ti*.

notes by *docd* until the moment *ti*.

to be improved and *coefRA* has a value close to 0.

average value of the received assessments.

*ExplicitAcceptationDegree Votes doc ,t normalPercentageVotes doc ,t evolutionVotes doc d i d i d i ,t* (5)

\_ Re

max

 , , *d 0i*

*valueAssessments doc , t t*

\_ max

*j 0i*

*d i*

*percentageVotes doc ,t* (6)

*j i*

*d i SA*

(8)

(9)

*d i*

*j d 0i*

,

,

*d 0i*

*j i*

(11)

*d i RA*

(7)

$$\text{Acceleration}\,\text{Degree}\left(\text{doc}\_{i},t\_{j}\right) = \begin{bmatrix} \text{ExplicitAccipation}\,\text{Degree}\{\text{doc}\_{i},t\_{j}\} \times \text{coef}\_{\mathbb{E}} +\\ \text{Im }\,\text{plicitAccipation}\,\text{Degree}\left(\text{doc}\_{i},t\_{j}\right) \times \text{coef}\_{I} \end{bmatrix} \times \text{Histor}\left(\text{doc}\_{i},\text{versionDoc}\_{i},t\_{j}\right) \tag{1}$$

The knowledge crystallisation mechanism deals with knowledge in evolution. The documents evolves through a sequence of document versions, how is this evolution is calculated in the "history degree" value, i.e. *History(doci, versionDoci, tj)*. This value is used in the calculation of the acceptation degree of a document in order to correct its social acceptation taking into account its evolution through several document versions. See Section 3.2.

The first idea in order to calculate the *ImplicitAcceptationDegree* of a selected document *docd* is to compare the number of the received access by *docd* with the received access by all the documents that are in the same topic that *docd*.

$$\text{percentageAcccess}(doc\_d, t\_i) = \frac{numberAcccess(doc\_d, \left[t\_0, t\_i\right])}{\sum\_j numberAcccess(doc\_j, \left[t\_0, t\_i\right])} \tag{2}$$

where,

*t0* the moment when the knowledge area was created.

*ti* the actual moment.

*numberAccess(docd,[t0,ti])* is the number of received access by *docd* from *t0* to *ti*.

*docj* is a document which is in the same topic than *docd*.

This measurement needs to be normalised because it is depends of the context where the document is located, so it is proposed the Formula 3 in order to obtain the implicit social acceptation degree of a document *docd*.

$$\text{Im } plicitAccipationDegree(doc\_{d'}, t\_i) = \frac{percentageAcccess(doc\_{d}, t\_i)}{\max\{percentageAcccess\left(doc\_{j}, t\_i\right)\}}\tag{3}$$

where:

*max(percentageAccess(docj,ti))* is the highest percentage of the received access from the document which are in the same topic than *docd*.

The explicit social acceptation degree of *docd* is calculated taking into account the following values: the value concerning the received votes, *ExplicitAcceptationDegree\_Votes*, the value concerning the received notes, *ExplicitAcceptationDegree\_Notes*, and the value concerning the received assessments, *ExplicitAcceptationDegree\_Assessments*.

$$\text{ExplicitAccipationDegree}(\text{doc}\_d, t\_i) = \begin{bmatrix} \text{ExplicitAccceptionDegree\\_Votes(doc}\_d, t\_i) \times \text{coef}\_{EV} + \\ \text{ExplicitAccceptionDegree\\_Votes(doc}\_d, t\_i) \times \text{coef}\_{EN} + \\ \text{ExplicitAccceptionDegree\\_Assessments(doc}\_d, t\_i) \times \text{coef}\_{EA} \end{bmatrix} \tag{4}$$

It is proposed that *coefEV* is higher than *coefEN* and *coefEA*, because the votes are realised by expert users while every community user can realise notes and assessments (e.g. *coefEV* = 0.8; *coefEN* = 0.1; *coefEA* = 0.1).

The *ExplicitAcceptationDegree\_Votes* of *docd* is calculated taking into account the normalised percentage of the received votes by *docd*, *normalPercentageVotes*, and a value concerning how theses votes have been received in time by it, i.e., the evolution of the number of received votes in time, *evolutionVotes*.

$$\text{ExplicitAccyptutionDegree\\_Votes(doc\\_dcc\\_t\_i\)} = \text{normalPercentageVotes(doc\\_dcc\\_t\_i\)} \times \text{reductionVotes(doc\\_dcc\\_t\_i\)} \tag{5}$$

where,

192 New Research on Knowledge Management Technology

The knowledge crystallisation mechanism deals with knowledge in evolution. The documents evolves through a sequence of document versions, how is this evolution is calculated in the "history degree" value, i.e. *History(doci, versionDoci, tj)*. This value is used in the calculation of the acceptation degree of a document in order to correct its social acceptation taking into account its evolution through several document versions. See

