Fuzzy set theory is circumscribed to the need to broaden the scope of classical mathematics meaning poten-tiation possibilities of mathematical modeling of real world systems. One can appreciate that the nature of reality and our way of thinking and the symbolism of interpersonal communication...

Possibilistic indicators of fuzzy numbers (expected value, variance, and covariance) are an efficient instrument in the modeling of uncertainty phenomena. Various models of uncertainty phenomena have led to several notions of variance and covariance. In particular, the possibilistic models of...

The interest rate and volatility may have different values in the different commercial banks and financial institutions. Moreover, the fluctuations of the underlying assets are rare events, and there are not enough historical data to estimate the jump intensity in a precise sense. This paper...

Stochastic volatility models for option pricing are suitable to explain many empirical stylized facts in financial markets. Among the other models, Heston provides a good analytical tractability because a quasi closed formula for the price of a European call option can be derived. The estimation...

In this article the theoretical generalization for representation of arithmetic operations with fuzzy numbers is considered. Fuzzy numbers are generalized by means of fuzzy measures. On the basis of this generalization the new algorithm of fuzzy arithmetic which uses a principle of entropy...

Grey system theory is one of the methods used to study uncertainty. GRA is part of grey system theory, which is suitable for solving problems with complicated interrelationships between multiple factors and variables. This method has been widely used to solve the uncertainty problems under the...

In this paper we extend the classical chain-ladder claims reserving method using fuzzy methods. Therefore, we derive new estimators for the claims development factors as well as new predictors for the ultimate claims. The advantage in using fuzzy numbers lies in the fact that the model...

The basic paradigm of simulation is the probabilistic approach to describing real world uncertainty. However, in many cases we do not have an information that would be precise enough to build the corresponding probabilistic model or there are some human factors that prevent doing so. In such...

Entropy is generally a measurement of the fuzziness degree for a fuzzy set. This paper studies the entropy calculation of the standard product of two general fuzzy intervals, i.e. C=A×B, and then provides some simple formulas to get the entropy of the product C. Those formulas are composed of...

The fuzzy Analytic Hierarchy Process (fuzzy AHP) is a very popular decision making method and literally thousands of papers have been published about it. However, we find the basic logic of this approach has problems. From its methodology, the definition and operational rules of fuzzy numbers...