Boris Kovalerchuk

Determining the most important criteria in maintenance decision making

Many maintenance decisions require the evaluation of alternative solutions in terms of complex maintenance criteria such as cost, repairability, reliability and availability requirements. Such problems can be formulated as multi‐criteria decision‐making problems. The relative importance of maintenance criteria is difficult to assess, and therefore a sensitivity analysis becomes a necessity. The sensitivity analysis approach presented reveals some counter‐intuitive results and can considerably enhance the application of decision analysis in complex maintenance management.

Fuzzy logic in computer-aided breast cancer diagnosis: analysis of lobulation.

This paper illustrates how a fuzzy logic approach can be used to formalize terms in the American College of Radiology (ACR) Breast Imaging Lexicon. In current practice, radiologists make a relatively subjective determination for many terms from the lexicon related to breast cancer diagnosis. Lobulation and microlobulation of nodules are two important features in the ACR lexicon. We offer an approach for formalizing the distinction of these features and also formalize the description of intermediate cases between lobulated and microlobulated masses. In this paper it is shown that fuzzy logic can be an effective tool in dealing with this kind of problem. The proposed formalization creates a basis for the next three steps (i) extended verification with blinded comparison studies. (ii) the automatic extraction of the related primitives from the image, and (iii) the detection of lobulated and microlobulated masses based on these primitives.

Consistent knowledge discovery in medical diagnosis

Discusses eliminating contradictions among rules in computer-aided systems, experts rules, and databases. The study has demonstrated how consistent data mining in medical diagnosis can create a set of logical diagnostic rules for computer-aided diagnostic systems. Consistency avoids contradiction among rules generated using data mining software, rules used by an experienced radiologist, and a database of pathologically confirmed cases. The authors identified major problems: to find contradiction between diagnostic rules and to eliminate contradiction. They applied two complimentary intelligent technologies for extraction of rules and recognition of their contradictions. The first technique is based on discovering statistically significant logical diagnostic rules. The second technique is based on the restoration of a monotone Boolean function to generate a minimal dynamic sequence of questions to a medical expert. The results of this mutual verification of expert and data-driven rules demonstrate feasibility of the approach for designing consistent computer-aided diagnostic systems.

Modelling phenomena and dynamic logic of phenomena

Modelling a complex phenomenon such as the mind presents tremendous computational complexity challenges. Modelling field theory (MFT) addresses these challenges in a non-traditional way. The main idea behind MFT is to match levels of uncertainty of the model (also, a problem or some theory) with levels of uncertainty of the evaluation criterion used to identify that model. When a model becomes more certain, then the evaluation criterion is adjusted dynamically to match that change to the model. This process is called the Dynamic Logic of Phenomena (DLP) for model construction and it mimics processes of the mind and natural evolution. This paper provides a formal description of DLP by specifying its syntax, semantics, and reasoning system. We also outline links between DLP and other logical approaches. Computational complexity issues that motivate this work are presented using an example of polynomial models.

Visual and Spatial Analysis

This chapter provides a conceptual link between the decision making process, visualization, visual discovery, and visual reasoning. A structural model of the decision making process is offered along with the relevant visual aspects. Examples of USS Cole incident in 2000 and the Cholera epidemic in London in 1854 illustrate the conceptual approach. A task-driven visualization is described as a part of the decision making process and illustrated with browsing and search tasks.

Dynamic logic of phenomena and cognition

Modeling of complex phenomena such as the mind presents tremendous computational complexity challenges. The neural modeling fields theory (NMF) addresses these challenges in a non-traditional way. The main idea behind success of NMF is matching the levels of uncertainty of the problem/model and the levels of uncertainty of the evaluation criterion used to identify the model. When a model becomes more certain then the evaluation criterion is also adjusted dynamically to match the adjusted model. This process is called dynamic logic (DL) of model construction, which mimics processes of the mind and natural evolution. This paper provides a formal description of phenomena dynamic logic (P-DL) and outlines its extension to the cognitive dynamic logic (C-DL). P-DL is presented with its syntactic, reasoning, and semantic parts. Computational complexity issues that motivate this paper are presented using an example of polynomial models.

