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147
A fuzzy model for representing uncertain, subjective and vague temporal knowledge in ontologies
 In Proceedings of the International Conference on Ontologies, Databases and Applications of Semantics, (ODBASE), volume 2888 of LNCS
, 2003
"... Abstract. Time modeling is a crucial feature in many application domains. However, temporal information often is not crisp, but is uncertain, subjective and vague. This is particularly true when representing historical information, as historical accounts are inherently imprecise. Similarly, we conje ..."
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Cited by 26 (3 self)
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Abstract. Time modeling is a crucial feature in many application domains. However, temporal information often is not crisp, but is uncertain, subjective and vague. This is particularly true when representing historical information, as historical accounts are inherently imprecise. Similarly, we conjecture that in the Semantic Web representing uncertain temporal information will be a common requirement. Hence, existing approaches for temporal modeling based on crisp representation of time cannot be applied to these advanced modeling tasks. To overcome these difficulties, in this paper we present fuzzy intervalbased temporal model capable of representing imprecise temporal knowledge. Our approach naturally subsumes existing crisp temporal models, i.e. crisp temporal relationships are intuitively represented in our system. Apart from presenting the fuzzy temporal model, we discuss how this model is integrated with the ontology model to allow annotating ontology definitions with time specifications. 1
Experimental Uncertainty Estimation and Statistics for Data Having Interval Uncertainty
, 2007
"... This report addresses the characterization of measurements that include epistemic uncertainties in the form of intervals. It reviews the application of basic descriptive statistics to data sets which contain intervals rather than exclusively point estimates. It describes algorithms to compute variou ..."
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Cited by 20 (14 self)
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This report addresses the characterization of measurements that include epistemic uncertainties in the form of intervals. It reviews the application of basic descriptive statistics to data sets which contain intervals rather than exclusively point estimates. It describes algorithms to compute various means, the median and other percentiles, variance, interquartile range, moments, confidence limits, and other important statistics and summarizes the computability of these statistics as a function of sample size and characteristics of the intervals in the data (degree of overlap, size and regularity of widths, etc.). It also reviews the prospects for analyzing such data sets with the methods of inferential statistics such as outlier detection and regressions. The report explores the tradeoff between measurement precision and sample size in statistical results that are sensitive to both. It also argues that an approach based on interval statistics could be a reasonable alternative to current standard methods for evaluating, expressing and propagating measurement uncertainties.
Towards Reliable SubDivision of Geological Areas: Interval Approach
, 2000
"... . An appropriate subdivision of a geophysical area into segments enables us to extrapolate the results obtained in some locations within the segment (where extensive research was done) to other locations within the same segment, and thus, get a good understanding of the locations which weren't thoro ..."
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Cited by 13 (10 self)
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. An appropriate subdivision of a geophysical area into segments enables us to extrapolate the results obtained in some locations within the segment (where extensive research was done) to other locations within the same segment, and thus, get a good understanding of the locations which weren't thoroughly analyzed. Often, different evidence and different experts' intuition support different subdivisions schemes. For example, in our area  Rio Grande rift zone  there is some geochemical evidence that this zone is divided into three segments, but, in the viewpoint of many researchers, this evidence is not yet sufficiently convincing. We show that if we use topographical information (this information, e.g., comes from satellite photos), then interval methods lead to a reliable justification for the tripartite subdivision of the Rio Grande rift zone. 1 Appropriate Subdivision Is Important In Geophysics In geophysics, appropriate subdivision of an area into segments is extremely import...
A Survey on Different Triangular NormBased Fuzzy Logics
, 1999
"... Among various approaches to fuzzy logics, we have chosen two of them, which are built up in a similar way. Although starting from different basic logical connectives, they both use interpretations based on Frank tnorms. Different interpretations of the implication lead to different axiomatizati ..."
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Cited by 13 (1 self)
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Among various approaches to fuzzy logics, we have chosen two of them, which are built up in a similar way. Although starting from different basic logical connectives, they both use interpretations based on Frank tnorms. Different interpretations of the implication lead to different axiomatizations, but most logics studied here are complete. We compare the properties, advantages and disadvantages of the two approaches. Key words: Fuzzy logic, manyvalued logic, Frank tnorm 1 Introduction A manyvalued propositional logic with a continuum of truth values modelled by the unit interval [0; 1] is quite often called a fuzzy logic. In such a logic, the conjunction is usually interpreted by a triangular norm. In this context, a (propositional) fuzzy logic is considered as an ordered pair P = (L; Q) of a language (syntax ) L and a structure (semantics) Q described as follows: (i) The language of P is a pair L = (A; C), where A is an at most countable set of atomic symbols and C is ...
How to Divide a Territory? A New Simple Differential Formalism for Optimization of Set Functions
 International Journal of Intelligent Systems
, 1999
"... In many practical problems, we must optimize a set function, i.e., find a set A for which f(A) ! max, where f is a function defined on the class of sets. Such problems appear in design, in image processing, in game theory, etc. Most optimization problems can be solved (or at least simplified) by usi ..."
