# Fuzzy associative matrix

﻿
Fuzzy associative matrix

A fuzzy associative matrix expresses fuzzy logic rules in matrix form. These rules usually take two variables as input, mapping cleanly to a two-dimensional matrix, although theoretically a matrix of any number of dimensions is possible.

Let's suppose we want to write fuzzy logic rules for a video game monster. We decide to start with two variables: hit points (HP) and firepower (FP). We might start with this:

This translates to:

IF MonsterHP IS VeryLowHP AND MonsterFP IS VeryWeakFP THEN Retreat IF MonsterHP IS LowHP AND MonsterFP IS VeryWeakFP THEN Retreat IF MonsterHP IS MediumHP AND MonsterFP is VeryWeakFP THEN Defend

...and so on. It is important to note that multiple rules can fire at once, and very often, they will. The distinction between "very low" and "low" is probably fuzzy at many points, and at such points, both rules will fire. If it is more "very low" than it is low, then the "very low" rule will generate a stronger response. The program will evaluate all the rules that fire and use an appropriate defuzzification method to generate its actual response.

An implementation of this system might use either the matrix or the explicit IF/THEN form. The matrix makes it easy to visualize the system, but it also makes it impossible to add a third variable just for one rule, so it is less flexible.

There is no inherent pattern in the matrix. It appears as if the rules were just made up, and indeed they were. This is both a strength and a weakness of fuzzy logic in general. It is often impractical or impossible to find an exact set of rules or formulae for dealing with a specific situation. For a sufficiently complex game, a mathematician would not be able to study the system and figure out a mathematically accurate set of rules. However, this weakness is intrinsic to the realities of the situation, not of fuzzy logic itself. The strength of the system is that even if one of the rules is wrong, even greatly wrong, other rules that are correct are likely to fire as well and they may compensate for the error.

This does not mean a fuzzy system should be sloppy. Depending on the system, it might get away with being sloppy, but it will underperform. While the rules are fairly arbitrary, they should be chosen carefully. If possible, an expert should decide on the rules, and the sets and rules should be tested vigorously and refined as needed. In this way, a fuzzy system is like an expert system. (Fuzzy logic is used in many true expert systems, as well.)

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Matrix - получить на Академике рабочий купон на скидку Строительный Двор или выгодно matrix купить с бесплатной доставкой на распродаже в Строительный Двор

• Fuzzy associative memory — Research on fuzzy associative memory (FAM) models originated in the early 1990 s with the advent of Kosko s FAM1,2. Like many other associative memory models, Kosko s FAM consists of a single layer feed forward fuzzy neural network that stores… …   Wikipedia

• Fuzzy logic — is a form of multi valued logic derived from fuzzy set theory to deal with reasoning that is approximate rather than precise. Just as in fuzzy set theory the set membership values can range (inclusively) between 0 and 1, in fuzzy logic the degree …   Wikipedia

• Fuzz — may refer to: *Vellus, a type of short, fine body hair on an animal *Tomentum, a filamentous hairlike growth on a plant *Focus (optics), a blur effect *Fuzzbox, an electric guitar distortion effect *A derogatory slang term for the police… …   Wikipedia

• List of matrices — This page lists some important classes of matrices used in mathematics, science and engineering: Matrices in mathematics*(0,1) matrix a matrix with all elements either 0 or 1. Also called a binary matrix . *Adjugate matrix * Alternant matrix a… …   Wikipedia

• Combs method — The Combs method is a method of writing fuzzy logic rules described by William E. Combs in 1997. It is designed to prevent combinatorial explosion in fuzzy logic rules. The Combs method takes advantage of the logical equality . Contents 1… …   Wikipedia

• FAM — or Fam can mean:* FAM (gang) * the Foreign Affairs Manual of the U.S. Department of State * file alteration monitor * Fat acceptance movement * fuzzy associative matrix * fuzzy associative memory * Free Aceh Movement * Fertility Awareness Method… …   Wikipedia

• Semantic memory — refers to the memory of meanings, understandings, and other concept based knowledge unrelated to specific experiences. The conscious recollection of factual information and general knowledge about the world,cite web… …   Wikipedia

• Function (mathematics) — f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a …   Wikipedia

• Interval arithmetic — Interval arithmetic, also called interval mathematics , interval analysis , and interval computation , is a method in mathematics. It has been developed by mathematicians since the 1950s and 1960s as an approach to putting bounds on rounding… …   Wikipedia

• Outline of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… …   Wikipedia