In this paper the issue of soft constraint satisfaction is discussed from a fuzzy set theoretical point of view. A fuzzy constraint is considered as a fuzzy relation. Different possible definitions for the degree of joint satisfaction of a set of fuzzy constraints are given, covering specific other soft constraint satisfaction problem (CSP) types such a partial and hierarchical CSP. It is shown that the classical CSP solving heuristics based on variable and value evaluations can be generalised and used to guide the solution construction process for solving fuzzy CSPs, and that the heuristic search can be replaced by branch-and-bound search. The solution process is illustrated with an example from the CSP literature. Finally, research issues are discussed. 1. Introduction In the recent years there has been a growing interest in soft constraint satisfaction. In general, in a soft CSP not all the given constraints need to be satisfied --- either because all of them cannot be met, theoret...

A counterpart to von Neumann and Morgenstern' expected utility theory is proposed in the framework of possibility theory. The existence of a utility function, representing a preference ordering among possibility distributions (on the consequences of decision-maker's actions) that satisfies a series of axioms pertaining to decision-maker's behavior, is established. The obtained utility is a generalization of Wald's criterion, which is recovered in case of total ignorance; when ignorance is only partial, the utility takes into account the fact that some situations are more plausible than others. Mathematically, the qualitative utility is nothing but the necessity measure of a fuzzy event in the sense of possibility theory (a so-called Sugeno integral). The possibilistic representation of uncertainty, which only requires a linearly ordered scale, is qualitative in nature. Only max, min and order-reversing operations are used on the scale. The axioms express a risk-averse behavior of the d...

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 – perception-based 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

: This paper proposes an extension of the constraint-based approach to job-shop scheduling, that accounts for the flexibility of temporal constraints and the uncertainty of operation durations. The set of solutions to a problem is viewed as a fuzzy set whose membership function reflects preference. This membership function is obtained by an egalitarist aggregation of local constraint-satisfaction levels. Uncertainty is qualitatively described is terms of possibility distributions. The paper formulates a simple mathematical model of jobshop scheduling under preference and uncertainty, relating it to the formal framework of constraint-satisfaction problems in Artificial Intelligence. A combinatorial search method that solves the problem is outlined, including fuzzy extensions of well-known look-ahead schemes. 1. Introduction There are traditionally three kinds of approaches to jobshop scheduling problems: priority rules, combinatorial optimization and constraint analysis. The first kind ...

This paper develops a fuzzy constraint based model for bilateral multi-issue negotiation in trading environments. In particular, we are concerned with the principled negotiation approach in which agents seek to strike a fair deal for both parties, but which, nevertheless, maximises their own payoff. Thus, there are elements of both competition and cooperation in the negotiation (hence semi-competitive environments) . One of the key intuitions of the approach is that there is often more than one option that can satisfy the interests of both parties. So, if the opponent cannot accept an offer then the proponent should endeavour to find an alternative that is equally acceptable to it, but more acceptable to the opponent. That is, the agent should make a trade-off. Only if such a trade-off is not possible should the agent make a concession. Against this background, our model ensures the agents reach a deal that is fair (Pareto-optimal) for both parties if such a solution exists. Moreover, this is achieved by minimising the amount of private information that is revealed. The model uses prioritised fuzzy constraints to represent trade-offs between the different possible values of the negotiation issues and to indicate how concessions should be made when they are necessary. Also by using constraints to express negotiation proposals, the model can cover the negotiation space more ef- ficiently since each exchange covers a region rather than a single point (which is what most existing models deal with). In addition, by incorporating the notion of a reward into our negotiation model, the agents can sometimes reach agreements that would not otherwise be possible.

. Increasing interest for configuration similarity is currently developing in the context of Digital Libraries, Spatial Databases and Geographical Information Systems. The corresponding queries retrieve all database configurations that match an input description (e.g., "find all configurations where an object x 0 is about 5km northeast of another x 1 , which, in turn, is inside object x 2 "). This paper introduces a framework for configuration similarity that takes into account all major types of spatial constraints (topological, direction, distance). We define appropriate fuzzy similarity measures for each type of constraint to provide flexibility and allow the system to capture real-life needs. Then we apply pre-processing techniques to explicate constraints in the query, and present algorithms that effectively solve the problem. Extensive experimental results demonstrate the applicability of our approach to images and queries of considerable size. 1. INTRODUCTION As opposed to visu...

Recent work in the field of artificial intelligence has shown that many problems can be represented as a set of constraints on a set of variables, i.e., as a constraint satisfaction problem. Unfortunately, real world problems tend to be inconsistent, and therefore the corresponding constraint satisfaction problems don't have solutions. A way to circumvent inconsistent constraint satisfaction problems is to make them fuzzy. The idea is to associate fuzzy values with the elements of the constraints, and to combine these fuzzy values in a reasonable way, i.e., a way that directly corresponds to the way how crisp constraint problems are handled.

In this paper, we employ the fuzzy repertory table technique to acquire the necessary domain knowledge for software a ents to act as sellers and buyers usin a bilateral, multi-al,g ne otiation model that can achieve optimal results in semi-competitive environments.

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: The formal framework for decision making in a fuzzy environment is based on a general maxmin, bottleneck-like 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 max-min 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 PERT-like scheduling problems. Introduction Flexible constraint satisfaction p...