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Cited by 12 (8 self)
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In many practical problems, we must optimize a set function, i.e., find a set A for which f(A) ! max, where f is a function defined on the class of sets. Such problems appear in design, in image processing, in game theory, etc. Most optimization problems can be solved (or at least simplified) by using the fact that small deviations from an optimal solution can only decrease the value of the objective function; as a result, some derivative must be equal to 0. This approach has been successfully used, e.g., for set functions in which the desired set A is a shape, i.e., a smooth (or piecewise smooth) surface. In some reallife problems, in particular, in the territorial division problem, the existing methods are not directly applicable. For such problems, we design a new simple differential formalism for optimizing set functions. 1 Introduction: Optimization of Set Functions is a Practically Important but Difficult Problem Optimization is important. In most application problems, we h...
Algebraic aspects of fuzzy sets and fuzzy logics
 Proc. Work. on Current Trends and Development in Fuzzy Logic, ThessalonikiGreece
, 1998
"... This paper is expository. It is mainly a survey of some of our work on the algebraic systems that arise in fuzzy set theory and logic. We include some of the proofs here ..."
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Cited by 10 (5 self)
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This paper is expository. It is mainly a survey of some of our work on the algebraic systems that arise in fuzzy set theory and logic. We include some of the proofs here
Strict Archimedean tNorms and tConorms as Universal Approximators
, 1998
"... In knowledge representation, when we have to use logical connectives, various continuous tnorms and tconorms are used. In this paper, we show that every continuous tnorm and tconorm can be approximated, to an arbitrary degree of accuracy, by a strict Archimedean tnorm (tconorm). Address corres ..."
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Cited by 9 (7 self)
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In knowledge representation, when we have to use logical connectives, various continuous tnorms and tconorms are used. In this paper, we show that every continuous tnorm and tconorm can be approximated, to an arbitrary degree of accuracy, by a strict Archimedean tnorm (tconorm). Address correspondence to Vladik Kreinovich, Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA, email vladik@cs.utep.edu. International Journal of Approximate Reasoning 199? ?:?? c fl 199? Elsevier Science Inc. 655 Avenue of the Americas, New York, NY 10010 0888613X/9?/$7.00 2 1. INTRODUCTION Brief idea. When we represent expert knowledge in expert systems and in intelligent control, it is important to adequately describe not only the experts' statements themselves, but also the experts' degrees of confidence in the corresponding statements. It is also important to adequately describe which operations with these degrees of confidence are best representing the expe...
Decision Making Beyond Arrow’s Impossibility Theorem
 International Journal of Intelligent Systems
, 2009
"... Abstract — In 1951, K. J. Arrow proved that, under certain assumptions, it is impossible to have group decision making rules which satisfy reasonable conditions like symmetry. This Impossibility Theorem is often cited as a proof that reasonable group decision making is impossible. We start our paper ..."
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Cited by 9 (8 self)
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Abstract — In 1951, K. J. Arrow proved that, under certain assumptions, it is impossible to have group decision making rules which satisfy reasonable conditions like symmetry. This Impossibility Theorem is often cited as a proof that reasonable group decision making is impossible. We start our paper by remarking that Arrow’s result only covers the situations when the only information we have about individual preferences is their binary preferences between the alternatives. If we follow the main ideas of modern decision making and game theory and also collect information about the preferences between lotteries (i.e., collect the utility values of different alternatives), then reasonable decision making rules are possible: e.g., Nash’s rule in which we select an alternative for which the product of utilities is the largest possible. We also deal with two related issues: how we can detect individual preferences if all we have is preferences of a subgroup, and how we take into account mutual attraction between participants.
Possible New Directions in Mathematical Foundations of Fuzzy Technology: A Contribution to the Mathematics of Fuzzy Theory
 Proceedings of the VietnamJapan Bilateral Symposium on Fuzzy Systems and Applications VJFUZZY'98, HaLong Bay, Vietnam, 30th September2nd
, 1998
"... this paper, we describe new possible applicationoriented directions towards formalizing these new ideas: ..."
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Cited by 7 (7 self)
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this paper, we describe new possible applicationoriented directions towards formalizing these new ideas:
The Lattice of Fuzzy Intervals and Sufficient Conditions for Its Distributivity
, 2001
"... Given a reference lattice (X, _), we define fuzzy intervals to be the fuzzy sets such that their p cuts are crisp closed intervals of (X, _). We show that: given a complete lattice (X, _) the collection of its fuzzy intervals is a complete lattice. Furthermore we show that: if (X, _) is completel ..."
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Cited by 7 (0 self)
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Given a reference lattice (X, _), we define fuzzy intervals to be the fuzzy sets such that their p cuts are crisp closed intervals of (X, _). We show that: given a complete lattice (X, _) the collection of its fuzzy intervals is a complete lattice. Furthermore we show that: if (X, _) is completely distributive then the lattice of its fuzzy intervals is distributive.