The first idea in order to calculate the *ImplicitAcceptationDegree* of a selected document *docd* is to compare the number of the received access by *docd* with the received access by all the

> *j numberAccess(doc , t t ) percentageAccess(doc ,t ) numberAccess(doc , t t )*

This measurement needs to be normalised because it is depends of the context where the document is located, so it is proposed the Formula 3 in order to obtain the implicit social

> Im max

*max(percentageAccess(docj,ti))* is the highest percentage of the received access from the

The explicit social acceptation degree of *docd* is calculated taking into account the following values: the value concerning the received votes, *ExplicitAcceptationDegree\_Votes*, the value concerning the received notes, *ExplicitAcceptationDegree\_Notes*, and the value concerning the

It is proposed that *coefEV* is higher than *coefEN* and *coefEA*, because the votes are realised by expert users while every community user can realise notes and assessments (e.g. *coefEV* = 0.8;

The *ExplicitAcceptationDegree\_Votes* of *docd* is calculated taking into account the normalised percentage of the received votes by *docd*, *normalPercentageVotes*, and a value concerning how theses votes have been received in time by it, i.e., the evolution of the number of received

*ExplicitAcceptationDegree(doc ,t ) ExplicitAcceptationDegree Notes(doc ,t ) coef*

*percentageAccess(doc ,t ) plicitAcceptationDegree(doc ,t )* 

*d i*

*d i*

*numberAccess(docd,[t0,ti])* is the number of received access by *docd* from *t0* to *ti*.

*Im plicitAcceptationDegree doc ,t coef*

*<sup>i</sup> <sup>i</sup> <sup>j</sup>*

 , , *d 0i*

*j 0i*

(2)

*d i*

*d i EV*

*d i EA*

(4)

*percentageAccess doc ,t* (3)

\_ \_ \_

*ExplicitAcceptationDegree Assessments(doc ,t ) coef* 

*ExplicitAcceptationDegree Votes(doc ,t ) coef*

*d i d i EN*

*j i*

 

*i j I i j E <sup>i</sup> <sup>j</sup> History doc ,versionDoc ,t*

 (1)

*ExplicitAcceptationDegree doc ,t coef AcceptationDegree doc ,t*

 

documents that are in the same topic that *docd*.

*t0* the moment when the knowledge area was created.

*docj* is a document which is in the same topic than *docd*.

acceptation degree of a document *docd*.

document which are in the same topic than *docd*.

received assessments, *ExplicitAcceptationDegree\_Assessments*.

Section 3.2.

where,

where:

*ti* the actual moment.

*coefEN* = 0.1; *coefEA* = 0.1).

votes in time, *evolutionVotes*.

$$\text{normalPercentageVoltes}(\text{doc}\_d, t\_i) = \frac{\text{percentageVoltes}(\text{doc}\_d, t\_i)}{\max\left(\text{percentageVoltes}\left(\text{doc}\_j, t\_i\right)\right)}\tag{6}$$

$$\text{PercentageVotes}\left(doc\_{d}, t\_{i}\right) = \frac{number\,Votes}\left(doc\_{d}, \left[t\_{0}, t\_{i}\right]\right) \tag{7}$$

$$\sum\_{j} number\,Votes}\left(doc\_{j}, \left[t\_{0}, t\_{i}\right]\right) \tag{8}$$

*evolutionVotes* is a value in the rank 0.95-1.10 when *docd* has a good evolution of the number of the received votes in time, e.g. *docd* receives constantly votes. However, *evolutionVotes* is a value in the rank 0.80-0.95 when *docd* has a bad evolution, e.g. *docd* received at the beginning a lot of votes but close to *ti* it doesn't receive new votes.

*ExplicitAcceptationDegree\_Notes* of *docd* is calculated taking into account on the one hand the received "support" annotations and on the other hand the received "review" annotations.

$$\text{ExplicitAccipationDegree\\_Notes} \left( \text{doc}\_{d}, t\_{i} \right) = \begin{bmatrix} \text{normalPercertageSupportNodes} \left( \text{doc}\_{d}, t\_{i} \right) \times \text{coef}\_{\text{SA}} + \\ \text{normalPercentage RevenueNodes} \left( \text{doc}\_{d}, t\_{i} \right) \times \text{coef}\_{\text{RA}} \end{bmatrix} \tag{8}$$

where,

*normalPercentageSupportNotes(docd,ti)* is the normalised percentage of the received "support" notes by *docd* until the moment *ti*.

