A Fuzzy Petri Nets Model for Computing With Words

Motivated by Zadeh's paradigm of computing with words rather than numbers, several formal models of computing with words have recently been proposed. These models are based on automata and thus are not well-suited for concurrent computing. In this paper, we incorporate the well-known model of concurrent computing, Petri nets, together with fuzzy set theory and thereby establish a concurrency model of computing with words--fuzzy Petri nets for computing with words (FPNCWs). The new feature of such fuzzy Petri nets is that the labels of transitions are some special words modeled by fuzzy sets. By employing the methodology of fuzzy reasoning, we give a faithful extension of an FPNCW which makes it possible for computing with more words. The language expressiveness of the two formal models of computing with words, fuzzy automata for computing with words and FPNCWs, is compared as well. A few small examples are provided to illustrate the theoretical development.Comment: double columns 14 pages, 8 figure

Decision Making in the Medical Domain: Comparing the Effectiveness of GP-Generated Fuzzy Intelligent Structures

ABSTRACT: In this work, we examine the effectiveness of two intelligent models in medical domains. Namely, we apply grammar-guided genetic programming to produce fuzzy intelligent structures, such as fuzzy rule-based systems and fuzzy Petri nets, in medical data mining tasks. First, we use two context-free grammars to describe fuzzy rule-based systems and fuzzy Petri nets with genetic programming. Then, we apply cellular encoding in order to express the fuzzy Petri nets with arbitrary size and topology. The models are examined thoroughly in four real-world medical data sets. Results are presented in detail and the competitive advantages and drawbacks of the selected methodologies are discussed, in respect to the nature of each application domain. Conclusions are drawn on the effectiveness and efficiency of the presented approach

Fuzzy-Petri-Net Reasoning Supervisory Controller and Estimating States of Markov Chain Models

Markov chain models are efficient tools for representing stochastic discrete event processes with wide applications in decision and control. A novel approach to fuzzy-Petri-net reasoning generated solution to initial or another state in Markov-chain models is proposed. Reasoning is performed by a fuzzy-Petri-net supervisory controller employing a fuzzy-rule production system design and a fuzzy-Petri-net reasoning algorithm, which has been developed and implemented in C++. The reasoning algorithm implements calculation of the degrees of fulfilment for all the rules and their appropriate assignment to places of Petri net representation structure. The reasoning process involves firing active transitions and calculating degrees of fulfilment for the output places, which represent propositions in the knowledge base, and determining of fuzzy-distributions for output variables as well as their defuzzified values. Finally, these values are transferred to assign the state of Markov-chain decision model in terms of transition probabilities

MODELLING CRISP AND FUZZY QUALITATIVE TEMPORAL RELATIONS

Building a model for temporal knowledge representation and reasoning assumes choosing basic notions - primitives, the time instant or/and the time interval. This paper considers primitives for modelling crisp and fuzzy qualitative temporal relations. Based on fuzzified Allen s temporal relations between intervals, new relations between the fuzzy time point and the fuzzy time interval are proposed

Graph Grammars for Knowledge Representation

This report consists of two papers presented at the March 1990 GRAGRA meeting in Bremen: the more general ''Representation of knowledge using graph grammars'' which argues for graphs as the universal KR formalism and the more specific ''The four musicians: analogies and expert systems -- a graphic approach'' which demonstrates the use of graphics for type inheritance and analogical reasoning

A review of applications of fuzzy sets to safety and reliability engineering

Safety and reliability are rigorously assessed during the design of dependable systems. Probabilistic risk assessment (PRA) processes are comprehensive, structured and logical methods widely used for this purpose. PRA approaches include, but not limited to Fault Tree Analysis (FTA), Failure Mode and Effects Analysis (FMEA), and Event Tree Analysis (ETA). In conventional PRA, failure data about components is required for the purposes of quantitative analysis. In practice, it is not always possible to fully obtain this data due to unavailability of primary observations and consequent scarcity of statistical data about the failure of components. To handle such situations, fuzzy set theory has been successfully used in novel PRA approaches for safety and reliability evaluation under conditions of uncertainty. This paper presents a review of fuzzy set theory based methodologies applied to safety and reliability engineering, which include fuzzy FTA, fuzzy FMEA, fuzzy ETA, fuzzy Bayesian networks, fuzzy Markov chains, and fuzzy Petri nets. Firstly, we describe relevant fundamentals of fuzzy set theory and then we review applications of fuzzy set theory to system safety and reliability analysis. The review shows the context in which each technique may be more appropriate and highlights the overall potential usefulness of fuzzy set theory in addressing uncertainty in safety and reliability engineering

Video semantic content analysis framework based on ontology combined MPEG-7

The rapid increase in the available amount of video data is creating a growing demand for efficient methods for understanding and managing it at the semantic level. New multimedia standard, MPEG-7, provides the rich functionalities to enable the generation of audiovisual descriptions and is expressed solely in XML Schema which provides little support for expressing semantic knowledge. In this paper, a video semantic content analysis framework based on ontology combined MPEG-7 is presented. Domain ontology is used to define high level semantic concepts and their relations in the context of the examined domain. MPEG-7 metadata terms of audiovisual descriptions and video content analysis algorithms are expressed in this ontology to enrich video semantic analysis. OWL is used for the ontology description. Rules in Description Logic are defined to describe how low-level features and algorithms for video analysis should be applied according to different perception content. Temporal Description Logic is used to describe the semantic events, and a reasoning algorithm is proposed for events detection. The proposed framework is demonstrated in sports video domain and shows promising results