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Partial Constraint Satisfaction
, 1992
"... . A constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed. In some cases it may be impossible or impractical to solve these problems completely. We may seek to partially solve the problem, in particular by satisfying ..."
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Cited by 443 (23 self)
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. A constraint satisfaction problem involves finding values for variables subject to constraints on which combinations of values are allowed. In some cases it may be impossible or impractical to solve these problems completely. We may seek to partially solve the problem, in particular by satisfying a maximal number of constraints. Standard backtracking and local consistency techniques for solving constraint satisfaction problems can be adapted to cope with, and take advantage of, the differences between partial and complete constraint satisfaction. Extensive experimentation on maximal satisfaction problems illuminates the relative and absolute effectiveness of these methods. A general model of partial constraint satisfaction is proposed. 1 Introduction Constraint satisfaction involves finding values for problem variables subject to constraints on acceptable combinations of values. Constraint satisfaction has wide application in artificial intelligence, in areas ranging from temporal r...
Valued constraint satisfaction problems: Hard and easy problems
 IJCAI’95: Proceedings International Joint Conference on Artificial Intelligence
, 1995
"... tschiexOtoulouse.inra.fr fargierOirit.fr verfailOcert.fr In order to deal with overconstrained Constraint Satisfaction Problems, various extensions of the CSP framework have been considered by taking into account costs, uncertainties, preferences, priorities...Each extension uses a specific mathema ..."
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Cited by 294 (41 self)
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tschiexOtoulouse.inra.fr fargierOirit.fr verfailOcert.fr In order to deal with overconstrained Constraint Satisfaction Problems, various extensions of the CSP framework have been considered by taking into account costs, uncertainties, preferences, priorities...Each extension uses a specific mathematical operator (+, max...) to aggregate constraint violations. In this paper, we consider a simple algebraic framework, related to Partial Constraint Satisfaction, which subsumes most of these proposals and use it to characterize existing proposals in terms of rationality and computational complexity. We exhibit simple relationships between these proposals, try to
From Computing With Numbers To Computing With Words From Manipulation Of Measurements To Manipulation of Perceptions
 Appl. Math. Comput. Sci
"... Computing, in its usual sense, is centered on manipulation of numbers and symbols. In contrast, computing with words, or CW for short, is a methodology in which the objects of computation are words and propositions drawn from a natural language, e.g., small, large, far, heavy, not very likely, the p ..."
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Cited by 111 (4 self)
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Computing, in its usual sense, is centered on manipulation of numbers and symbols. In contrast, computing with words, or CW for short, is a methodology in which the objects of computation are words and propositions drawn from a natural language, e.g., small, large, far, heavy, not very likely, the price of gas is low and declining, Berkeley is near San Francisco, it is very unlikely that there will be a significant increase in the price of oil in the near future, etc. Computing with words is inspired by the remarkable human capability to perform a wide variety of physical and mental tasks without any measurements and any computations. Familiar examples of such tasks are parking a car, driving in heavy traffic, playing golf, riding a bicycle, understanding speech and summarizing a story. Underlying this remarkable capability is the brain’s crucial ability to manipulate perceptions – perceptions of distance, size, weight, color, speed, time, direction, force, number, truth, likelihood and other characteristics of physical and mental objects. Manipulation of perceptions plays a key role in human recognition, decision and execution processes. As a methodology, computing with words provides a foundation for a computational theory of perceptions – a theory which may have an important bearing on how humans make – and machines might make – perceptionbased rational decisions in an environment of imprecision, uncertainty and partial truth. A basic difference between perceptions and measurements is that, in general, measurements are crisp whereas perceptions are fuzzy. One of the fundamental aims of science has been and continues to be that of progressing from perceptions to measurements. Pursuit of this aim has led to brilliant successes. We have sent men to the moon; we can build computers
Semiringbased CSPs and Valued CSPs: Frameworks, Properties, and Comparison
 Constraints
, 1999
"... In this paper we describe and compare two frameworks for constraint solving where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. One is based on a semiring, and the other one on a totally ordered commutative monoid. While comparing the two ..."
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Cited by 103 (27 self)
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In this paper we describe and compare two frameworks for constraint solving where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. One is based on a semiring, and the other one on a totally ordered commutative monoid. While comparing the two approaches, we show how to pass from one to the other one, and we discuss when this is possible. The two frameworks have been independently introduced in [2], [3] and [35].
Possibility theory in constraint satisfaction problems: Handling priority, preference and uncertainty
 Applied Intelligence
, 1996
"... In classical Constraint Satisfaction Problems (CSPs) knowledge is embedded in a set of hard constraints, each one restricting the possible values of a set of variables. However constraints in real world problems are seldom hard, and CSP's are often idealizations that do not account for the pref ..."
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Cited by 88 (15 self)
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In classical Constraint Satisfaction Problems (CSPs) knowledge is embedded in a set of hard constraints, each one restricting the possible values of a set of variables. However constraints in real world problems are seldom hard, and CSP's are often idealizations that do not account for the preference among feasible solutions. Moreover some constraints may have priority over others. Lastly, constraints may involve uncertain parameters. This paper advocates the use of fuzzy sets and possibility theory as a realistic approach for the representation of these three aspects. Fuzzy constraints encompass both preference relations among possible instanciations and priorities among constraints. In a Fuzzy Constraint Satisfaction Problem (FCSP), a constraint is satisfied to a degree (rather than satisfied or not satisfied) and the acceptability of a potential solution becomes a gradual notion. Even if the FCSP is partially inconsistent, best instanciations are provided owing to the relaxation of ...
Semiringbased CSPs and Valued CSPs: Basic Properties and Comparison
, 1996
"... . We introduce two frameworks for constraint solving where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. One is based on a semiring, and the other one on a totally ordered commutative monoid. We then compare the two approaches and we discu ..."
