ON LACUNARY CONVERGENCE IN CREDIBILITY SPACE

In this paper, we present the notions of lacunary statistically convergent sequence for fuzzy variables, lacunary statistically Cauchy sequence in credibility space, and present a kind of lacunary statistical completeness for credibility space. Also, we present lacunary strong convergence concepts of sequences of fuzzy variables of different types

ON SOME GENERALIZED DEFERRED STATISTICAL CONVERGENCE OF ORDER αβ FOR FUZZY VARIABLE SEQUENCES IN CREDIBILITY SPACE

In this paper, we investigate the concepts of deferred statistical convergence of order αβ and strongly s-deferred Cesaro summability of order αβ for fuzzy variable sequences in credibility space. Furthermore, the conditions of deferred statistical convergence almost surely of order αβ, deferred statistical convergence in credibility of order αβ, deferred statistical convergence in mean of order αβ, deferred statistical convergence in distribution of order αβ, and deferred statistical convergence uniformly almost surely of order αβ of fuzzy variable sequences have been examined. We have proved relations between these notions

(R1958) On Deferred Statistical Convergence of Fuzzy Variables

In this paper, within framework credibility theory, we examine several notions of convergence and statistical convergence of fuzzy variable sequences. The convergence of fuzzy variable sequences such as the notion of convergence in credibility, convergence in distribution, convergence in mean, and convergence uniformly virtually certainly via postponed Cesàro mean and a regular matrix are researched using fuzzy variables. We investigate the connections between these concepts. Significant results on deferred statistical convergence for fuzzy variable sequences are thoroughly investigated

Analytical Properties of Credibilistic Expectation Functions

The expectation function of fuzzy variable is an important and widely used criterion in fuzzy optimization, and sound properties on the expectation function may help in model analysis and solution algorithm design for the fuzzy optimization problems. The present paper deals with some analytical properties of credibilistic expectation functions of fuzzy variables that lie in three aspects. First, some continuity theorems on the continuity and semicontinuity conditions are proved for the expectation functions. Second, a differentiation formula of the expectation function is derived which tells that, under certain conditions, the derivative of the fuzzy expectation function with respect to the parameter equals the expectation of the derivative of the fuzzy function with respect to the parameter. Finally, a law of large numbers for fuzzy variable sequences is obtained leveraging on the Chebyshev Inequality of fuzzy variables. Some examples are provided to verify the results obtained

Towards a Credibility Assessment of Models and Simulations

A scale is presented to evaluate the rigor of modeling and simulation (M&S) practices for the purpose of supporting a credibility assessment of the M&S results. The scale distinguishes required and achieved levels of rigor for a set of M&S elements that contribute to credibility including both technical and process measures. The work has its origins in an interest within NASA to include a Credibility Assessment Scale in development of a NASA standard for models and simulations

Bayesian epistemic values: focus on surprise, measure probability!

The e-value or epistemic value, ev(H), measures the statistical significance of H, a hypothesis about the parameter θ of a Bayesian model. The e-value is obtained by a probability-possibility transformation of the model’s posterior measure, p(θ), and can, in turn, be used to define the FBST or Full Bayesian Significance Test. This article investigates the relation of this novel approach to more standard probability-possibility transformations. In particular, we show how and why the e-value focus on or conforms with s(θ)=p(θ)/r(θ), the model's surprise function relative to the reference density r(θ), while it keeps itself consistent with the model’s posterior probability measure. In addition, we investigate traditional objections raised in decision theoretic Bayesian statistics against measures of significance engendered by probability-possibility transformations

Three implications of learning behaviour for price processes.

no abstract availableConsumers' preferences; Economics -- Psychological aspects;

Communication, learning and optimal monetary policy

The second part of the thesis deals with interest rate policy under inflation targeting when there is uncertainty in the term structure of interest rates emanating from unobserved, possibly volatile, market sentiments. In situations where expectations depend on the state of the economy--the rate of inflation and the level of the output gap, the central bank faces uncertainty about the degree of persistence in aggregate demand and inflation. Interestingly, the speed of learning about the degree of persistence depends on the interest rate policy followed and the resulting variability in inflation and the output gap, where higher variability speeds up learning and improves control of inflation in the long run. The analysis shows that passive and active learning scenarios have different implications for the degree of response of the rate of interest to the state of the economy and thus for the short-run conduct of monetary policy.