International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

An important feature of some financial laws is the decomposability property. This is a theoretical issue for a financial law admitting that the cash flow does not change when the economic subject disinvests and immediately re-invests a capital. Decomposable laws are exponential. In the recent past, the notion of decomposability has been generalized, modelling non homogeneity of the time in financial processes by the action of triangular t-conorms over the times. In this more general setting, our aim is to compare and measure the advantages or disadvantages that the economic subject obtains when he interrupts a flow.

In this paper, we provide the necessary and sufficient condition for a Choquet integral model to be decomposable into a canonical hierarchical Choquet integral model constructed by hierarchical combinations of some ordinary Choquet integral models. This condition is characterized by the pre-Znclusion-Exclusion Covering (pre-IEC). Moreover, we show that the pre-IEC is the subdivision of an IEC and that the additive hierarchical structure is the most fundamental one on considering a hierarchical decomposition of the Choquet integral model.

In this paper, we will develop a class of logics for reasoning about qualitative and quantitative uncertainty. The semantics of the logics is uniformly based on possibility theory. Each logic in the class is parameterized by a t-norm operation on [0,1], and we express the degree of implication between the possibilities of two formulas explicitly by using residuated implication with respect to the t-norm. The logics are then shown to be applicable to possibilistic reasoning, approximate reasoning, and nonmonotonic reasoning.

Textbooks often claim that quantum mechanics explained the periodic system: namely, the actual configuration of electronic orbits that is responsible for the element's chemical properties can be described as the one that minimizes the total energy, and the energy of each configuration can be computed by using quantum mechanics.

However, a careful analysis of this explanation reveals that, in addition to the basic equations of quantum mechanics, we need some heuristic rules that do not directly follow from quantum physics. One reason why additional heuristics are necessary is that the corresponding numerical equations are extremely difficult to solve, and as we move to atoms with larger and larger atomic numbers Z, they become even more difficult. Moreover, as Z grows, we must take relativistic effects into consideration, and this means going from partial differential equations to even more mathematically difficult operator equations.

In this paper, we show that if instead of the (often impossible) numerical optimization, we consider the (available) ordinal information, we can then explain the observed periodic system.

The "take-them-in-or-leave-them-out" of prior probabilities is a key problem in uncertain reasonings. The EMYCIN uncertain reasoning model is inconsistent with probability theory, due to 'leaving them out', while the PROSPECTOR uncertain reasoning model is substantially consistent with probability theory, due to 'taking them in'. This presents a difficult task for human experts when supplying prior probabilities. In this paper, in order to overcome the difficulty, we propose a hybrid uncertain reasoning model, by combing rule strengths in the PROSPECTOR model with rule strengths in the EMYCIN model. Moreover, different forms of rule strength will enable human experts to supply values for the rule strengths more flexibly in a knowledge base. Finally, an example is given to illustrate the power of our methodology.

This section is maintained by Vladik Kreinovich. Please send your abstract (or copies of papers that you want to see reviewed here), to vladik@cs.utep.edu, or by regular mail to: Vladik Kreinovich, Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA.