## 2 Human-Centric Aggregation
### Ordered Weighted Aggregation (OWA)  
OWA has been applied extensively in the research literature, especially as a way to deal with uncertainty [12; 13; 15; 16; 17; 18; 19; 20; 21]. Authors have used various OWA-based applications, which include techniques for randomized queries for searching the Web [22; 23], applying aggregation operators based on fuzzy concepts for recommender systems [24], social networking [25], GIS applications [6; 17], environments [26; 27; 28], and combination of OWA and opinion mining for book recommendation [29]. OWA is also used in the context of sport management [30] and for analyzing the talents and skills of the players in different sports [3]. The frequent use of OWA in multi-criteria decision-making has been reported in a range of studies [5; 19; 31; 32; 33; 34; 35], whereas the fuzzy methods are supposed to yield impressive results in decision-making problems, also [36; 37; 38; 39; 40; 41]. Ordered weighted aggregation (OWA) can be termed as a function from \(R^{n}\to R\), where '\(W\)'-weight vectors are associated with them in such a way that \(\sum_{k=1}^{n}(W_{k})=1\) and \(W_{k}\in[0,1]\). Mathematically it is given as:  
\[\text{OWA}\ (d_{1},d_{2},\ \ldots\ldots,d_{n})=\sum_{k=1}^{n}(W_{k}C_{k}) \tag{1}\]  
where if we sort \(C_{k}\), \(k^{\text{th}}\) largest element would be \(d_{k}\). We primarily intended to incorporate human-specific aggregation for the recommendation process (books) with the help of OWA [42]. Therefore, the points that must be addressed are how many books to recommend, how many users are needed to be involved, some, almost all, most, etc. Therefore, we use linguistic quantifiers. For fuzzy linguistic quantifier, we define Function Q(r) for relative quantifier as:  
\[\text{Q}(\tau)=\left\{ \begin{array}{ll}0&\text{if }\tau\,<\,\text{a}\\ \left(\frac{\tau-\text{a}}{\text{b}-\text{a}}\right)&\text{if }\text{a}\leq\text{r}\leq\text{b}\\ 1&\text{if }\tau\,>\,\text{b}\end{array} \right. \tag{2}\]  
where Q(0) = 0, \(\exists\text{r}\in[0,1]\) such that Q(r) = 1, and a, b \(\in[0,1]\). For the above condition, we have Q: \([0,1]\to[0,1]\). The weights '\(W_{k}\)' for the OWA operator is calculated by the following equation [4, 17]:  
\[W_{k}=\left\{Q\left(\frac{k}{m}\right)-Q\left(\frac{k-1}{m}\right)\right\} \tag{3}\]  
where \(k=1,\,2\,\ldots\,\,m\). Different weights can be obtained by using different linguistic quantifiers. For example, for the 'Most' linguistic quantifier, a = 0.3 and b = 0.8; using these quantifiers, those books are preferred that are recommended by most universities. Similarly, 'as many as possible' and 'at least half' are other quantifiers for which the values of (a, b) are (0.5, 1) and (0, 0.5), respectively. Graphical representations of these fuzzy linguistic quantifiers are shown for'most', 'as many as possible', and 'at least half', in Figure 1.  
Now we consider a situation when we need to rank the voters, i.e., rankers are valued, and they influence decision-making [43, 44]. We suggest OWA with a modification in the weight assignment of Equation (3) and term it as OWA (most preferred first). For this, we define weight assignment as:  
\[W_{k}=\frac{u+1-k}{N} \tag{4}\]  
Figure 1: Graphical representation of linguistic quantifier ‘as many as possible’, ‘at most’ and ‘at least half’ quantifiers colored in violet, blue and brown, respectively. where  
'\(u\)' is the total number of universities. \(N=\sum_{i=1}^{u}(k)\), giving the sum of the number of universities, and '\(K\)' is a variable that can have any value from \(i=1\) to \(i\) = number of universities involved ('\(u\)' in this case). \(W_{k}\)\(\varepsilon\) [0, 1] and \(\sum_{1}^{u}W_{k}\) = 1. OWA (most preferred first) is given as:  
\[\text{OWA (most preferred first)}=\sum_{k=1}^{n}(W_{k}C_{k}) \tag{5}\]  
where \(W_{k}\) is the weight obtained from Equation (4), and \(C_{k}\) is the score given to a book by \(k^{\text{th}}\) ranked university.