There is a well-known interpretation of fuzzy interval in the framework of the theory of imprecise probabilities [1, 2]. To get this, we associate with any fuzzy interval a possibility or necessity measure, and then consider that values of the pointed measures give us lower or upper assessments of probabilities. This interpretation was discussed in detail in [3], and there it is proposed to use...

This paper proposes a novel approach to decision analysis with uncertainty based on integrated case-based inference and approximate reasoning. The strength of case-based inference is utilized for building a situation dependent decision model without complete domain knowledge. This is achieved by deriving states probabilities and general utility estimates from the subset of retrieved cases and t...

Modern axiomatic uncertainty theories (fuzzy logic, probability theory and others) provide a calculus for manipulating with probabilities, membership functions, and degrees of belief when the initial values such as probabilities of elementary events are already given. These theories do not include a mechanism for getting initial uncertainty values. The value of these theories is in computing un...

In real system application, the interacting multiple model (IMM) based algorithm operates with the following problems: it requires less computing resources as well as a good performance with respect to the various target maneuvering, it requires a robust performance with respect to the time-varying measurement noise, and further, it requires an easy design procedure in terms of its structures a...

In the real system application, the interacting multiple model (IMM) based algorithm requires less computing resources as well as a good performance with respect to the various target maneuverings. And it further requires an easy design procedure in terms of its structures and parameters. To solve these problems, a fuzzy interacting multiple model (FIMM) algorithm, which is based on the basis s...

Experts in machine learning and fuzzy system frequently identify understanding the data with the use of logical rules. Reasons for inadequacy of crisp and fuzzy rule-based explanations are presented. An approach based on analysis of probabilities of classification p(Ci|X;ρ) as a function of the size of the neighborhood ρ of the given case X is presented. Probabilities are evaluated using Monte ...

According to the current literature, there are two different approaches to the definition of the variance of a fuzzy random variable. In the first one, the variance is defined as a fuzzy interval, offering a gradual description of our incomplete knowledge about the variance of an underlying, imprecisely observed, classical random variable. In the second case, the variance of the fuzzy random va...

Interval-valued fuzzy sets were proposed thirty years ago as a natural extension of fuzzy sets. Many variants of these mathematical objects exist, under various names. One popular variant proposed by Atanassov starts by the specification of membership and non-membership functions. This paper focuses on interpretations of such extensions of fuzzy sets, whereby the two membership functions that d...

This paper presents a methodology for analysing Air Traffic Incidents based on an estimate of the probability of an Air Traffic Incident developing into an Air Traffic Accident (Air Traffic Incidents are officially defined as events which are dangerous but without a catastrophic impact). A new approach is presented as previous research in this area has focused more on defining accident occurren...

Complex decision making tasks of different natures, e.g. economics, safety engineering, ecology and biology, are based on vague, sparse, partially inconsistent and subjective knowledge. Moreover, decision making economists / engineers are usually not willing to invest too much time into study of complex formal theories. They require such decisions which can be (re)checked by human like common s...