Approximate Reasoning in the Possibility Theory Framework: where are we practically?

Approximate reasoning has been a very important source of motivations for the development of fuzzy sets and possibility theory. It has also been at the origin of some of the most popular applications of fuzzy set theory. This long chapter is an attempt at providing a coherent view of the abundant body of results published in the field. After restating the necessary background, the paper discusses the representation of different kinds of fuzzy statements, and presents the basic machinery for approximate reasoning based on the combination and projection of possibility distributions. Reasoning with fuzzy rules is especially considered. Then specialized forms of approximate reasoning, such as interpolative reasoning, reasoning about preferences, temporal and qualitative reasoning, are surveyed as well as different fuzzy set-based and possibility theory-based models of plausible reasoning, including similarity-based and case-based reasoning, default reasoning, abductive reasoning, and reasoning with fuzzy quantifiers. The connection between approximate reasoning and certainty factor methods for uncertainty handling is also discussed.KeywordsFuzzy RulePlausible ReasoningFuzzy RelationPossibility DistributionPossibility TheoryThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Handling exceptions in a knowledge-based system is an important issue in many application domains, such as medical domain. Recently, there is an increasing interest in nonmonotonic extension of description logics to handle exceptions in ontologies. In this paper, we propose three preferential semantics for plausible subsumption to deal with exceptions in description logic-based knowledge bases. Our preferential semantics are defined in the framework of possibility theory, which is an uncertainty theory devoted to handling incomplete information. We consider the properties of these semantics and their relationships. We also discuss the relationship between two of our preferential semantics and two existing preferential semantics. We extend a description logic-based knowledge base by adding preferential subsumptions. Entailment of plausible subsumptions relative to an extended knowledge base is defined. Properties of the preferential subsumption relations relative to an extended description logic-based knowledge base are discussed. Finally, we show that our semantics for plausible subsumption can be reduced to standard semantics of an expressive description logic. Thus, the problem of plausible subsumption checking under our semantics can be reduced to the problem of subsumption checking under the classical semantics.

This contribution is a response to the 2025 NASA and DNV challenge on optimization under uncertainty.Three typical engineering problems in the form of parameter identification, forward propagation of uncertainty, and optimization are addressed.The framework of possibility theory is outlined and applied to the problems of the challenge.Given the nature of possibility theory, the results provide a rigorous and deliberately cautious perspective on the challenge problems.Accordingly, this approach is expected to be among the more conservative responses, offering a robust and well-substantiated analysis of uncertainty.The analysis is implemented through a samplingbased approach, returning statistically valid confidence distributions with all prior information explicitly stated.

What role does metareasoning play in models of bounded rationality?We examine the various existing computational approaches to bounded rationality and divide them into three classes.Only one of these classes significantly relies on a metareasoning component.We explore the characteristics of this class of models and argue that it offers desirable properties.In fact, many of the effective approaches to bounded rationality that have been developed since the early 1980's match this particular paradigm.We conclude with some open research problems and challenges. Computational models of bounded rationalityIn the pursuit of building decision-making machines, artificial intelligence researchers often turn to theories of "rationality" in decision theory and economics.Rationality is a desired property of intelligent agents since it provides well-defined normative evaluation criteria and since it establishes formal frameworks to analyze agents (Doyle 1990;Russell and Wefald 1991).But in general, rationality requires making optimal choices with respect to one's desires and goals.As early as 1947, Herbert Simon observed that optimal decision making is impractical in complex domains since it requires one to perform intractable computations within a limited amount of time (Simon 1947;1982).Moreover, the vast computational resources required to select optimal actions often reduce the utility of the result.Simon suggested that some criterion must be used to determine that an adequate, or satisfactory, decision has been found.He used the Scottish word "satisficing," which means satisfying, to denote decision making that searches until an alternative is found that is satisfactory by the agent's aspiration level criterion.Simon's notion of satisficing has inspired much work within the social sciences and within artificial intelligence in the areas of problem solving, planning and search.In the social sciences, much of the work has focused on developing descriptive theories of human decision making (Gigerenzer 2000).These theories attempt to explain how people make decisions in the real-world, coping with complex situations, uncertainty, and limited amount of time.The answer is often based on a variety of heuristic methods that

This report summarizes techniques that use possibility theory to estimate the risk of terrorist acts. These techniques were developed under the sponsorship of the Department of Homeland Security (DHS) as part of the National Infrastructure Simulation Analysis Center (NISAC) project. The techniques have been used to estimate the risk of various terrorist scenarios to support NISAC analyses during 2004. The techniques are based on the Logic Evolved Decision (LED) methodology developed over the past few years by Terry Bott and Steve Eisenhawer at LANL. [LED] The LED methodology involves the use of fuzzy sets, possibility theory, and approximate reasoning. LED captures the uncertainty due to vagueness and imprecision that is inherent in the fidelity of the information available for terrorist acts; probability theory cannot capture these uncertainties. This report does not address the philosophy supporting the development of nonprobabilistic approaches, and it does not discuss possibility theory in detail. The references provide a detailed discussion of these subjects. [Shafer] [Klir and Yuan] [Dubois and Prade] Suffice to say that these approaches were developed to address types of uncertainty that cannot be addressed by a probability measure. An earlier report discussed in detail the problems with using a probability measure to evaluate terrorist risk. [Darby Methodology]. Two related techniques are discussed in this report: (1) a numerical technique, and (2) a linguistic technique. The numerical technique uses traditional possibility theory applied to crisp sets, while the linguistic technique applies possibility theory to fuzzy sets. Both of these techniques as applied to terrorist risk for NISAC applications are implemented in software called PossibleRisk. The techniques implemented in PossibleRisk were developed specifically for use in estimating terrorist risk for the NISAC program. The LEDTools code can be used to perform the same linguistic evaluation as performed in PossibleRisk. [LEDTools] LEDTools is a general purpose linguistic evaluation tool and allows user defined universes of discourse and approximate reasoning rules, whereas PossibleRisk uses predefined universes of discourse (risk, attack, success, loss, and consequence) and rules. Also LEDTools has the capability to model a large number of threat scenarios with a graph and to integrate the scenarios (paths from the graph) into the linguistic evaluation. Example uses of PossibleRisk and LEDTools for the possibilistic evaluation of terrorist risk are provided in this report.

