Physical Plithogenic Set

Let $U$ be a universe of discourse. A Plithogenic Set is a set $P$ included in $U$, such that each element $x$ in \quad $P$ is characterized by one or more attributes $\alpha_{\mathrm{1}}$, $\alpha_{\mathrm{2}}$, \textellipsis , $\alpha_{\mathrm{m}}$, and each attribute $\alpha_{i\thinspace }$has many values. The element $x$ is characterized by all attributes' values: $V =$\textit{ \textbraceleft v}$_{1}, v_{2}$\textit{, \textellipsis , v}$_{n}$\textit{\textbraceright . } Each attributes value $v $ in $V$ has a corresponding \textit{degree of appurtenance d(x, v)} of the element $x,$ to the set $P$, with respect to some given criteria. For each attribute $\alpha_{i\thinspace }$there is a \textit{dominant (most important) attribute value}, and one computes the \textit{contradiction degree} function between any attribute values $v $and its corresponding dominant attribute value $v_{D}$, \quad denoted by $c(v_{D}, v).$ Plithogenic aggregation operators are further constructed for practical applications.