Applications of fuzzy logic in heuristic control have been highly successful, but which aspects of fuzzy logic are essential to its practical usefulness? This paper shows that an apparently reasonable version of fuzzy logic collapses mathematically to two-valued logic. Moreover, there are few if any published reports of expert systems in real-world use that reason about uncertainty using fuzzy logic. It appears that the limitations of fuzzy logic have not been detrimental in control applications because current fuzzy controllers are far simpler than other knowledge-based systems. In the future, the technical limitations of fuzzy logic can be expected to become important in practice, and work on fuzzy controllers will also encounter several problems of scale already known for other knowledge-based systems. 1

Abstract- Scheduling is the process of devising or designing a procedure for a particular objective, specifying the sequence or time for each item in the procedure. Qpical scheduling problems are railway time-tabling, project scheduling, production scheduling, and scheduling computer systems as in flexible manufacturing systems and multiprocessor scheduling. Further, there are a number of related problems belonging to the larger class of planning problems, such as the early stage of project management and resource allocation in a job shop. Scheduling is a rich area demanding the application of efficient methods to tackle the combinatorial explosion that results in real world applications. Recent developments in artificial intelligence (AI) have led to the use of knowledge-based techniques for solving scheduling problems. In this paper, we survey several existing intelligent planning and scheduling systems with the aim of providing a guide to the main AI techniques used. In view of the prevailing difference in usage of the terms planning and scheduling between AI and OR, we present a taxonomy of planning and scheduling problems. We illustrate the modeling of real world problems b m closed deterministic worlds to complex real worlds with the project scheduling example. We survey some of the more successful planning and scheduling systems, and highlight their features. Finally, we consolidate the AI approaches to knowledge representation and problem solving in the project management context. Index Tern- Intelligent systems, knowledge-based systems, planning, project management, scheduling.

Flexible manufacturing systems (FMS) are distinguished by the use of computer control in place of the hard automation usually found in transfer lines. The high investment required for a FMS and the potential of FMS as a strategic competitive tool make it attractive to engage in research in this area. This paper presents a review of literature concerning the operations aspect of FMS. Articles emphasizing many methodological perspectives are critically reviewed. The review is done from multiple viewpoints. Future research directions are suggested.

Constraint propagation is a matter of logical deduction, but this is not usually sufficient to reach a solution to a problem. Heuristic knowledge is usually needed to go on with the solution search when logical deduction becomes inefficient. The way this second type of knowledge is handled has more to do with decision rather than deduction. In this paper we suggest a mechanism to handle heuristic knowledge based on social choice theory. An analogy is proposed between the cooperation problem among heuristics expressed as decision rules and the voting problem. This analogy allows to define and justify aggregation modes for results provided by each decision rule, with a view to providing a global decision ranking. An application to job-shop scheduling has been carried out.

Scheduling has been examined for many years both in theory and practice. Theoretical scheduling methods, which are concerned with searching for optimal schedules subject to a limited number of constraints, are rarely applicable to real world problems with various types of constraints and preferences where optimal solutions are not necessary. Some important differences between the two worlds are analyzed. The knowledge-based scheduling system WIZARD is presented. It was designed to cope with many requirements from industrial scheduling. In this paper it is applied to standardized problem instances taken from Operations Research literature and used on benchmark data to evaluate WIZARD's performance. 1 OR MODELS AND REAL WORLD SCHEDULING Scheduling as "the allocation of limited resources to tasks over time" ([15]) has for a long time been one of the main research topics of Operations Research. The basic structure of scheduling problems is as follows. There are a number of jobs ...

: This paper is an attempt at providing a fuzzy set-based approach to case-based decision. Case-based decision consists in selecting an action to be applied to a current problem on the basis of a set of cases storing the results of various actions applied to similar, previously encountered, problems. Recently, Gilboa and Schmeidler have presented an axiomatic justification of a counterpart of the expected utility used in decision under uncertainty, where similarity degrees play a role somewhat analogous to probability, and have proposed to apply it to case-based decision. This proposal resembles Sugeno's approach to fuzzy control. The relation between the two approaches is investigated. Besides, another approach, based on possibility and necessity measures, is presented and discussed. The idea is to favor actions which have never given bad results in problems similar to the current problem. A much more permissive view considers all the actions which have given good results (at least on...

Due to imprecision that is often inherent in the estimates of future demand for various products in a batch type production system, there are cases where the lot sizing problem may be more naturally treated using fuzzy concepts. Triangular fuzzy sets may be employed in order to represent qualitative estimates that are expressed linguistically. In this paper the above approach is introduced in order to derive an appropriate number of production runs and the corresponding lot sizes. Keywords: Fuzzy sets, Production Planning, Lot size Scheduling. Introduction This paper is concerned with the problem of lot sizing in a batch-type production system, i.e., a type of production which lies between job shop and flow shop production. In such systems the manager has to determine the lot size for a batch to be produced at one time as well as to schedule the batch on the resources. Lot sizing is dependent on two conflicting kinds of costs: the setup and the inventory holding costs. Small lot sizes ...

This paper is an attempt at providing a fuzzy set-based formalization of case-based reasoning. The proposed approach, which does not take into account the learning aspects of case-based reasoning, assumes a principle stating that "the more similar are the problem description attributes, the more similar are the outcome attributes". A weaker form of this principle concluding only on the graded possibility of the similarity of the outcome attributes, is also considered. These two forms of the case-based reasoning principle are modelled in terms of fuzzy rules. Then an approximate reasoning machinery taking advantage of this principle enables us to apply the information stored in the memory of previous cases to the current problem. A particular instance of case-based reasoning, named case-based decision is especially investigated. A logical formalization of the basic case-based reasoning inference is also proposed. Extensions of the proposed approach in order to handle imprecise or fuzzy descriptions or to manage more general forms of the principle underlying case-based reasoning are briefly discussed in the conclusion.

The responses to my article provide an that I have is whether the distinction is re- knowledge becomes implicit background exceptionally wide range of perspectives ally well defined. On the one hand, there knowledge that must be used tacitly in tunon the current state of research on fuzzy may be multiple types of imprecision and ing the allowed interactions between the logic and its applications. Overall, I find vagueness. Is the domain-independent im- items of explicit shallow knowledge. To that with most commentators I agree more precision involved in “around 1.80m ” the quote Garcia, “The dogma of generality than I disagree. I shall try here to steer a same as the human-specific imprecision versus efficiency strikes again, and knowlmiddle course between simply repeating involved in “tall”? On the other hand, it edge engineering and machine learning are points of agreement and narrowly counter- may be possible to model some types of not exempted.” ing points of disagreement. imprecision probabilistically. For example, the degree of truth of the assertion “ 1.SOm Fuzzy logic in expert systems. Only three The foundations of fuzzy logic. Some is tall ” might be modeled as the probability of the responses give references in an atcommentators take a more extreme posi- that an individual with height 1.80m would tempt to dispute the claim that there are tion than I do concerning the coherence of be labeled as tall given incomplete knowl- very few deployed expert systems that acfuzzy logic. I do not agree with Attikiouzel edge, that is, given no other information on tually use fuzzy logic as their principal