*normalPercentageReviewNotes(docd,ti)* is the normalised percentage of the received "review" notes by *docd* until the moment *ti*.

It is proposed that *coefSA*=1 and the following function is used in order to calculate the coefficient *coefRA.*. With this function the following two cases are distinguished: if a document receives few "review" notes means that this document has social interest and *coefRA* is close to value 1; if it receives a lot of "review" notes means that the document needs to be improved and *coefRA* has a value close to 0.

(9)

*ExplicitAcceptationDegree\_Assessments* of *docd* is calculated taking into account the normalised average value of the received assessments.

$$\text{ExplicitAccipationDegree\\_Assumptions(doc\\_t.t\_i)} = \frac{\text{averageValueAssenessments(doc\\_t.t\_i)}}{\max\left(averageValueAssenessments(doc\\_t.t\_i)\right)} \tag{10}$$

where,

$$average\text{ValueAssenessments}\left(doc\_{d'},t\_{i}\right) = \frac{\sum value\text{Assgences}\_{f}\left(doc\_{d'},\left[t\_{0},t\_{i}\right]\right)}{number\text{Assgences}\_{i}\left(doc\_{d'},\left[t\_{0},t\_{i}\right]\right)}\tag{11}$$

Knowledge Crystallisation Supported by the KnowCat System 195

minimum quorum of positive votes from other members of the community will be

This minimum quorum, *MinimumQuorum,* of positive votes for a selected proposed change

*numberActiveExperts* is the number of active member of the virtual community where

KnowCat has been tested for more than ten years in several research studies with student communities at Universidad Autónoma de Madrid (UAM, Spain), Universitat de Lleida (UdL, Spain) and Universidad Pontificia Bolivariana (UPB, Colombia), among others. Table

Most of these research studies have corroborated these design hypotheses of KnowCat (Alamán & Cobos, 1999; Cobos & Alamán, 2002; Cobos, 2003; Cobos & Pifarré, 2008; Diez &

 When a set of people having a certain level of knowledge engage in a reasonable interaction with the system, the result converges to some consensus. This consensus is

 The use of document annotations is useful for motivating document authors in generating new document versions. If a document author takes into account the received notes in the creation of a new document version of his/her annotated

The knowledge area resulted by the user community interactions and the Knowledge

These research studies took the form of longitudinal case studies conducted in authentic university environments. In order to illustrate the research methodology of these studies, an

1. Both students and instructors supported the creation of a common frame of reference before using the KnowCat system. They shared the study's common values and pedagogical goals, and the collaborative tasks were coordinated in advance – i.e., the tasks and the timetable were agreed on previously between instructors and students. Moreover, the students, who needed it, received formation about how to use KnowCat

2. The main procedure of the students' work with the KnowCat system was as follows:

a. The students were distributed into the topics that were established by the instructor in the knowledge tree. Normally, there were between five to ten students

Crystallisation mechanism represents the social interests of its community.

example about how the system could be used for any community is exposed:

closely related to an objective measurement of "quality" of the contributions. The knowledge classification through a tree structure has been exposed as a suitable

1 shows a summary of the participants'communites of these research studies.

*MinimumQuorum propChangeStruct ,t numberActiveExperts propChangeStruct ,t*

*p i*

*percentageExperts*

*p i*

(15)

necessary for consolidating the change.

where,

in the structure *propChangeStructp* is calculated as follows:

*percentageExperts* is a configurable value, e.g. 0.8

**4. Research studies supported by KnowCat** 

Cobos, 2007; Gómez, Gutiérrez, Cobos & Alaman, 2001):

approach for managing and organising the knowledge.

document, the new document version will improve.

*propChangeStructp* is proposed.

features.

*valueAssessmentsj(docd,[t0,ti])* is the value of the assessments identified as *j* for the *docd*.

#### **3.2 Notes and document versions' crystallisation process**

As it is shown in the previous section, a social accepted document can "crystallise", however a social accepted annotation can "stay" in the knowledge area and a social accepted proposal of a document version can "consolidate".

The annotations receive votes, too. These votes can be "in favour" or "against" the annotation. The knowledge crystallisation mechanism calculates per annotation the number of the received votes of each type in this way:

*AgainstDegree note ,t n mberVotesAgainst note ,t n mberVotesInFavour note ,t a i a i a i* (12)

If *AgainstDegree* of a selected annotation *notea* is higher than the average of received votes by the annotations which are in the same location as *notea* then this annotation is delete from the knowledge area, in another case the annotation "stay" in the knowledge area.

The documents' assessments don't receive votes, therefore, they don't have a crystallisation mechanism associated.

