Deviant logic fuzzy logic haack pdf download

Graeme Heald. A short summary of this paper. Historically, fuzzy logic is founded upon a probability based many valued logic of Lukasiewicz. The fuzzy membership function and the probability density function closely resemble as they both have similar shapes and have values that range between zero and one. Vague linguistic terms can be viewed as being probabilistic. The fuzzy rules of inference can be identified with probabilistic inference of inductive reasoning. The centroid method of calculating the output of fuzzy control is identical to that used in probability density functions, is namely the mean.

Fuzzy logic could be probability as there as are so many close resemblances. Introduction Literature abounds highlighting the difference between fuzzy logic and probability [1, 2, 3]. On the contrary, probability deals with crisp notions and propositions, propositions that are either true or false; the probability of a proposition is the degree of belief on the truth of that proposition.

If we want to consider both as uncertainty degrees we have to stress that they represent very different sorts of uncertainty Zimmermann calls them linguistic and stochastic uncertainty, respectively. From an independent point of view, there are many similarities between fuzzy logic and probability. Haack has viewed fuzzy logic as an extension of classical logic and says that we do not need fuzzy logic [4]. From its inception fuzzy logic has had a close relationship with probability.

History Fuzzy logic is an infinite valued logic originally based upon the work of Polish logician Jan Lukasiewicz circa Lukasiewicz reasoning was based upon a future contingent matter whether he would be in Warsaw in the following year. He reasoned that at present the matter was neither true nor false but potentially either. It is thus possible, but not necessary, that I shall be in Warsaw at the given time. For if it were today true, then my future presence in Warsaw would have to be necessary, and this contradicts the assumption.

It belongs to the classes of t-norm fuzzy logics. Hence, fuzzy logic is founded upon an infinite valued probabilistic logic. Please see figure 1. This value, called membership value or degree of membership, quantifies the grade of membership of the element in X to the fuzzy set A.

Membership functions allow the user to graphically represent a fuzzy set. The x axis represents the universe of discourse, whereas the y axis represents the degrees of membership in the [0,1] interval.

A fuzzy membership function, however, lacks the normalisation requirement of a probability density function. The fuzzy membership function across the universe of discourse does not always sum to one, as shown in figure 1. Even among those forms of deviance that were extensively discussed in the edition, there are some—such as vagueness—whose account is now seriously defec- tive.

On the other hand, as a defense of a philosophical position, Deviant Logic retains its significance. The introduction goes a few steps in this direction. I have the same complaint about the two essays on fuzzy logic, which are included in the volume precisely to fill in at least one of the gaps of Deviant Logic.

The ar- gument for methodological extravagance ff. I find that this argument continues to apply, in spite of the work of an entire genera- tion of modern fuzzy logicians. One may also agree that the commercial suc- cess of fuzzy technology does nothing to substantiate the philosophical bona fides of fuzzy logic. But the crucial argument here is the one for the linguistic incorrectness of fuzzy logic f. Now, this sounds all right—but where is the evidence? Seventeen years later it is legitimate to ask whether any such detailed work has been done, and with what results.

With all this, it seems to me that the most interesting part of the book—as it stands today—is to be found in the essays on the nature of deductive rea- soning. And this is itself an instance of modus ponens. Of course the last step of MM' is deductively invalid being itself an instance of modus morons from lines 2 and 3. If Haack is right, this distinction collapses. Cognitive Science: General Works. Philosophy: Logic and Philosophy of Language. Get the latest updates on new releases, special offers, and media highlights when you subscribe to our email lists!

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