A fuzzy model for competency-based employee evaluation and selection

In this chapter, the steps necessary to develop a fuzzy expert system (FES) from the initial model design through to final system evaluation will be presented The current state-of-the-art of fuzzy modelling can be summed up informally as “anything goes” What this actually means is that the developer of the fuzzy model is faced with many steps in the process each with many options from which selections must be made In general, there is no specific or prescriptive method that can be used to make these choices, there are simply heuristics (“rules-of-thumb”) which may be employed to help guide the process Each of the steps will be described in detail, a summary of the main options available will be provided and the available heuristics to guide selection will be reviewed The steps will be illustrated by describing two cases studies: one will be a mock example of a fuzzy expert system for financial forecasting and the other will be a real example of a fuzzy expert system for a medical application The expert system framework considered here is restricted to rule-based systems While there are other frameworks that have been proposed for processing information utilising fuzzy methodologies, these are generally less popular in the context of fuzzy expert systems As a note on terminology, the term model is used to refer to the abstract conception of the process being studied and hence fuzzy model is the notional representation of the process in terms of fuzzy variables, rules and methods that together define the input-output mapping relationship In contrast, the term system (as in fuzzy expert system) is used to refer to the embodiment, realisation or implementation of the theoretical model in some software language or package A single model may be realised in different forms, for example, via differing software languages or differing hardware platforms Thus it should be realised that there is a subtle, but important, distinction between the evaluation of a fuzzy model of expertise and the evaluation of (one or more of) its corresponding fuzzy expert systems A model may be evaluated as accurately capturing or representing the domain problem under consideration, whereas

Fuzzy Expert Systems

Issues of combination of rules or their consequences in fuzzy expert systems using Compositional Rule of Inference (CRI) are investigated. First, implication operators are classified as the ‘Expansion Type Implication’, the ‘Reduction Type Implication’, and the ‘Other Type Implication’. Further, fuzzy inference processes based on CRI are classified into three categories in terms of their inference results, i.e., the ‘Expansion Type Inference’, the ‘Reduction Type Inference’, and the ‘Other Type Inference’. Finally combination of rules or their consequences is investigated for inference processes based on CRI. It is shown that in order for the basic requirement for fuzzy reasoning to be satisfied, it is necessary that for inference processes using Sup-T composition in the context of CRI, the combination operator be ‘min’ if the implication operator F(a, b) is an ‘Expansion Type’, i.e., F(a, b) = a → b ⩾ b for all aϵ [0, 1], and is a ‘non-increasing’ function of a, i.e., if a1 ⩾ a2, then F(a1, b) ⩽ F(a2, b); and the combination operator be ‘max’ if the implication operator F(a, b) is a ‘Reduction Type’, i.e., F(a, b) = a → b ⩽ b for all aϵ [0,1], and is a ‘non-decreasing’ function of a, i.e., if a1 ⩾ a2, then F(a1, b) ⩾ F(a2, b). The impact of the overlap is studied between membership functions of the antecedent of a rule and an observation on the inference results. In particular, the cases of R-implication for Sup-T composition and min combination are investigated. We also discuss the consistency of our conclusions with respect to the existing conclusions in the current literature. An example is given to illustrate the proposed method for the selection of combination operators.

Combination of rules or their consequences in fuzzy expert systems

There exist in the literature today many contributions dealing with the incorporation of fuzzy logic in expert systems. However, unfortunately, much of what has been proposed can only be applied to small-scale expert systems; that is, when the number of rules is in the dozens as opposed to in the hundreds. The more traditional (nonfuzzy) expert systems are able to cope with large numbers of rules by using Rete networks for maintaining matches of all the rules and all the facts. (A Rete network obviates the need to match the rules with the facts on every cycle of the inference engine.) In this paper, we present a more general Rete network that is particularly suitable for reasoning with fuzzy logic. The generalized Rete network consists of a cascade of three networks: the pattern network, the join network, and the evidence aggregation network. The first two layers are modified versions of similar layers for the traditional Rete networks and the last, the aggregation layer, is a new concept that allows fuzzy evidence to be aggregated when fuzzy inferences are made about the same fuzzy variable by different rules.

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FuzzyShell: a large-scale expert system shell using fuzzy logic for uncertainty reasoning

A fuzzy expert system must do rule chaining differently than a nonfuzzy expert system. In particular, any rule that can fire with a particular linguistic variable in its consequent must fire before any rule whose antecedent conditions depend upon the resultant fuzzy set value of the consequent linguistic variable is allowed to fire. The dependent rules would be considered in a chain with the fuzzy rules which generate or assert the needed fuzzy linguistic variable. A recent paper by J. Pan et al. (1998) points out that a version of the FuzzyCLIPS expert system shell does not operate with chained fuzzy rules as one would expect. They introduce FuzzyShell which is described as the only known shell to have the expected fuzzy rule chaining performance. We show several approaches to obtaining the desired behavior in FuzzyCLIPS. Further, a potential pitfall with the FuzzyShell approach to dealing with chaining is pointed out.

Rule chaining in fuzzy expert systems

This paper presents the design of an approximate reasoning framework for an expert system prototype for a service centre of spare parts, to which customers bring failed items for repair. The design development is fundamentally based upon an analysis of a queuing model associated with the service centre system problem. This queuing model provides a prerequisite insight and the knowledge about such a service system. The building process for the framework is described in a case study utilizing the queuing model, namely, M/M/c repair systems with spares. The objective here is to aid management in determining certain decision policies and the capacities which are critical to them. Within the approximate reasoning framework, the identification and the construction of the basic rules that contain uncertain (vague, ambiguous, fuzzy) linguistic terms are described, as well as the specification of the membership functions that represent the meaning of such linguistic terms. Consistency of rules is studied in accordance with the internal relationships between system variables. Approximate Analogical Reasoning with a tree search is used as the inference engine of the expert system. Approximate reasoning results are compared with analytical results.

M. Berg

Papers

A fuzzy expert system for a service centre of spare parts