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Figure 6.5 Example of valid Mbfs

6.6 Output Singleton

The Decision Processor uses a particular kind of

membership function called Singleton for its output

variables. A Singleton doesn’t have a shape, like a

traditional Mbf, and is characterized by a single

point identified by the couple (X, w), where w is

calculated by the Inference Unit as described

earlier. Often, a Singleton is simply identified with

its Crisp Value X.

Figure 6.6 Output Membership Functions

6.7 Fuzzy Rules

Rules can have the following structures:

if A op B op C...........then Z

if (A op B) op (C op D op E...) ...........then Z

where

op is one of the possible linguistic operators

(AND/OR)

In the first case the rule operators are managed

sequentially; in the second one, the priority of the

operator is fixed by the brackets.

Each rule is codified by using an instruction set, the

inference time for a rule with 4 antecedents and 1

consequent is about 3 microseconds at 20 MHz.

The Assembler Instruction Set used to manage the

Fuzzy operations is reported in the table below.

i-th OUTPUT

j-th Singleton

Table 6.1 Fuzzy Instructions Set

Instruction

Description

MBF

n_mbf Ivd v rvd

Stores the Mbf

n_mbf with the shape identified by the parameters Ivd, v and rvd

LDP

Fixes the alpha value of the input

n with the Mbf m and stores it in internal registers

LDN

Calculates the complementary alpha value of the input

n with the Mbf m. and stores the result

in internal registers

FZAND

Implements the Fuzzy operation AND between the last two values stored in internal registers

FZOR

Implements the Fuzzy operation OR between the last two values stored in internal registers

LDK

Stores the result of the last Fuzzy operation executed in internal registers

SKM

Loads the result of the last performed Fuzzy operation (stored in the temporary register K) in

the temporary buffer M.

LDM

Copies the value of register M in the data stack

CON

crisp

Multiplies the

crisp value with the last

ω weight

OUT

n_out

Performs Defuzzyfication and stores the currently Fuzzy output in the RAM

n_out location

FUZZY

Starts the Fuzzy algorithm

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