Set-valued uncertain process: definition and some properties

Some phenomena develop over time, while they are uncertain sets at each moment. From an set, we mean unsharp concept that is not clearly defined, even for expert. The potential values of parameters describing this guide one to explain it quantitatively. For instance, in “recovering” from some disease, different levels health might be meaning specific being healthy measured by belonging parameter a set with belief degree. Clearly speaking, the defining “recovery” beginning stage disease would entirely or partially non-identical other stages. These extracted using imprecisely observed data, expert opinion defines them degrees. An essential feature these their variation time considering sequence evolving time. Such concepts direct employ uncertainty theory as solid axiomatic mathematical framework modeling human reasoning. Analyzing behavior such motivated us define set-valued process. This combines process, and new concept. Here, introduce main idea; properties clarified, along illustrative examples. We also put forward state-of-the-art applications.