Various theories of

imprecise probability include the Dempster-Shafer evidence theory [7, 8], the coherent lower prevision theory [9], probability bound analysis [10], and the fuzzy probability [11].

One of these models is the random set modeling, which is a type of

imprecise probability (Walley 1990).

[29] Augustin T, Doria S, Marinacci M (2016) Special Issue: Ninth International Symposium on

Imprecise Probability: Theory and Applications (ISIPTA'15).

Similarly, in the classical probability and in

imprecise probability the probability of an event has to belong to, or respectively be included in, the interval [0, 1].

I can pick up the theoretical developments with emergence of the field of

imprecise probability. (37) This modern field of mathematics provides a useful extension of probability theory whenever information is scarce or conflicting.

Computer scientists and statisticians introduce graduate students, researchers, and consultants to

imprecise probability, a new framework for quantifying uncertainty and making inferences and decisions under it.

Also, he suggested an extension of the classical probability and

imprecise probability to "neutrosophic probability".

The aim of this paper is to propose a game-theoretic framework that can deal with

imprecise probability theories.

The second interesting elaboration of the new logic involves developments in the field of

imprecise probability. (11) This field of mathematics provides a useful extension of probability theory whenever information is conflicting or scarce.

In many systems (technical, economical or social) it is impossible to precisely calculate the relation, so we deal with the problem of

imprecise probability. In fact, the aim of risk analysis is to answer how and why an adverse outcome produces.

(1996) stated that "Many people believe that assigning an exact number to an expert's opinion is too restrictive, and the assignment of an interval of values is more realistic", which is somehow similar with the

imprecise probability theory where instead of a crisp probability one has an interval (upper and lower) probabilities as in Walley (1991).

Fuzzy probability is characterized by a possibility distribution of probability, which represents an

imprecise probability by means of a subjective possibility measure associated with judgmental uncertainty.