Modeling uncertainty reasoning with possibilistic petri nets (original) (raw)

Fuzzy reasoning and the logics of uncertainty

International Symposium on Multiple-Valued Logic, 1976

This paper is concerned with the foundations of fuzzy reasoning and its relationships with other logics of uncertainty. The definitions of fuzzy logics are first examined and the role of fuzzification discussed. It is shown that fuzzification of PC gives a known multivalued logic but with inappropriate semantics of implication and various alternative forms of implication are discussed. In the main section the discussion is broadened to other logics of uncertainty and it is argued that there are close links, both formal and semantic, between fuzzy logic and probability logics. A basic multivalued logic is developed in terms of a truth function over a lattice of propositions that encompasses a wide range of logics of uncertainty. Various degrees of truth functionality are then defined and used to derive specific logics including probability logic and Lukasiewicz infinitely valued logic. Quantification and modal operators over the basic logic are introduced. Finally, a semantics for the basic logic is introduced in terms of a population (of events, or people, or neurons) and the semantic significance of the constraints giving rise to different logics is discussed.

Fuzzy and Probability Uncertainty Logics

Readings in Fuzzy Sets for Intelligent Systems, 1993

Probability theory and fuzzy logic have been presented as quite distinct theoretical foundations for reasoning and decision making in situations of uncertainty. This paper establishes a common basis for both forms of logic of uncertainty in which a basic uncertainty logic is defined in terms of a valuation on a lattice of propositions. The (non-truth-functional) connectives for conjunction, disjunction, equivalence, implication, and negation are defined in terms which closely resemble those of probability theory. Addition of the axiom of the excluded middle tO the basic logic gives a standard probability logic. Alternatively, addition of a requirement for strong truth-functionality (truth-value of connective determined by truth-value of constituents) gives a fuzzy logic with connectives, including implication, as in Lukasiewicz' infinitely valued logic. A common semantics for all such variants is given in terms of binary responses from a population. The type of population, e.g., physical events, people, or neurons, determines whether the model is of physical probability, subjective belief, or human decision-making. The formal theory and the semantics together illustrate clearly the precise similarities and differences between fuzzy and probability logics.

A Hybrid Approach for Handling Uncertainty-Probabilistic Theory, Certainty Factor and Fuzzy Logic

2013

Real world is actually revolving around data i.e. data plays a very important role in the current information era. Different types of uncertainty are addressed in different forms of data. Till date, probabilistic theory, fuzzy logic, certainty factor was developed to handle uncertainty. All these approaches were quite successful in handling uncertainty but there are some situations where when these methods taken individually, failed to handle uncertainty. So there was a need to develop a hybrid approach which will handle uncertainty to a high level. In this paper, we present an approach wherein we integrate probabilistic theory, certainty factor and fuzzy logic concepts. Once we use all these approaches together, uncertainty model is developed which will address the various limitations inherent in these approaches when applied individually. Keywords—Certainty Factor; Probability Theory; Fuzzy Logic; Uncertainty; Transitive Dependency; Baye’s Theorem

A qualitative fuzzy possibilistic logic

International Journal of Approximate Reasoning, 1995

A formal logical system dealing with both uncertainty (possibility) and vagueness (fuzziness) is investigated. It is many-valued and modal. The system is related to a many-valued tense logic. A completeness theorem is exhibited.

A new paradigm for uncertain knowledge representation by Plausible Petri nets

Information Sciences, 2018

This paper presents a new model for Petri nets (PNs) which combines PN principles with the foundations of information theory for uncertain knowledge representation. The resulting framework has been named Plausible Petri nets (PPNs). The main feature of PPNs resides in their efficiency to jointly consider the evolution of a discrete event system together with uncertain information about the system state using states of information. The paper overviews relevant concepts of information theory and uncertainty representation, and presents an algebraic method to formally consider the evolution of uncertain state variables within the PN dynamics. To illustrate some of the real-world challenges relating to uncertainty that can be handled using a PPN, an example of an expert system is provided, demonstrating how condition monitoring data and expert opinion can be modelled.

Uncertainty in Computational Perception and Cognition

Forging New Frontiers: Fuzzy Pioneers I, 2007

Humans often mimic nature in the development of new machines or systems. The human brain, particularly its faculty for perception and cognition, is the most intriguing model for developing intelligent systems. Human cognitive processes have a great tolerance for imprecision or uncertainty. This is of great value in solving many engineering problems as there are innumerable uncertainties in real-world phenomena. These uncertainties can be broadly classified as either uncertainties arising from the random behavior of physical processes or uncertainties arising from human perception and cognition processes. Statistical theory can be used to model the former, but lacks the sophistication to process the latter. The theory of fuzzy logic has proven to be very effective in processing the latter. The methodology of computing with words and the computational theory of perceptions are branches of fuzzy logic that deal with the manipulation of words that act as labels for perceptions expressed in natural language propositions. New computing methods based on fuzzy logic can lead to greater adaptability, tractability, robustness, a lower cost solution, and better rapport with reality in the development of intelligent systems.

Important New Terms and Classifications in Uncertainty and Fuzzy Logic

Fifty Years of Fuzzy Logic and its Applications, 2015

Human cognitive and perception processes have a great tolerance for imprecision or uncertainty. For this reason, the notions of perception and cognition have great importance in solving many decision making problems in engineering, medicine, science, and social science as there are innumerable uncertainties in real-world phenomena. These uncertainties can be broadly classified as either type one uncertainty arising from the random behavior of physical processes or type two uncertainty arising from human perception and cognition processes. Statistical theory can be used to model the former, but lacks the sophistication to process the latter. The theory of fuzzy logic has proven to be very effective in processing type two uncertainty. New computing methods based on fuzzy logic can lead to greater adaptability, tractability, robustness, a lower cost solution, and better rapport with reality in the development of intelligent systems. Fuzzy logic is needed to properly pose and answer queries about quantitatively defining imprecise linguistic terms like middle class, poor, low inflation, medium inflation, and high inflation. Imprecise terms like these in natural languages should be considered to have qualitative definitions, quantitative definitions, crisp quantitative definitions, fuzzy quantitative definitions, type-one fuzzy quantitative definitions, and interval type-two fuzzy quantitative definitions. There can be crisp queries, crisp answers, type-one fuzzy queries, typeone fuzzy answers, interval type-two fuzzy queries, and interval type-two fuzzy answers.

Formal Fuzzy Logic and Its Use in Modeling of Vagueness and Computing with Words

Neural Networks and Soft Computing, 2003

In this paper, we briefly discuss the indeterminacy phenomenon as a phenomenon having two facets: uncertainty and vagueness. Then, we describe some basic principles of modern mathematical fuzzy logic and show that it constitutes a group of well established formal systems. We argue that until now, fuzzy logic provides the most successful solutions when trying to grasp vagueness. Its model of vagueness is based on introducing degrees of truth with well established and substantiated structure that non-trivially generalizes classical logic. We also outline formal theories that model some of the essential manifestations of vagueness headed by an analysis of sorites.