Use of approximate reasoning techniques for locating underground utilities

It is a truism that much of human reasoning is approximate in nature. Spatial reasoning is an area where humans consistently reason approximately with demonstrably good results. The unique mental processes behind these actions are not well understood. However, it is important that we try to incorporate such approximate reasoning techniques in our computer systems. Approximate spatial reasoning is very important for intelligent mobile agents (e.g., robots), specially for those operating in uncertain or unknown or dynamic domains. In such situations, besides the hazard in the domain, the real constraints (e.g., limited memory and limited time for observations and/or inferencing) faced by agents makes the use of approximate reasoning techniques imperative. In this paper we present a model for approximate spatial reasoning using fuzzy logic to represent the uncertainty in the environment. We develop algorithms to reason about spatial information expressed in the form of approximate linguistic descriptions, very similar to the kind of spatial information processed by humans. We only deal with static spatial reasoning in this paper.

Breast cancer early diagnosis is a major concern for reducing deadly cases. Automation of microcalcification detection is becoming increasingly important given their tiny scale. At this step, a high false negative rate is observed, leading to high ambiguity. In this context, conventional approaches are unable to handle such ambiguity. Possibility theory offers a powerful paradigm enabling to handle a high uncertainty level. Therefore, in this research,new possibilistic modeling strategy for microcalcification detection is proposed. The developed system is based on k-means clustering followed by a fusion of the corresponding possibility distributions, for decision making. For enhancing classification's accuracy, two aspects may be taken into consideration: scattering within classes and the class discrimination power. A high inter-class variance may be regarded as an evidence of good discrimination. Nevertheless, in case of existing highly scattered classes, miss-classifications of samples at the class margins are still encountered, even at high inter-class variance. Clustering solves this problem by redefining classes in a more compact way. Under this paradigm, the clustering optimization is performed using a criteria based on the Area Under Curve(AUC), where the confidence degree level is based on the consistency principle of Dubois and Prade. The above strategy has been applied for the detection of microcalcifications, based on a set of pyramidal and multi-resolution based features. Validation on the Digital Database for Screening Mammography (DDSM) public dataset has been undertaken. The proposed system, which gives 99.4 % detection accuracy, can be used to assist medical practitioners.

WEIGHTED FUZZY PATTERN MATCHING

Layers of protection analysis in the framework of possibility theory

An approximate reasoning based technique for oil assessment

The paper is dedicated to the memory of Lotfi Zadeh, the founder of fuzzy logic. His ideas and theories brought about a considerable shift of modern scientific paradigm, related to the development of «human-centric» mathematical theories with applications. Some pages of Zadeh’s extraordinary biography are discussed. The main components of his scientific contribution, including fuzzy sets and linguistic variables, fuzzy logic and approximate reasoning, possibility theory and soft computing, information granulation and computing with words, are reviewed. An attempt to trace the chronology of Zadeh’s scientific works is made.KeywordsFuzzy setFuzzy logicApproximate reasoningPossibility theorySoft computingComputing with wordsInformation granulationGeneralized uncertainty theory

This paper discusses fuzzy reasoning for approximately realizing nonlinear functions by a small number of fuzzy if-then rules with different specificity levels. Our fuzzy rule base is a mixture of general and specific rules, which overlap with each other in the input space. General rules work as default rules in our fuzzy rule base. First, we briefly describe existing approaches to the handling of default rules in the framework of possibility theory. Next, we show that standard interpolation-based fuzzy reasoning leads to counterintuitive results when general rules include specific rules with different consequents. Then, we demonstrate that intuitively acceptable results are obtained from a non-standard inclusion-based fuzzy reasoning method. Our approach is based on the preference for more specific rules, which is a commonly used idea in the field of default reasoning. When a general rule includes a specific rule and they are both compatible with an input vector, the weight of the general rule is discounted in fuzzy reasoning. We also discuss the case where general rules do not perfectly but partially include specific rules. Then we propose a genetics-based machine learning (GBML) algorithm for extracting a small number of fuzzy if-then rules with different specificity levels from numerical data using our inclusion-based fuzzy reasoning method. Finally, we describe how our approach can be applied to the approximate realization of fuzzy number-valued nonlinear functions

Possibilistic randomisation in strategic-form games

The paper survey recent AI-oriented works in qualitative decision developed by the authors in the framework of possibility theory. Lottery-based and act-based axiomatics underlying pessimistic and optimistic criteria for decision under uncertainty are first briefly restated, when uncertainty and preferences are encoded with an ordinal scale. A logical machinery capable of computing optimal decisions in the sense of these criteria is presented. Then an approach to qualitative decision under uncertainty which does not require a commensurateness hypothesis between the uncertainty and the preference scales is proposed; this approach is closely related to nonmonotonic reasoning, but turns our to be ineffective for practical decision. Lastly, the modeling of preference as prioritized sets of goals, as sets of solutions reaching some given level of satisfaction, or in terms of possibilistic constraints is discussed briefly.