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A Treatise on ManyValued Logics
 Studies in Logic and Computation
, 2001
"... The paper considers the fundamental notions of many valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with som ..."
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Cited by 53 (3 self)
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The paper considers the fundamental notions of many valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite valued logics. Key words: mathematical fuzzy logic, algebraic semantics, continuous tnorms, leftcontinuous tnorms, Pavelkastyle fuzzy logic, fuzzy set theory, nonmonotonic fuzzy reasoning 1 Basic ideas 1.1 From classical to manyvalued logic Logical systems in general are based on some formalized language which includes a notion of well formed formula, and then are determined either semantically or syntactically. That a logical system is semantically determined means that one has a notion of interpretation or model 1 in the sense that w.r.t. each such interpretation every well formed formula has some (truth) value or represents a function into
Sorites paradox and vague geographies
, 2000
"... The sorites paradox is ranked among the top ve paradoxes of philosophy (Sainsbury, Paradoxes, 2nd ed., Cambridge University Press, Cambridge, 1995). It is simply stated as ‘what is a heap’. Deriving from the paradox is a de nition of vagueness, which is contrary to the Boolean concept of the world i ..."
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Cited by 17 (0 self)
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The sorites paradox is ranked among the top ve paradoxes of philosophy (Sainsbury, Paradoxes, 2nd ed., Cambridge University Press, Cambridge, 1995). It is simply stated as ‘what is a heap’. Deriving from the paradox is a de nition of vagueness, which is contrary to the Boolean concept of the world implicit in much geographical teaching and thought, and the representation of geographical information in modern geographical information system. The argument of Sorites Paradox is suggested as a test of whether a concept is vague. If that concept is sorites susceptible, then it should be modelled as a vague concept, otherwise a Boolean model may be appropriate. The recognition of whether or not a particular concept is sorites susceptible does not have to in uence the methods of analysis. It should merely inform the interpretation, and the investigator and reader should be aware that the outcome of the analysis is only one of a set of possible outcomes, which depends on how the vague concept is crispened. Furthermore, it is argued here that very many geographical phenomena (relations, objects and processes) can be shown to be sorites susceptible, and so vague, both generically and genetically. Vagueness can be addressed by multivalued logic and applications of fuzzy set theory (the most common method of implementing multivalued logic) to geography are reviewed. A formal recognition of vagueness in geographical phenomena is long overdue, and should be
Probabilistic Arithmetic
, 1989
"... This thesis develops the idea of probabilistic arithmetic. The aim is to replace arithmetic operations on numbers with arithmetic operations on random variables. Specifically, we are interested in numerical methods of calculating convolutions of probability distributions. The longterm goal is to ..."
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Cited by 15 (0 self)
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This thesis develops the idea of probabilistic arithmetic. The aim is to replace arithmetic operations on numbers with arithmetic operations on random variables. Specifically, we are interested in numerical methods of calculating convolutions of probability distributions. The longterm goal is to be able to handle random problems (such as the determination of the distribution of the roots of random algebraic equations) using algorithms which have been developed for the deterministic case. To this end, in this thesis we survey a number of previously proposed methods for calculating convolutions and representing probability distributions and examine their defects. We develop some new results for some of these methods (the Laguerre transform and the histogram method), but ultimately find them unsuitable. We find that the details on how the ordinary convolution equations are calculated are
2004), Intransitivity and Vagueness
 Proceedings of the Ninth International Conference on Principles of Knowledge Representation and Reasoning (KR
"... There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an ..."
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Cited by 14 (2 self)
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There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an agent reports that two things are indistinguishable are both carefully modeled, the problems disappear, and indistinguishability can indeed be taken to be an equivalence relation. Moreover, this model also suggests a logic of vagueness that seems to solve many of the problems related to vagueness discussed in the philosophical literature. In particular, it is shown here how the logic can handle the sorites paradox. 1
Intelligent Techniques for Handling Uncertainty in the Assessment of Neonatal Outcome
, 1997
"... a rulebased expert system. This expert system checks results to ensure their consistency, identifies whether the results come from arterial or venous vessels, and then produces an interpretation of their meaning. This `crisp' expert system was validated, verified and commercially released, and ..."
