# Evaluating the Degree of Uncertainty of Research Activities in Industry 4.0
## 1 Introduction  
Research and development (R&D) is always oriented towards new discoveries, based on original innovation topics or hypotheses [1; 2; 3; 4; 5; 6; 7; 8], and their concluding outcome is often uncertain [9; 10; 11]. The present work focused on the degree of uncertainty of R&D activities. In fact, uncertainty makes it difficult to quantify the time and resources needed to achieve an outcome, develop a useful plan, and budget and finalize the resulting \"innovative\" products or services that could be transferred or exchanged in a specific market [12; 13; 14; 15]. Innovation is particularly critical and risky in dynamic and uncertain markets where the product or service uses new and uncertain technologies [3; 7; 10; 12; 16; 17; 18; 19]. The literature on new product development offers several tools to support, while on approaches and methods for measuring the degree of uncertainty is restricted for R&D activities [9; 10; 20; 21; 22; 23; 24]. An uncertainty theory was instituted as a division of mathematics grounded on monotonicity, normality, self-duality, and countable subadditivity axioms [25; 26; 27; 28; 29]. From a management viewpoint, uncertainty is associated with the lack of precise knowledge regardless of the reason for this deficit [10; 11; 14; 30]. Each decision or set of decisions has related advances or losses which are typically reliant on numerous random variables and, therefore, highly uncertain [14]. Thus, uncertainty is a term generally used in several contexts [31; 32; 33], revealing, in general, other related concepts:* _Uncertainty:_ lack of certainty, an inadequate state of knowledge in which it is intolerable to define precisely the current state, future outcomes or more than one conceivable result (e.g., [2; 33]). * _Uncertainty measure:_ a series of possible states in which results or probabilities are assigned to each possible state or result--this also includes the application of a probability density function to continuous variables. * _Risk_: A state of uncertainty in which some possible results have an unwanted effect or a significant loss. * _Risk measurement_: a series of measured uncertainties in which some results are possible losses, and the extent of such losses--also including the formulates of loss on continuous variables. The definition of R&D assumed in the present paper is provided in the Manual of Frascati [34]. The Frascati framework offers information approximating the funding and the performance of R&D [35; 36]. It includes a set of creative activities carried out in a systematic way with the aim of to develop and increase new knowledge and to use existing knowledge for new applications. The Manual of Frascati outlines and defines the common characteristics of the R&D activities, the objectives--which may be specific or general--and the criteria for identifying them, with the aim of providing guidance for the measurement of other related activities. Five criteria must be met to classify an R&D activity, mainly:  
* \"novelty\", since the activity must produce new results;
* \"originality\", since each activity must be aimed at developing new concepts and ideas;
* \"uncertainty of the results\", as at an early stage, it is not possible to define precisely the type of result and the costs in relation to the objectives to be achieved;
* \"orderliness\", since the activity must be conducted in a planned and accountable manner, and both the process and the results must be retained;
* \"reproducibility\", since the results of the activity must ensure the transferability of knowledge and the reproducibility of the results within other R&D activities. The present work attempts to indicate the degree of uncertainty of the research activities developed by a set of firms. The method used aims to quantify the five criteria defined by the Manual of Frascati. Through a cloud as a validated scientific method [37; 38; 39; 40; 41], a cone of uncertainty was defined following an approach based on project management.