# An Intelligent System to Ensure Interoperability for the Dairy Farm Business Model
## 5 Collaborative Negotiation System
### Negotiation Model
#### 5.2.3 Coordination Components in Open Environment
Precisely, FCA reveals a conceptual hierarchy (i.e., a lattice of concepts) that clusters DFs with common attributes (e.g., type of milk). For each generated formal concept \(c\) (i.e., cluster), domain experts are able to propose a profile (e.g., organic DF) and/or define a satisfaction degree \(\sigma_{c}\) (which measures the overall experience with that specific group of DFs). Next, we present a manner to compute the satisfaction degree. Let \(K=(G,M,I)\) be the formal context of the analysed DFs, where \(G\) is the set of DFs, \(M\) is the set of the characteristics of DFs, and \(I\subseteq G\times M\) is a binary relation that specifies the characteristics for each DF. Firstly, domain experts categorise the characteristics of DFs as good or bad (see Table 3) according to their positive or negative impact on the quality of dairy products. Secondly, to discriminate between the \"more or less\" negative effect of bad characteristics, a penalty function \(\forall:\mathcal{B}\rightarrow\mathcal{P}\)--where \(\mathcal{B}=\{x\in M|x\text{ {belong to the bad category}}\}\) and \(\mathcal{P}=\{p\in\mathbb{N}^{*}|\exists b\in\mathcal{B}\ \exists p\text{ {a penalty defined by domain experts}}\}\)--is used. Lastly, for a formal concept \(c=(X,Y)\) generated from \(K\), the satisfaction degree \(\sigma_{c}\) is computed by using Equation (1):  
\[\sigma_{c}=\frac{|\{m\in Y|m\text{ {belong to the good category}}\}|}{|Y|}\times 100-\sum_{i=1}^{n}\sqrt{(x_{i})} \tag{1}\]  
where \(n=|\mathcal{B}|\) and \(x_{i}\in\mathcal{B}\). Figure 4: The interactions among the NegA, Outsrc, and Broker. Equation (1) can be generalised for a family of penalised categories \(\mathfrak{B}=\{\mathcal{B}_{1},\ldots,\mathcal{B}_{l}\}\) as follows:  
\[\sigma_{c}=\frac{\left|\{m\in Y|m\text{ {belong to the unpenalised category}}\}\right|}{|Y|}\times 100-\sum_{i=1}^{| \mathfrak{B}|}\sum_{j=1}^{n_{i}}\sqrt{\left(x_{j}\right)} \tag{2}\]  
where \(n_{i}=|\mathcal{B}_{i}|\), \(\mathcal{B}_{i}\in\mathfrak{B}\), and \(x_{j}\in\mathcal{B}_{i}\). It is worthwhile to mention that the satisfaction degree may enhance the negotiation task since DFs can be easily ranked. For instance, a negotiation path with a DF can be ceased if the proposal is not consistent with its satisfaction degree, or the proposal with the highest satisfaction degree can be chosen among similar ones. As a result, the Broker component is underpinned by the annotated lattice of concepts that represents the search space of potential DF partners. This search space is exploited by the Broker component in two ways, as follows:  
* To retrieve the set of DFs that share a given set of attributes (denoted by \(Y\)). The query is the set of attributes \(Y\); the lattice is browsed for a matching concept \(c_{1}=\left(X_{1},\ Y_{1}\right)\) with \(Y=Y_{1}\) (if it exists) or the most general concept \(c_{2}=\left(X_{2},\ Y_{2}\right)\) with \(Y\subset Y_{2}\). This can be done with various algorithms/tools (e.g., [30]) without modifying the queried lattice. * To find the satisfaction degree of a given DF identifier (denoted by \(DF_{ID}\)) by looking for the most specific concept whose extent contains \(DF_{ID}\). Thus, even if \(DF_{ID}\) may exist in many concepts of the lattice, only the concept that introduces \(DF_{ID}\) provides the accurate profile of the analysed DF. For example, let us say that the Broker component has to pick two DFs whose key characteristics are animals fed with natural forage, produce pasteurised milk, and location next to forest. Relying on the search space of concepts \(L_{K}\) illustrated in Figure 1(a), the Broker component finds an exact match, precisely concept CK_10. As a result, there are only four DFs that may attend the negotiation, namely DF1, DF2, DF4, and DF6. To choose only two DFs, the Broker component yet again makes use of the search space of partners. However, this time, the Broker component focuses on the satisfaction degree that annotates each most specific concept.