# Review of Intelligent Methods and Their Potential Use towards a Smart Grid Negotiation Framework
## 5 Future Directions
### Fuzzy Negotiation  
Considering the aforementioned notes, the authors will furtherly enquire Fuzzy negotiation methodologies based on similarity operators and Fuzzy sets described in [17; 18]. Assuming that seller and buyer act uniformly, the generalized methodology described below is common for both unless stated otherwise:  
1. Firstly, an initial offer is made from the first negotiator which can be a buyer or a seller. The other participant can accept the offer ending the process or submit a counteroffer. The counteroffer creation is described as follows: The opponent negotiator evaluates the offer employing a utility function which allocates values to the available options (Equation (1)). \[U(x)=\frac{\sum_{i=1}^{m}w_{i}\cdot u_{i}(x_{i})}{\sum_{i=1}^{m}w_{i}},\] (1) In Equation (1), \(U(x)\) is the overall utility value for the offer \(x= \begin{bmatrix}x_{1}\\ \vdots\\ x_{m}\end{bmatrix} \) and \(u_{i}\) is the utility value assigned to issue \(i\). Each utility value \(u_{i}\) is assigned to its corresponding weight, \(w_{i}\). Some options--the qualitative ones--may be predefined, and can be assigned to certain values in the [0,1] interval-valued q-ROFS, while the quantitative options may have more vague definitions and can be expressed by fuzzy sets and q-ROFS. For \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Retailers** & **Aggregation Values** & **Scores** & **Ranking** \\ \hline R\({}_{1}\) & \(Agg_{1}(\alpha_{i})\) & \(S(Agg_{1})\) & Supposing that the selected supplier \\ \hline R\({}_{2}\) & \(Agg_{2}(\alpha_{2i})\) & \(S(Agg_{2})\) & should be the retailer \(R_{2}\). \\ \hline R\({}_{3}\) & \(Agg_{3}(\alpha_{3j})\) & \(S(Agg_{3})\) & \(R_{2}>R_{1}>R_{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Score values of the aggregated preferences. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Retailers** & **C\({}_{1}\)** & **C\({}_{2}\)** & **C\({}_{3}\)** & **C\({}_{4}\)** \\ \hline R\({}_{1}\) & \(\alpha_{11}=(\mu_{11},\
u_{11})\) & \(\alpha_{12}=(\mu_{12},\
u_{12})\) & \(\alpha_{13}=(\mu_{13},\
u_{13})\) & \(\alpha_{14}=(\mu_{14},\
u_{14})\) \\ \hline R\({}_{2}\example, the option \"price\" which is common option for both seller and buyer has a diverse significance for them. From the seller's point of view, the price is expected to lead to a benefit and from the buyer's perspective the cost is the issue which the price option incorporates. Naturally, the option \"benefit\" for the seller should be the larger while for the buyer the option \"cost\" should be the smaller. Moreover, the participants are setting the higher and the lower bounds they are willing to accept. Thus, these bounds are forming the constraints of the problem. The weights of the options as they are set by every participant along with the respective values form the submitted offer. The negotiating agent of the participant is now set. In Figure 3, the utility function of the price issue is shown. \(\mathrm{P_{I}}\) and \(\mathrm{P_{h}}\) stand for the lower and the higher bounds of the price the buyer is expecting to pay while the \(\mathrm{B_{I}}\) and \(\mathrm{B_{h}}\) the lower and the higher benefit bounds the seller is expecting to achieve. 2. As the utility function is now formulated, the participant can guess the opponent's preferences employing a metaheuristic algorithm such as GA, PSO, or BA, assigning values to the utility functions' weights. A counteroffer is now created based on Fuzzy inference. The weights are updated at every round of the negotiation, according to the opponent's weights' deviation from the estimated weights. The offer for each issue is compared to the participant's expectation by means of similarity measure. In case of multiple opponents, a score is assigned to each of their offers, according to Section 5.1, and the selected offer is the base of the counteroffer.