Diversity and Multi-Version Systems - Nuclear Power Plant Instrumentation and Control Systems for Safety and Security - page 227

identified fuzzy diversity score D ij , and each of
the defined linguistic terms with reference to d i (3)
(smallest distance). Then, a i (r) (r= 1, 2, 3) can be
defined as follow:

The exploitation stage: During this stage all
diversity strategies are ranked by using the col-
lective linguistic assessment obtained in the
previous stage, taking into account the cost of
each diversity strategies C ij . The rational diverse
strategy could be found with the following crite-
rion:

1
d

( )

r

α ij = , r = 1, 2, 3.

(15)

( )

r

ij

(r)

( )

β

3

d

* ij

S = argmax (17)

ij

ij

c

*

ij

If d i (3) = 0 it follows that a i (3) is equal to 1 and
the others are equal to 0. Then, a i (r) (r = 1, 2, 3)
can be normalized by:

where β i (r) represents the extent to which D ij
belongs to the r th defined linguistic terms; C i *
- cost of S ij reduced to

∑

C , ij
ij

- number of

( )

r

α

diversity strategy.
According to the cost-effective approach sug-
gested in the section, the strategy S 31 (the primary
RTS is FLASH - based RTS (A3PE1500, ProASIC
3/E family, Actel) and the secondary RTS - FPGA
SRAM - based RTS (EP1SGX40G, Cyclone IV
GX family, Altera)) might be recommended as a
secondary one.
The selection of the rational diverse alterna-
tive is based on processing of the expert's judg-
ment, represented as linguistic values on each of
the diversity criterion. Two additional diversity
strategies are represented. Each diversity strategy
is characterized by the fuzzy diversity score of
similarity (difference) between a proposed alter-
native for the secondary RTS and fixed primary
RTS. The cost of strategy realization is also taken
into consideration. The rational diversity strategy
is taken with the suggested criterion. This ap-
proach might be useful during the initial stage of
modernization of RTS, when a decision-maker
is suggested to complete the initial set of alter-
natives for the primary RTS, which has been
already determined. This stage is characterized
by a high degree of uncertainty. When the initial
set of diversity strategies is evaluated, it might
be recommended to amend the given decision by
application of metric-oriented methods.

( )

r

ij

β = , r = 1, 2, 3. (16)

ij

3

( )

r

∑

α

ij

r=1

Each β i (r) represents the extent, to which D ij
belongs to the r th defined linguistic terms. It can
be noted that if D ij , completely belongs to the r th
expression, then it is equal to 1, and the others
are equal to 0. The sum of values of these indices
for D ij , is equal to 1. Thus, β i (r) could be viewed
as a degree of confidence that obtained fuzzy
scores for all diversity strategies S ij belong to the
r th defined linguistic terms.
Results obtained for all diversity strategies are
represented in the Table 12.

Table 12. Results obtained for all diversity strate-
gies

Degree to which D ij belongs to the Initial
Terms

Diversity
Strategies

Same Nearly Same Different

S 31 0,12 0,39 0, 49

S 32 0, 36 0,28 0,38

S 33 0,33 0, 63 0, 04