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Cited by 45 (9 self)
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. We introduce two frameworks for constraint solving where classical CSPs, fuzzy CSPs, weighted CSPs, partial constraint satisfaction, and others can be easily cast. One is based on a semiring, and the other one on a totally ordered commutative monoid. We then compare the two approaches and we discuss the relationship between them. 1 Introduction Classical constraint satisfaction problems (CSPs) [19, 17] are a very expressive and natural formalism to specify many kinds of reallife problems. In fact, problems ranging from map coloring, vision, robotics, jobshop scheduling, VLSI design, etc., can easily be cast as CSPs and solved using one of the many techniques that have been developed for such problems or subclasses of them [8, 9, 18, 16, 19]. However, they also have evident limitations, mainly due to the fact that they are not very flexible when trying to represent reallife scenarios where the knowledge is not completely available nor crisp. In fact, in such situations, the abilit...
Computing Improved Optimal Solutions to MaxMin Flexible Constraint Satisfaction Problems
 European Journal of Operational Research
, 1999
"... : The formal framework for decision making in a fuzzy environment is based on a general maxmin, bottlenecklike optimization problem, proposed by Zadeh. It is also the basis for extending the constraint satisfaction paradigm of Artificial Intelligence to accommodating flexible or prioritized constra ..."
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Cited by 13 (3 self)
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: The formal framework for decision making in a fuzzy environment is based on a general maxmin, bottlenecklike optimization problem, proposed by Zadeh. It is also the basis for extending the constraint satisfaction paradigm of Artificial Intelligence to accommodating flexible or prioritized constraints. This paper surveys refinements of the ordering of solutions supplied by the maxmin formulation, namely the discrimin partial ordering and the leximin complete preordering. A general algorithm is given which computes all maximal solutions in the sense of these relations. It also sheds light on the structure of the set of best solutions. Moreover, classes of problems for which there is a unique best discrimin and leximin solution are exhibited, namely, continuous problems with convex domains, and so called isotonic problems. Noticeable examples of such problems are fuzzy linear programming problems and fuzzy PERTlike scheduling problems. Introduction Flexible constraint satisfaction p...
Domain Independent Temporal Reasoning With Recurring Events
, 1996
"... interpretation of four 89relations between I and J) 89 d ! = fhR I \ThetaJ ; R 2 i : R I \ThetaJ ` R 2 R I \ThetaJ is a total function R I \ThetaJ is oneone.g 89! = fhR I \ThetaJ ; R 2 i : R I \ThetaJ ` R 2 R I \ThetaJ is a total function.g 89 d = fhR I \ThetaJ ; R 2 i : R I \ThetaJ ` R 2 ..."
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Cited by 12 (0 self)
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interpretation of four 89relations between I and J) 89 d ! = fhR I \ThetaJ ; R 2 i : R I \ThetaJ ` R 2 R I \ThetaJ is a total function R I \ThetaJ is oneone.g 89! = fhR I \ThetaJ ; R 2 i : R I \ThetaJ ` R 2 R I \ThetaJ is a total function.g 89 d = fhR I \ThetaJ ; R 2 i : R I \ThetaJ ` R 2 R I \ThetaJ is a total relation [8i; i 0 : I; 8j : JR I \ThetaJ (i; j) R I \ThetaJ (i 0 ; j) ! i = i 0 ]g 89 = fhR I \ThetaJ ; R 2 i : R I \ThetaJ ` R 2 R I \ThetaJ is a total relationg 14 IJCAI Spatial and Temporal Workshop For recurrence relations based on simple correlation, R I \ThetaJ is instantiated to COR I \ThetaJ , and R 2 to a relation in CR. Thus, the quantifier construction creates a class of relations which places restrictions on the temporal order of the pairs of correlated intervals. What distinguishes the 89 class from other operators is the condition that R I \ThetaJ ` R 2 . To summarize: the construction of recurrence relations using quantification, and the rel...
Lexical Imprecision in Fuzzy Constraint Networks
 In Proceedings of AAAI92
, 1992
"... We define fuzzy constraint networks and prove a theorem about their relationship to fuzzy logic. Then we introduce Khayyam, a fuzzy constraintbased programming language in which any sentence in the firstorder fuzzy predicate calculus is a wellformed constraint statement. Finally, using Khayyam to ..."
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Cited by 10 (4 self)
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We define fuzzy constraint networks and prove a theorem about their relationship to fuzzy logic. Then we introduce Khayyam, a fuzzy constraintbased programming language in which any sentence in the firstorder fuzzy predicate calculus is a wellformed constraint statement. Finally, using Khayyam to address an equipment selection application, we illustrate the expressive power of fuzzy constraintbased languages.
ConPlan/SIEDAplan: Personnel Assignment as a Problem of Hierarchical Constraint Satisfaction
, 1997
"... The ConPlan project conducted by the German Research Center for Artificial Intelligence in collaboration with the SIEDA Software house aimed at representing and solving nurse scheduling problems as a problem of optimizing constraint satisfaction. Shifts are assigned to the personnel complying with l ..."
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Cited by 4 (0 self)
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The ConPlan project conducted by the German Research Center for Artificial Intelligence in collaboration with the SIEDA Software house aimed at representing and solving nurse scheduling problems as a problem of optimizing constraint satisfaction. Shifts are assigned to the personnel complying with legal regulations, avoiding overtime work as far as possible and meeting as many additional requirements as possible. These requirements are encoded in a hierarchical constraint satisfaction problem (HCSP) comprising 600 to 800 variables. This paper explains on the one hand how nurse scheduling has been represented as a problem of optimizing consistency with constraints. On the other hand, the used search algorithm is described.