Agents’ model of uncertainty

Multi-agent systems play an increasing role in sensor networks, software engineering, web design, e-commerce, robotics, and many others areas. Uncertainty is a fundamental property of these areas. Agent-based systems use probabilistic and other uncertainty models developed earlier without explicit consideration of agents. This paper explores the impact of agents on uncertainty models and theories. We compare two methods of introducing agents to uncertainty theories and propose a new theory called the agent-based uncertainty theory (AUT). We show advantages of AUT for advancing multi-agent systems and for solving an internal fundamental question of uncertainty theories, that is identifying coherent approaches to uncertainty. The advantages of AUT are that it provides a uniform agent-based representation and an operational empirical interpretation for several uncertainty theories such as rough set theory, fuzzy sets theory, evidence theory, and probability theory. We show also that the introduction of agents to intuitionist uncertainty formalisms can reduce their conceptual complexity. To build such uniformity the AUT exploits the fact that agents as independent entities can give conflicting evaluations of the same attribute. The AUT is based on complex aggregations of crisp (non-fuzzy) conflicting judgments of agents. The generality of AUT is derived from the logical classification of types (orders) of conflicts in the agent populations. At the first order of conflict, the two agent populations are disjoint and there is no interference of logic values assigned to any statement p and its negation by agents. The second order of conflict models superposition (interference) of logic values for overlapping agent populations where an agent assigns conflicting logic values (true, false) to the same attribute simultaneously.

Comparison of empirical and computed values of fuzzy conjunction

Abstract The necessity for further experiments such as in [4] for the foundation of fuzzy sets theory is shown. Generality of the experimental results on fuzzy conjunction in the paper by Thole, Zimmermann and Zisno (1979) [4] for the other objects and language is verified for other conditions. Usually the minimum, the product and the restricted sum operators are used as an intersection (conjunction) of fuzzy sets in fuzzy optimization (F-optimization). On the basis of experiments, it is shown that these operators are correct for F-optimization. Their correctness is founded on the stability of the extremal point (a decision in Bellman-Zadehs scheme) under a positive linear mapping. It is shown that these mappings exist between empirical conjunction and considered operators as a statistical result of linear regression analysis.

Agent-based uncertainty logic network

Boolean and discrete networks play an important role in many domains such as cellular automata. This paper generalizes that concept of Boolean networks for complex situations with multiple agents acting under uncertainty. This paper creates a logic network using a concept of the Agent-based Uncertainty Theory (AUT). The AUT is based on complex fusion of crisp (non-fuzzy) conflicting judgments of agents. It provides a uniform representation and an operational empirical interpretation for several uncertainty theories such as rough set theory, fuzzy sets theory, evidence theory, and probability theory. The AUT models conflicting evaluations that are fused in the same evaluation context. An AUT network extend the traditional inferential process by using a set of logic matrices obtained from AUT logic evaluation samples connected in a network. This network computes transformations of AUT logic vectors and gives logic rules for uncertainty situation. The AUT logic network is a generalization of the Boolean network. A Boolean network consists of a set of Boolean variables whose states are determined by other variables in the network An AUT logic network consists of a set of agents presented as vector variables whose states or logic vector evaluations are determined by other variables in the network.

LINGUISTIC CONTEXT SPACES: NECESSARY FRAMES FOR CORRECT APPROXIMATE REASONING

Effective inference under uncertainty in Artificial Intelligence depends on context. Inferences based on Bayesian conditional probabilities use context effectively. However, newer approaches, such as fuzzy reasoning (and others—e.g., Dempster-Shafer, rough sets, etc.) cannot take context appropriately into account without further development of linguistic context. We develop the new concept of “context space” for fuzzy sets theory. Many-valued fuzzy sets were introduced by Nakanishi [1989]. We use them in this paper to describe context (context space) as an analog of probability space. Such a description of context space allows one to usefully construct fuzzy sets for specific applications, and thus improves the foundation for fuzzy sets theory. In addition, the problem of establishing membership functions (MFs) is considered for context spaces. It is shown that semantic operational procedures [Hisdal, 1984] and modal logic [Resconi, et al., 1992] are preferable when used jointly with a complete and exact...