Possibility expectation and its decision making algorithm

The fuzzy integral has been shown to be an effective tool for the aggregation of evidence in decision making. Of primary importance in the development of a fuzzy integral pattern recognition algorithm is the choice (construction) of the measure which embodies the importance of subsets of sources of evidence. Sugeno fuzzy measures have received the most attention due to the recursive nature of the fabrication of the measure on nested sequences of subsets. Possibility measures exhibit an even simpler generation capability, but usually require that one of the sources of information possess complete credibility. In real applications, such normalization may not be possible, or even desirable. In this report, both the theory and a decision making algorithm for a variation of the fuzzy integral are presented. This integral is based on a possibility measure where it is not required that the measure of the universe be unity. A training algorithm for the possibility densities in a pattern recognition application is also presented with the results demonstrated on the shuttle-earth-space training and testing images

Uncertainty measures and actuarial application

Predmet istraživanja ovog rada su mere neodređenosti, posebno mera kredibliteta, kao i mogućnost njihove primene u aktuarstvu. U cilju generalizacije teorije kredibiliteta, uvedena je nova mera, nazvana mera c- kredibiliteta. Mera c-kredibiliteta na X je skupovna funkcija takva da su zadovoljene osobine normalnosti, monotonosti, samodualnosti i maksimalnosti. Za nju su dokazane neke osobine kao što su npr. subaditivnost i poluneprekidnost. Nadalje, definisan je integral zasnovan na meri c- kredibiliteta, a navedena su i dokazana određena svojstva. Nova mera je uvedena i u fazi okruženju kao agregirana vrednost mera mogućnosti i neophodnosti.This thesis studies uncertainty measures, especially credibility measure, as well as the possibility of their application in actuaries. In order to generalize credibility theory, a new fuzzy measure is proposed, called c − credibility measure. C − credibility measure on X is a set function that satisfies normality, monotonicity, self-duality and maximality. Certain properties of the c−credibility measure are proved, such as, for example, subadditivity and semicontinuity. Furthermore, an integral based on this measure is defined, in analogy to the existing integrals, and its properties are proved. Then, the credibility measure in a fuzzy environment is introduced as the aggregate value of the possibility and necessity measures

Uncertainty measures and actuarial application

Predmet istraživanja ovog rada su mere neodređenosti, posebno mera kredibliteta, kao i mogućnost njihove primene u aktuarstvu. U cilju generalizacije teorije kredibiliteta, uvedena je nova mera, nazvana mera c- kredibiliteta. Mera c-kredibiliteta na X je skupovna funkcija takva da su zadovoljene osobine normalnosti, monotonosti, samodualnosti i maksimalnosti. Za nju su dokazane neke osobine kao što su npr. subaditivnost i poluneprekidnost. Nadalje, definisan je integral zasnovan na meri c- kredibiliteta, a navedena su i dokazana određena svojstva. Nova mera je uvedena i u fazi okruženju kao agregirana vrednost mera mogućnosti i neophodnosti.This thesis studies uncertainty measures, especially credibility measure, as well as the possibility of their application in actuaries. In order to generalize credibility theory, a new fuzzy measure is proposed, called c − credibility measure. C − credibility measure on X is a set function that satisfies normality, monotonicity, self-duality and maximality. Certain properties of the c−credibility measure are proved, such as, for example, subadditivity and semicontinuity. Furthermore, an integral based on this measure is defined, in analogy to the existing integrals, and its properties are proved. Then, the credibility measure in a fuzzy environment is introduced as the aggregate value of the possibility and necessity measures

Pricing options in a fuzzy environment

Includes abstract.Includes bibliographical references (leaves 114-116).Although Fuzzy Logic is not new, it is however only since 2004 that an axiomatic theory has been created that has all the desirable effects of Fuzzy Logic. This theory, named Credibility theory was proposed by Dr. Liu. Within this thesis we aim to utilize credibility theory to model the psychological impacts of market participants on European options. Specifically this is done by modifying the approach that was originally taken by Black and Scholes. The Hew model, which is known as the fuzzy drift parameter model, begins by replacing the deterministic drift within Brownian motion with a fuzzy parameter. This fuzzy parameter models the psychological impacts of market participants. Naturally as we are dealing in Chance theory 1 the risk neutral dynamics change from that of Black and Scholes and thus so does the price of European call options

FUZZY COMPARATIVE CONCORDANCE ANALYSIS. Proposal and evaluation by a case study

In this paper it is proposed a fuzzy multiple attribute analysis, that we have called comparative concordance, as a help instrument to the decision-making process in an environment of lack of precise information as it generally is the decision-making in regional planning. Through an application to the selection of proceeding programs of the Environmental Plan of Andalusia, 1995-2000, it will be compared to other methods.fuzzy sets, multiple attribute decision, environmental planning

A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid

The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a better interpretation of the models and a better use of the Choquet integral in multi-criteria decision aid. Parallel to these theoretical works, the Choquet integral has been applied to many new fields, and several softwares and libraries dedicated to this model have been developed.Choquet integral, Sugeno integral, capacity, bipolarity, preferences