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Cited by 7 (6 self)
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a rulebased expert system. This expert system checks results to ensure their consistency, identifies whether the results come from arterial or venous vessels, and then produces an interpretation of their meaning. This `crisp' expert system was validated, verified and commercially released, and has since been installed at twenty two hospitals all around the United Kingdom. The assessment of umbilical acidbase status is characterised by uncertainty in both the basic data and the knowledge required for its interpretation. Fuzzy logic provides a technique for representing both these forms of uncertainty in a single framework. A `preliminary' fuzzylogic based expert system to interpret errorfree results was developed, based on the knowledge embedded in the crisp expert system. Its performance was compared against clinicians in a validation test, but initially its performance was found to be poor in comparison with the clinicians and inferior to the crisp expert system. An automatic tuni
Fundamentals of Fuzzy Quantification Plausible Models, Constructive Principles, and Efficient Implementation
, 2003
"... ..."
Global Stability of Generalized Additive Fuzzy Systems
 IEEE Trans. Systems, Man, and Cybernetics  C
, 1998
"... This paper explores the stability of a class of feedback fuzzy systems. The class consists of generalized additive fuzzy systems that compute a system output as a convex sum of linear operators. Continuous versions of these systems are globally asymptotically stable if all rule matrices are stable ( ..."
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Cited by 5 (0 self)
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This paper explores the stability of a class of feedback fuzzy systems. The class consists of generalized additive fuzzy systems that compute a system output as a convex sum of linear operators. Continuous versions of these systems are globally asymptotically stable if all rule matrices are stable (negative definite). So local rule stability leads to global system stability. This relationship between local and global system stability does not hold for the better known discrete versions of feedback fuzzy systems. A corollary shows that it does hold for the discrete versions in the special but practical case of diagonal rule matrices. The paper first reviews additive fuzzy systems and then extends them to the class of generalized additive fuzzy systems. The Appendix derives the basic ratio structure of additive fuzzy systems and shows how supervised learning can tune their parameters.
Hybrid soft computing systems: industrial and commercial applications
 Proceedings of the IEEE,vol
, 1999
"... Soft computing (SC) is an association of computing methodologies that includes as its principal members fuzzy logic, neurocomputing, evolutionary computing and probabilistic computing. We present a collection of methods and tools that can be used to perform diagnostics, estimation, and control. Thes ..."
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Cited by 3 (1 self)
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Soft computing (SC) is an association of computing methodologies that includes as its principal members fuzzy logic, neurocomputing, evolutionary computing and probabilistic computing. We present a collection of methods and tools that can be used to perform diagnostics, estimation, and control. These tools are a great match for realworld applications that are characterized by imprecise, uncertain data and incomplete domain knowledge. We outline the advantages of applying SC techniques and in particular the synergy derived from the use of hybrid SC systems. We illustrate some combinations of hybrid SC systems, such as fuzzy logic controllers (FLC’s) tuned by neural networks (NN’s) and evolutionary computing (EC), NN’s tuned by EC or FLC’s, and EC controlled by FLC’s. We discuss three successful realworld examples of SC applications to industrial equipment diagnostics, freight train control, and residential property valuation.
Classification and Approximation with RuleBased Networks
, 1993
"... This thesis describes the architecture of learning systems which can explain their decisions through a rulebased knowledge representation. Two problems in learning are addressed: pattern classification and function approximation. In Part I, a pattern classifier for discretevalued problems is prese ..."
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This thesis describes the architecture of learning systems which can explain their decisions through a rulebased knowledge representation. Two problems in learning are addressed: pattern classification and function approximation. In Part I, a pattern classifier for discretevalued problems is presented. The system utilizes an informationtheoretic algorithm for constructing informative rules from example data. These rules are then used to construct a computational network to perform parallel inference and posterior probability estimation. The network can be extended incrementally; that is, new data can be incorporated without repeating the training on previous data. It is shown that this technique performs comparably with other techniques including the backpropagation network while having unique advantages in incremental learning capability, training efficiency, and knowledge representation. Examples are shown of rulebased classification and explanation. In Part II, we present a metho...
unknown title
"... session in which the following exchange takes place between patient and counselor. “Where psychoanalysis has failed, syllogism is sure to succeed. Tell me more about what’s been troubling you.” “Well, there’s my job.” “Yes?” “I’m an I.R.S. auditor.” “Ahh. And what would you most like to be?” “I’ve a ..."
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session in which the following exchange takes place between patient and counselor. “Where psychoanalysis has failed, syllogism is sure to succeed. Tell me more about what’s been troubling you.” “Well, there’s my job.” “Yes?” “I’m an I.R.S. auditor.” “Ahh. And what would you most like to be?” “I’ve always wanted to be an orthodontist—nothing beats orthodontia.” “Let’s reflect on this. You’ll agree that auditing is better than nothing.” “That’s certainly true.” “And you have just granted that nothing is better than orthodontia.” “Yes.” “It follows, therefore, that auditing is better than orthodontia.” “That makes me fell a little better. I’m starting to see the value of this therapy.”