In each moment, it is possible to have a proposal of a new document version, *versionDoci*, of a document, *doci*. The knowledge crystallisation mechanism determinates when a new document version replaces the previous one, i.e., the new document version "consolidate". For this matter, the members of the virtual community of the topic of a document with a new proposal of version have to give their opinions about the following characteristics of the new document version:


With the received opinions concerning the first characteristic is obtained the "continuity degree", *ContinuityDegree*, of the new document version (a value between 0-10, 10 the maximum value), with the received opinions concerning the second characteristic is obtained the "improvement degree", *ImprovementDegree*, of the new document version (a value between 0-10). If the continuity degree is higher than a determined value called "continuity point" (for example, 5) then the new document version replace the previous one. The history degree, which is used in Formula 1, is calculated as a function of the improvement degree as follows:

History(doci, versionDoci, tj) = funHistoryDoc(ImprovementDegree(versionDoci,tj)) (13)

 0.02 \* 0.88 , , 0 6 0.05 \* 0.7 , , 6 10 *i j i j x when x ImprovementDegree versionDoc t x and x funHistoryDoc x x when x ImprovementDegree versionDoc t x and x* (14)

#### **3.3 Structure's crystallisation process**

The last aspect of knowledge crystallisation is the evolution of the structure of the knowledge tree. If a member of a virtual community proposes to add a new subject to a topic, remove a subject from a topic or move a subject from one topic to another topic, then a minimum quorum of positive votes from other members of the community will be necessary for consolidating the change.

This minimum quorum, *MinimumQuorum,* of positive votes for a selected proposed change in the structure *propChangeStructp* is calculated as follows:

$$\begin{aligned} \text{Minimum Quantum} \left( \text{propChangeStrcut}\_p, t\_i \right) = \begin{bmatrix} \text{percentageExpents} \times \\ \text{numberActiveExpents} \left( \text{propChangeStrcut}\_p, t\_i \right) \end{bmatrix} \end{aligned} \tag{15}$$

where,

194 New Research on Knowledge Management Technology

As it is shown in the previous section, a social accepted document can "crystallise", however a social accepted annotation can "stay" in the knowledge area and a social accepted

The annotations receive votes, too. These votes can be "in favour" or "against" the annotation. The knowledge crystallisation mechanism calculates per annotation the number

If *AgainstDegree* of a selected annotation *notea* is higher than the average of received votes by the annotations which are in the same location as *notea* then this annotation is delete from the knowledge area, in another case the annotation "stay" in the knowledge

The documents' assessments don't receive votes, therefore, they don't have a crystallisation

In each moment, it is possible to have a proposal of a new document version, *versionDoci*, of a document, *doci*. The knowledge crystallisation mechanism determinates when a new document version replaces the previous one, i.e., the new document version "consolidate". For this matter, the members of the virtual community of the topic of a document with a new proposal of version have to give their opinions about the following characteristics of

Continuity: that is, if the new document version deals the content of the previous one in

History(doci, versionDoci, tj) = funHistoryDoc(ImprovementDegree(versionDoci,tj)) (13)

0.02 \* 0.88 , , 0 6

*x when x ImprovementDegree versionDoc t x and x*

0.05 \* 0.7 , , 6 10

*x when x ImprovementDegree versionDoc t x and x* 

The last aspect of knowledge crystallisation is the evolution of the structure of the knowledge tree. If a member of a virtual community proposes to add a new subject to a topic, remove a subject from a topic or move a subject from one topic to another topic, then a

 Improvement: that is, if the new document is an improvement of the previous one. With the received opinions concerning the first characteristic is obtained the "continuity degree", *ContinuityDegree*, of the new document version (a value between 0-10, 10 the maximum value), with the received opinions concerning the second characteristic is obtained the "improvement degree", *ImprovementDegree*, of the new document version (a value between 0-10). If the continuity degree is higher than a determined value called "continuity point" (for example, 5) then the new document version replace the previous one. The history degree, which is used in Formula 1, is calculated as a function of the

 

*a i a i* (12)

*i j i j*

(14)

*AgainstDegree note ,t n mberVotesAgainst note ,t n mberVotesInFavour note ,t a i*

*valueAssessmentsj(docd,[t0,ti])* is the value of the assessments identified as *j* for the *docd*.

**3.2 Notes and document versions' crystallisation process** 

proposal of a document version can "consolidate".

of the received votes of each type in this way:

area.

mechanism associated.

the new document version:

improvement degree as follows:

**3.3 Structure's crystallisation process** 

*funHistoryDoc x*

a similar way.

*percentageExperts* is a configurable value, e.g. 0.8

*numberActiveExperts* is the number of active member of the virtual community where *propChangeStructp* is proposed.
