Numerical possibility distributions can encode special convex families of probability measures. The connection between possibility theory and probability theory is potentially fruitful in the scope of statistical reasoning when uncertainty due to variability of observations should be distinguished from uncertainty due to incomplete information. This paper proposes an overview of numerical possi...

Vague and incomplete data represented as linguistic values massively exists in diverse real-word applications. The task of forecasting fuzzy time series under uncertain circumstances is thus of great important but difficult. The inherent uncertainty involving time evolution usually makes the transition of states in a system probabilistic. In this paper, we proposed a new forecasting model based...

The uncertainty of a financial market is traditionally dealt with probabilistic approaches. However, there are many non-probabilistic factors that affect the financial markets such that the return rate of risky assets may be regarded as fuzzy number, which is a powerful tool used to describe an uncertain environment with vagueness and ambiguity and some type of fuzziness. In this paper, the con...

For medical diagnosis, fuzzy Dempster-Shafer theory is extended to model domain knowledge under probabilistic and fuzzy uncertainty. However, there are some information loss using discrete fuzzy sets and traditional matching degree method. This study aims to provide a new evidential structure to reduce information loss. This paper proposes a new intuitionistic fuzzy evidential reasoning (IFER) ...

in this paper, we formalize the menger probabilistic normed space as a category in which its objects are the menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. so, we can easily apply the results of topological vector spaces...

This paper presents a fuzzy set based decision support model for taking uncertainty into account when making security investment decisions for distributed systems. The proposed model is complementary to probabilistic approaches and useful in situations where probabilistic information is either unavailable or not appropriate to reliably predict future conditions. We first present the specificati...

We present a novel approach to representing uncertain information in ontologies based on design patterns. We provide a brief description of our approach, present its use in case of fuzzy information and probabilistic information, and describe the possibility to model multiple types of uncertainty in a single ontology. We also shortly present an appropriate fuzzy reasoning tool and define a comp...

The problem of matching vague terms must be addressed in knowledge-based systems involving uncertainty. Fril is a logic programming language extended by an integrated set of features for handling uncertain knowledge, based on the theoretical foundations provided by Baldwin’s mass assignment theory. This combines probabilistic and fuzzy uncertainty into a single framework. One of the fundamental...

This article introduces a general framework of multi-granulation fuzzy probabilistic roughsets (MG-FPRSs) models in multi-granulation fuzzy probabilistic approximation space over twouniverses. Four types of MG-FPRSs are established, by the four different conditional probabilitiesof fuzzy event. For different constraints on parameters, we obtain four kinds of each type MG-FPRSs...

Hierarchical structures and uncertainty measures are two main aspects in granular computing, approximate reasoning and cognitive process. Typical hesitant fuzzy sets, as a prime extension of fuzzy sets, are more flexible to reflect the hesitance and ambiguity in knowledge representation and decision making. In this paper, we mainly investigate the hierarchical structures and uncertainty measure...