Download Computing with Words in Information/Intelligent Systems 1: by Lotfi A. Zadeh (auth.), Prof. Lotfi A. Zadeh, Prof. Janusz PDF

By Lotfi A. Zadeh (auth.), Prof. Lotfi A. Zadeh, Prof. Janusz Kacprzyk (eds.)

The quantity is the 1st one on the earth literature that is a entire, modern account on computing with phrases, a brand new path in greatly perceived clever structures, proposed and endorsed by way of Professor Zadeh, the founding father of fuzzy units thought and fuzzy good judgment. traditionally, computing was once fascinated by manipulation of numbers. in spite of the fact that, in recent times it turned progressively more visible that computing were encompassing not just this, but additionally manipulation on sign, sounds, photos and textual content; the latter features of computing have gotten progressively more proper. notwithstanding, the conventional manipulation of textual content (e.g., laptop translation, spell checking, etc.) doesn't disguise the mainstream of computing with phrases, typically the illustration and manipulation of propositions from traditional language describing operations and kinfolk. Such difficulties can't be solved through traditional tools of common sense, likelihood thought and numerical research. Fuzzy good judgment is proven to be a good instrument to deal with such difficulties.
Computing with phrases may possibly shape a foundation of a computational conception of perceptions encouraged by way of a striking human skill to accomplish a wide selection of projects simply at the foundation of imprecise and obscure details expressed in average language.
In Part 1 foundations of computing with phrases with regards to linguistic facets, fuzzy good judgment and approximate reasoning, granularity, calculations on verbal amounts, and common architectures for the implementation of computing with phrases are presented.

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Extra info for Computing with Words in Information/Intelligent Systems 1: Foundations

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It should be noted that the terms s 'i are built as conjunctions of negations of terms in S, while the terms s"i are disjunctions of terms in S. ;. (40) 43 (41) This last result means that the computation cost can be reduced by using the lower and upper approximations given by Eq. (37) and (38), in the same manner as in the disjunctive normal form. However, as a main difference with the conjunctive approach, it should be noted that it is no longer possible to perform the inference at the symbolic level directly on the initial rule base; this leads to search for a logical machinery.

3 - THE TWO LEVELS OF REPRESENTATION FOR FUZZY RULES AND THE TWO REASONING VIEWS Let U and Vbe two universes of discourse, S = {sl> ... , sm} and T= {II, ... , In} be two sets of terms whose meanings are defmed on U and V respectively. In the following, since we are dealing with four sets, indices will be added to the fuzzy meanings and descriptors with respect to the universe on which they are defmed. s;) and Mv{ljl are fuzzy sets of U and Vrespectively. Let us assume that we have a set of rules of the form "if Xis s; then Yis ~i)" for i = 1, m.

A t-norm), or a fuzzy implication. The set of rules defmes a fuzzy relation R on the Cartesian product U x V. , Dubois and Prade (1991). Depending on the chosen interpretation for the rules, we may have R = RT or R = R~, with (13) (14) where T is a conjunction operation, ~ an implication (and IlFTG = IlF T IlG, IlF~G = IlF~ IlG), and where U i and (li stand for rnax- and min-based dis- junction and conjunction respectively. This will be referred to as the numerical representation of the rules.

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