Conditional operations on fuzzy numbers

An estimate of a joint possibility distribution of two fuzzy numbers, based on fuzzy relations with a third fuzzy variable, is suggested. This leads to the operations of conditional addition and conditional multiplication, of interactive fuzzy numbers for which joint possibility distributions with a fuzzy variable are known

The Principal-Agent Model with an Informative Signal to the Advantage of the Agent

This article deals with the problem of negative impact of information asymmetry on the market and methods for mitigating it. This problem is solved by using the methods of the economic theory of contracts. In the work, methods for reducing the information gap with the help of developing optimal contracts are considered. In particular, the application of market signaling, studied by M. Spence, which is used by a more effective agent to inform the principal about his / her “good” type, is examined. Naturally, the signal reduces the asymmetry of information, which increases the advantage of the principal, but reduces it for less efficient customers. The requirements for market signaling models are analyzed, their basic types are classified, and the main equilibrium types are considered. Based on the fact that signaling, obviously, positively solves the problem of adverse selection but increases the cost of the contract due to the costs of signaling, the basic conditions for self-selection of participants in the contract process are given. The article develops a model of information signal for the principal and the agent, which can belong to one of the two types – “good” (more effective) and “bad” (less effective). While with the classical model the agent sends a market signal in order to tell the principal his / her type, we propose a model of information signal sent by the environment and received by the agent (but not by the principal, as usual). Unlike a binary signal, in this model the signal determines the probability of the agent’s belonging to each type. The article describes the conditions of self-selection of agents at a known signal distribution function. Depending on these conditions, the agent chooses one of the two proposed contracts or refuses the contract at all. There developed a method for constructing a pair of contracts that is optimal from the point of view of the principal if he knows the distribution of the informative signal and the utility function of the agent is concave upward

Dissipated damaging and degradation od steel properties of oil and gas pipelines

Тривала експлуатація нафтових та газових трубопроводів часто супроводжується втратою вихідних властивостей, що негативно впливає на подальшу роботоздатність трубопровідної мережі. В роботі на прикладі магістральних нафтових та газових трубопроводів, експлуатованих упродовж 28…40 років, показано роль розсіяної пошкодженості як окремої стадії деградації механічних та корозійно-механічних властивостей. Особлива увага приділена вивченню поведінки водню в металі як індикатора інтенсивності розсіяної пошкодженості.Long-term service of oil and gas pipelines is often accompanied by a loss of as-received properties that effects negatively on a further workability of pipelines network. The role of dissipated damaging, as a separate stage of materials degradation, in a change of its mechanical and corrosion-mechanical properties is considered in the work by the example of trunk oil and gas pipelines exploited during 28…40 years. The special attention is devoted to a study of hydrogen behaviour as indicator of an intensity of dissipated damaging

Inclusion hyperspaces and capacities on Tychonoff spaces: functors and monads

The inclusion hyperspace functor, the capacity functor and monads for these functors have been extended from the category of compact Hausdorff spaces to the category of Tychonoff spaces. Properties of spaces and maps of inclusion hyperspaces and capacities (non-additive measures) on Tychonoff spaces are investigated

Hyperspace of convex compacta of nonmetrizable compact convex subspaces of locally convex spaces

Our main result states that the hyperspace of convex compact subsets of a compact convex subset $X$ in a locally convex space is an absolute retract if and only if $X$ is an absolute retract of weight $\le\omega_1$. It is also proved that the hyperspace of convex compact subsets of the Tychonov cube $I^{\omega_1}$ is homeomorphic to $I^{\omega_1}$. An analogous result is also proved for the cone over $I^{\omega_1}$. Our proofs are based on analysis of maps of hyperspaces of compact convex subsets, in particular, selection theorems for such maps are proved