Decision Making by Hybrid Probabilistic - Possibilistic Utility Theory

It is presented an approach to decision theory based upon nonprobabilistic uncertainty. There is an axiomatization of the hybrid probabilisticpossibilistic mixtures based on a pair of triangular conorm and triangular norm satisfying restricted distributivity law, and the corresponding non-additive Smeasure. This is characterized by the families of operations involved in generalized mixtures, based upon a previous result on the characterization of the pair of continuous t-norm and t-conorm such that the former is restrictedly distributive over the latter. The obtained family of mixtures combines probabilistic and idempotent (possibilistic) mixtures via a threshold.Decision making, Utility theory, Possibilistic mixture, Hybrid probabilistic- possibilistic mixture, Triangular norm, Triangular conorm, Pseudoadditive measure.

Functional analytic background for a theory of infinite-dimensional reductive Lie groups

Motivated by the interesting and yet scattered developments in representation theory of Banach-Lie groups, we discuss several functional analytic issues which should underlie the notion of infinite-dimensional reductive Lie group: norm ideals, triangular integrals, operator factorizations, and amenability.Comment: 17 page

Алгебрична модель обробки зображень на основі генератора трикутної норми

Побудовано алгебричну параметричну модель для обробки зображень, яка базується на трикутній нормі Міцумото. Встановлено аналітичні вирази для обчислення арифметичних операцій. Наведено приклади експериментів. Algebraic parametric model for image processing based on Mitsumoto triangular norm is proposed. Analitical expressions for computation of arithmetic operations are defined. Examples of experimental study are shown.Воробель Р.А - Фізико-механічний інститут ім. Г.В. Карпенка НАН України Боцян В.В - Фізико-механічний інститут ім. Г.В. Карпенка НАН України Степанюк С.І. - Волинський національний університет імені Лесі УкраїнкиAlgebraic parametric model for image processing based on Mitsumoto triangular norm is proposed. Analitical expressions for computation of arithmetic operations are defined. Examples of experimental study are show