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On the Hardness of Approximate Reasoning
, 1996
"... Many AI problems, when formalized, reduce to evaluating the probability that a propositional expression is true. In this paper we show that this problem is computationally intractable even in surprisingly restricted cases and even if we settle for an approximation to this probability. We consider va ..."
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Cited by 289 (13 self)
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various methods used in approximate reasoning such as computing degree of belief and Bayesian belief networks, as well as reasoning techniques such as constraint satisfaction and knowledge compilation, that use approximation to avoid computational difficulties, and reduce them to modelcounting problems
The Concept of a Linguistic Variable and its Application to Approximate Reasoning
 Journal of Information Science
, 1975
"... By a linguistic variable we mean a variable whose values are words or sentences in a natural or artificial language. I:or example, Age is a linguistic variable if its values are linguistic rather than numerical, i.e., young, not young, very young, quite young, old, not very oldand not very young, et ..."
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Cited by 1430 (9 self)
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By a linguistic variable we mean a variable whose values are words or sentences in a natural or artificial language. I:or example, Age is a linguistic variable if its values are linguistic rather than numerical, i.e., young, not young, very young, quite young, old, not very oldand not very young, etc., rather than 20, 21, 22, 23, In more specific terms, a linguistic variable is characterized by a quintuple (&?, T(z), U, G,M) in which &? is the name of the variable; T(s) is the termset of2, that is, the collection of its linguistic values; U is a universe of discourse; G is a syntactic rule which generates the terms in T(z); and M is a semantic rule which associates with each linguistic value X its meaning, M(X), where M(X) denotes a fuzzy subset of U The meaning of a linguistic value X is characterized by a compatibility function, c: l / + [0, I], which associates with each u in U its compatibility with X. Thus, the COItIpdtibiiity of age 27 with young might be 0.7, while that of 35 might be 0.2. The function of the semantic rule is to relate the compdtibihties of the socalled primary terms in a composite linguistic valuee.g.,.young and old in not very young and not very oldto the compatibility of the composite value. To this end, the hedges
What Is Approximate Reasoning? ⋆
"... Abstract. Approximate reasoning for the Semantic Web is based on the idea of sacrificing soundness or completeness for a significant speedup of reasoning. This is to be done in such a way that the number of introduced mistakes is at least outweighed by the obtained speedup. When pursuing such appro ..."
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Cited by 15 (5 self)
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Abstract. Approximate reasoning for the Semantic Web is based on the idea of sacrificing soundness or completeness for a significant speedup of reasoning. This is to be done in such a way that the number of introduced mistakes is at least outweighed by the obtained speedup. When pursuing
Approximate reasoning in fuzzy resolution
 In Fuzzy Information Processing Society (NAFIPS), 2012 Annual Meeting of the North American
, 2012
"... Copyright © 2013 Banibrata Mondal, Swapan Raha. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Resolution is an useful tool for mec ..."
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Cited by 2 (0 self)
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for mechanical theorem proving in modelling the refutation proof procedure, which is mostly used in constructing a “proof ” of a “theorem”. An attempt is made to utilize approximate reasoning methodology in fuzzy resolution. Approximate reasoning is a methodology which can deduce a specific information from
On approximate reasoning with graded rules
 Fuzzy Sets and Systems
"... This contribution presents a comprehensive view on problems of approximate reasoning with imprecise knowledge in the form of a collection of fuzzy IFTHEN rules formalized by approximating formulas of a special type. Two alternatives that follow from the dual character of approximating formulas are ..."
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Cited by 10 (3 self)
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This contribution presents a comprehensive view on problems of approximate reasoning with imprecise knowledge in the form of a collection of fuzzy IFTHEN rules formalized by approximating formulas of a special type. Two alternatives that follow from the dual character of approximating formulas
Approximate Reasoning by Agents
"... Abstract. We present an approach to approximate reasoning by agents in distributed environments based on calculi of information granules. Approximate reasoning schemes are basic schemes of information granule construction. An important property of such schemes is their robustness with respect to inp ..."
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Abstract. We present an approach to approximate reasoning by agents in distributed environments based on calculi of information granules. Approximate reasoning schemes are basic schemes of information granule construction. An important property of such schemes is their robustness with respect
Approximate Reasoning in Distributed Systems
 In Proc.Fifth EUFIT European Congress, Aachen. Verlag Mainz
, 1997
"... : In this exposition we sum up our results on approximate reasoning in distributed systems obtained in the last few years. The presented scheme for approximate reasoning is based on rough mereology and encompasses schemes based on fuzzy set theory. 1. INTRODUCTION We present a formal model of appr ..."
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Cited by 2 (2 self)
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: In this exposition we sum up our results on approximate reasoning in distributed systems obtained in the last few years. The presented scheme for approximate reasoning is based on rough mereology and encompasses schemes based on fuzzy set theory. 1. INTRODUCTION We present a formal model
Similarity in Approximate Reasoning
"... Abstract — This paper presents an approach to similarity based approximate reasoning that elucidates the connection between similarity and existing approaches to inference in approximate reasoning methodology. A set of axioms is proposed to compute a reasonable measure of similarity between two fuzz ..."
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Abstract — This paper presents an approach to similarity based approximate reasoning that elucidates the connection between similarity and existing approaches to inference in approximate reasoning methodology. A set of axioms is proposed to compute a reasonable measure of similarity between two
Approximate Reasoning with Fuzzy Booleans
 IPMU 2004, 10th international conference on Information Processing and Management of Uncertainty in KnowledgeBased Systems
"... This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp ante ..."
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Cited by 1 (0 self)
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This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp
On Consequence in Approximate Reasoning
 J. of Applied NonClassical Logics
"... The purpose of this paper is to explore the notion of consequence in Approximate Reasoning. While logical consequence has an standard (semantic and syntactic) definition in Exact Logic, several different definitions of that concept can be considered in the Approximate Reasoning framework. In this pa ..."
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Cited by 11 (1 self)
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The purpose of this paper is to explore the notion of consequence in Approximate Reasoning. While logical consequence has an standard (semantic and syntactic) definition in Exact Logic, several different definitions of that concept can be considered in the Approximate Reasoning framework
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