International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

Conditional preference networks (CP-nets) are a compact but powerful formalism to represent and reason with qualitative preferences using the notion of conditional preferential independence. However, they suffer from incomparabilities between possible outcomes. Several works have attempted to overcome this weakness by quantifying CP-nets. This paper proposes a new approach combining two of the most interesting extensions of CP-nets, namely Probabilistic CP-nets (PCP-nets) using probability distribution to model uncertainty in different preference statements and Weighted CP-nets (WCP-nets) adding weights to express the relative importance of some attribute values regarding others. The new model so-called PWCP-nets combines the two models by handling both uncertainty and weights. Experimental results show the efficiency of this rich extension of CP-nets compared to PCP-nets and WCP-nets.

In this note — starting from d-dimensional (with d > 1) fuzzy vectors — we prove Donsker’s classical invariance principle. We consider a fuzzy random walk $S_n^{*}=X_1^{*}+\cdots +X_n^{*}$, where ${\left\{X_i^{*}\right\}}_1^{\infty }$ is a sequence of mutually independent and identically distributed d-dimensional fuzzy random variables whose α-cuts are assumed to be compact and convex.

Our reasoning and technique are based on the well known conjugacy correspondence between convex sets and support functions, which allows for the association of an appropriately normalized and interpolated time-continuous fuzzy random process with a real valued random process in the space of support functions.

We show that each member of the associated family of dual sequences tends in distribution to a standard Brownian motion.

In the highly competitive environment, capturing and disseminating of tacit knowledge are significant to an organization’s success with the development of knowledge-based systems. However, in practical knowledge acquisition process, domain experts tend to express their judgments using multigranularity linguistic term sets, and there usually exists uncertain and incomplete information since expert knowledge is experience-based and tacit. In addition, although the technical capabilities of expert systems based on fuzzy Petri nets (FPNs) are expanding, they still fall short of meeting the increasingly complex knowledge demands. Therefore, this paper develops a theoretical model based on linguistic interval 2-tuples and interval-valued intuitionistic FPNs (IVIFPNs) for acquiring and representing tacit knowledge to increase and sustain the competitive advantages of knowledge intensive organizations. An empirical case study in medical practice is provided to demonstrate the application and feasibility of the proposed model, and the results show that it can well capture experts’ tacit knowledge and reuse the acquired knowledge productively.

The present paper proposes an improved score function for solving multi-criteria decision-making (MCDM) problem with partially known weight information, In it, the preferences related to criteria are taken in the form of interval-valued Pythagorean fuzzy sets. Based on these preferences and an improved score function, a score matrix has been formulated and then a linear programming based method has been proposed to solve MCDM problems with unknown attribute weights. Some generalized properties have also been proven for justification. Illustrative examples have been given for showing the superiority of the approach with the other existing functions in the decision-making process.

In this note we provide a new proof of Sklar’s theorem by using Zorn’s lemma.

Bayesian network (BN) is the well-accepted framework for representing and inferring uncertain knowledge. To learn the BN-based uncertain knowledge incrementally in response to the new data is useful for analysis, prediction, decision making, etc. In this paper, we propose an approach for incremental learning of BNs by focusing on the incremental revision of BN’s graphical structures. First, we give the concept of influence degree to describe the influence of new data on the existing BN by measuring the variation of BN’s probability parameters w.r.t. the likelihood of the new data. Then, for the nodes ordered decreasingly by their influence degrees, we give the scoring-based algorithm for revising BN’s subgraphs iteratively by hill-climbing search for reversing, adding or deleting edges. In the incremental revision, we emphasize the preservation of probabilistic conditional independencies implied in the BN based on the concept and properties of Markov equivalence. Experimental results show the correctness, precision and efficiency of our approach.

In this paper, for the stochastic nonlinear systems the adaptive fuzzy tracking controllers are constructed by using the fuzzy logic systems (FLS) and the classical quadratic functions. Compared with the existing results for adaptive fuzzy control, the stochastic nonlinear systems investigated in this paper are much more complex since the systems not only have distributed state time-varying delays in the noise jamming intensity terms but also have the time-varying delays in the input signals. During the controller design procedure, through appropriate assumptions and a state transformation the system with time-varying input delay can be easily transformed into a system without input delay. The other main advantage is that quadratic functions are used as Lyapunov functions to analyze the stability of systems, other than the fourth moment approach proposed by H. Deng and M. Krstic, and the hyperbolic tangent functions are introduced to deal with the Hessian terms. The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded in probability and the tracking error can converge to a small residual set around the origin in the mean square sense.

The aim of this paper is pricing the vulnerable options in a vague world. Due to the vulnerability of financial markets and the economy environment in the real world, investors cannot always have precise information about firm value and default recovery rate in vulnerable option pricing. Therefore, following the framework of Klein in 1996, a fuzzy binomial tree pricing model is derived by modelling the firm value and default recovery rate as fuzzy numbers. The numerical results show that the precise information assumption about the firm value and recovery rate in Klein model may lead to underestimate the credit risk on the values of vulnerable options. This study aims to provide insights for future research on defaultable options pricing under imprecise market information.

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