I.B. Turksen and Y. Tian. Combination of rules or their consequences in fuzzy expert systems. Fuzzy Sets Systems, 58:3--40, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....method for performing a single fuzzy inference, it leaves the problem for combination of inference from a set of fuzzy rules. Given a set of N fuzzy rules of the form IF X is A i THEN Y is B i , i 1 aa N, there are two main approaches for performing combined inference on an observation A [124]. Firstly, the CRI may be applied to each rule i 1 aa N to produce conclusion sets B i which are then combined to the single conclusion B through the use of a combination operator; or secondly, by combining the relations R i into a single relation R with a combination operator and then ....

....the rules are used, the overall structure and the exact number, form and content of each must be determined. In general, two rules of the form IF X 1 is A 1 THEN Y is B, and IF X 2 is A 2 THEN Y is B , will give different results to the combined rule IF X 1 is A 1 OR X 2 is A 2 THEN Y is B [124]. It is generally accepted that the use of linguistic hedges such as very or slightly should be avoided in the initial rule set, unless absolutely necessary, but in the later stages of tuning the fuzzy model such hedges may be introduced to refine the effects of specific rules. Hedges are ....

I.B. Turksen and Y. Tian. Combination of rules or their consequences in fuzzy expert systems. Fuzzy Sets Systems, 58:3--40, 1993.

....for crisp sets. Obviously, with the choice of transform( and aggregate( there are some important design decisions left [8] In the past, there have been lots of efforts to support these design decisions, most of them by conducting and evaluating experiments, others by theoretical considerations [14, 15]. In our work we use two complementary inference mechanisms, the well known possibilistic approach [3, 4, 5] and a new method called oe reasoning that has been developed recently [16] This new approach builds the theoretical justification for the well known Mamdani approach to fuzzy control [9] ....

I. B. Turksen and Y. Tian. Combination of rules or their consequences in fuzzy expert systems. Fuzzy Sets and Systems, 58:3--40, 1993.

....easily, this approach overcomes the problem of defining a large number of operations for each image, as only a few algebraic operations are required. Fuzzy Logic Reasoning Framework A large amount of publications have been written on fuzzy logic reasoning (for example, Dubois 80] Lee 90] Turksen 93] Zimmermann 91] After investigating the available literature, we concluded that the knowledge graph shown in Figure 4 conforms to the concepts in most of these publications. LinguisticVariable supplies Rule Fact G.M.P. supplies fuzzifies fuzzifies Conclusion infers requests ....

....The node G.M.P. may be implemented by the max min compositional rule of inference defined by Zadeh [Zadeh 73] The node Conclusion may implement the connective ALSO as a fuzzy union which uses the maximum. Not all the possible combinations, however, can produce logically meaningful conclusions [Turksen 93] Marcelloni 96] This means that fuzzy set theory is constrained by the logic theory in the fuzzy logic domain. Overview of the Constraints and the Adaptability Space As illustrated by Table 2, all the three frameworks require interaction and composability constraints to guarantee correct ....

I.B. Turksen & Y. Tian, Combination of rules or their consequences in fuzzy expert systems, Fuzzy Sets and Systems, Vol. 58, 1993, pp. 3-40.

....distribution represents knowledge that is perfectly consistent, whereas the distribution x j 0 is completely inconsistent. Now in accordance with [6] we extend this notion of gradual consistency to fuzzy rule bases: 1 For a general overview about degrees of freedom in fuzzy reasoning see [3], e.g. Definition 1 In the context of reasoning, a fuzzy rule base [ A i ) B i ] is called ffl consistent iff for the corresponding meta rule RG = T i G i (see equation (1) it holds inf u2Ux sup v2Uy fRG (u; v)g = ffl: 3) It is very easy to show, that using this definition ....

I. B. Turksen and Y. Tian. Combination of rules or their consequences in fuzzy expert systems. Fuzzy Sets and Systems, 58:3--40, 1993.

....specifications easily, this approach overcomes the problem of defining a large number of operations for each image, as only a few algebraic operations are required. Fuzzy Logic Reasoning Framework A large amount of publications have been written on fuzzy logic reasoning (for example [Lee 90] Turksen 93] Dubois 80] Zimmermann 91] After investigating the available literature, we concluded that the architecture shown in Figure 5 conforms to the concepts in most of these publications. We selected the so called generalized modus ponens (G.M.P. as the basic inferencing technique because of ....

....implemented by the max min compositional rule of inference defined by Zadeh [Zadeh 73] The component Result may implement the connective ALSO as a union among fuzzy sets which uses the maximum. Not all the possible combinations, however, can produce meaningful results from a logical view point [Turksen 93] Marcelloni 95b] This means that fuzzy set theory is constrained by the logic theory in the fuzzy logic domain. 11 Overview of the Constraints and the Adaptability Space As illustrated by Table 3, all the three frameworks require interaction and composability constraints to guarantee ....

I.B. Turksen & Y. Tian, Combination of rules or their consequences in fuzzy expert systems, Fuzzy Sets and Systems, Vol. 58, 1993, pp. 3-40.

....rules FITA or FATI ffl how to aggregate several implication relations R i ffl how to aggregate several seperately computed results B 0 i Combining every conceivable answer to any of these questions we get a vast amount of possible mechanisms. For further details we reference to [1, 9, 15], e.g. On the other hand, it has already been mentioned, that there is an inference mechanism that is by far the most common one: SFC, the mechanism presented in 1975 by Mamdani and Assilian [10] We are convinced that this approach originally was a purely heuristic one that has been developed ....

....bodies of evidence. oe distributions correspond to dissonant bodies of evidence. Within the context of reasoning, to get new information means to get new arguments against distinct assumptions, i.e. the corresponding possibility distribution gets smaller (cf. reduction type inference, [15]) Within the context of oe reasoning, to get new information means to get new arguments in favour of distinct assumptions, i.e. the corresponding oe distribution gets bigger (cf. expansion type inference, 15] All these observations endorse the expectation, that and oe reasoning show ....

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I. B. Turksen and Y. Tian. Combination of rules or their consequences in fuzzy expert systems. Fuzzy Sets and Systems, 58:3--40, 1993.

.... means of classical logic modus ponens, which can be schematically described by: given the rule: IF A THEN B given the fact: A infer the result: B (1) For processing vague information and using linguistic variables and fuzzy or vague rules a generalized modus ponens has been proposed and studied [8, 5]. It enables an approximate deductive reasoning with the following general scheme: given the rule: IF x is A THEN y is B given the fact: x is A 0 infer the result: y is B 0 (2) Here, x and y are linguistic variables and A, B, A 0 , and B 0 are fuzzy sets describing ....

....fact and the fuzzy premise. And therefore the result of the reasoning process, B 0 , will approximate more or less the rule conclusion; the deduction is an approximate one. Various fuzzy operators and implication relations have been proposed for implementing the generalized modus ponens [3, 5]. The results have been evaluated in a mainly empirical manner, according to how they match our expectations and in relation to the specific domain were this reasoning is applied. The largest experience comes from fuzzy control. The approach using the Mamdani implication relation and the max min ....

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I.B. Turksen and Y. Tian. Combination of rules or their consequences in fuzzy expert systems. Fuzzy Sets and Systems, 58:3--40, 1993.

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I.B. Turksen and Y. Tian. Combination of rules or their consequences in fuzzy expert systems. Fuzzy Sets Systems, 58:3--40, 1993.

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