parameter is ed fuzzzy number

8/3/2019 Parameter is Ed Fuzzzy Number

http://slidepdf.com/reader/full/parameter-is-ed-fuzzzy-number 1/4

DESIGN OF A PARAMETERIZED FUZZY

PROCESSOR AND ITS APPLICATIONS

Bor-Tuw Chent, Yung-Sheng Chentt, an d Wen-Hsing Hsutvttt

fhStitute of Electrical Engineering, National ?sing Hu a University, Hsinchu, 'hiwan 300,R.O.C.

ftDepartment of Electrical Engineering, Yuan-ZeMtute d T c b m i o g ~ y u a n , biwan 320, R 0 . C .

ttthshte of Infornabon rice, Academia SiniCa,hiwan, R 0 . C .

Abspact - This paper desaibes the design of a hrameteriradPmcessar (PFP) which plays a role of the man-machine

interface. The set of instrnctions is designed for supporting the

versatility of the fuzzy information. And the architectureof the

PFP$ presented. Then. some applications of human inferenceand mtuitlve control are shown that the PFP is feasible.

1 INTRODUCTIONIn the human-machine system, the machine w i l l produce

numeric input to the plant and accept nu& output from theplant And, eople in this system are allowed to input to the plantBut here are some troubles for the interaction between people andmachinq that is, we talk o machine by sentences and words, andmachine just h o w numerical data Hence, in order to employ

trditional approaches of scientific thinking by formulation theproblems of humanistic systems and analyzing them in quantitativeterms, Zadeh[l, 5 31, DubOis[41, Miznmoto[S, 61 and many otherresearcher47, 8, 9, 10, 11, 121 proposed the ideas of fuzzy settheory one after another.

In this paper, based on parameterized fuzzy -131, wedesign a set of fuzzy instructions to provide some inferenu? rules

and f u y arithmetic for applications. And an architecture fm PFPis designed for handling these operations. Several experimentshave been applied to this PFP o confrkn its feasibility.

In Section II, we introduce the linguistic meanings and itsarithmeticoperations. SectionIDwi l l describe the instruction setAnd the algorithms of these operalions and the related WW are

outlined in Section W. urthermore, we present the applicaitonsin SectionV. And finally, we give a conclusion in Section VI.

11. FUZZY OPERATIONS

A. Linguistic meaningsOne of the basic tools for fuzzy logic and approximate rea-

soning is the notion_of a linguistic variab_le[l4], that is, the lin-

guisti. m e g . f A =I Some t ime ',B =' 4 short while ',and A (+) B can be learned as "more or less long t h e . " .

EL = a v y and B = l i g h we take the maximum operationof two fuzzy numbers, the answerwillbe"Heavy", otherwise, withminimum operation, we have the ''light'' answer. The meaningsof the othu operations of two linguistic values are similar.

Besides. the process of the inferencecan be shown as

( A n t l ) i f 2 = 2 then y = B( An t a ) 2 =A'

(Con)

Iy = B'

B . ArifhmeticBy the concept of the fuzzy set, the concepts of the bz~y

number[9] and the related arithmetic will be defined. A fuzzynumba in R is a fuzzy subset of R hat is convex and normal.

Then, therrwill exist the operations between hese fuzzynumbers.that is, the max-min convolution operations:

i.e., A (+) B, A -1 B, A XJ 8, A (4) ,A A) B ,A (v ) .Based on the fuzzg dation R = (((2, Y ) , P A 2, Y) ) I(2, Y) ){EX x Y } we canknow that R, s more feasible than the otherrelahon for inference(5,7], therefore we choose it to be concerned.

Then, ombined with the ma-& composition op&onare the general inference method, it canbe written as B' = A o R ,that is,

111. THE INSTRUCTION SET

A. Datu form&Because the nconsistentdomain and a largeamount datawi l l

drop the performance of the disuete type fuzzy number. Basedon the L-Rfuzzy reference fmtion[9], we use continue type datato p e n t t and after the modification of the parametas. just fourparameters are used to p s m t a fuzzy numba[l3]. In Fig.1, wecall the A and B main values and the a and b margin values.

a : i b

A B

D

31 I5 IA I B l l b

Figure 1 The data format of a fuzzy n u m b

According to our test, we find that general discrete-typefuzzy number seems to behave as similar as ou r parameterizedfuzzy number. That s to say. though we may approximate somecomplicated fuzzy number by considering the tradeoffbetweea theerror and the process complexity, we choose the continuous datatype which seems to be feasible and acceptable.

61692CH3179-9/92/$3.00 0 992 IEEE



B. InstructionsEighteen fuzzy nstructions proposed for our PFP are shown

in Table 1.

6

7

8

9

10

bo1 Instruction I Function 1

FMMdstSrc minimum

FINCsrc,x data shift

FZFdst,(a,b) fuzzification

FMNsrc defuzzification

FTSTsrc,src two fuzzynumbers’ distance

addition

15

16

17

FMOVdst,src data movement

FXCHGdst,src data exchangement

FPUSHsrc push into stack

11) FDTdst,src

121 FCNsrc I centralimtion

1 two fuzzy numbers’ crosspoint

(131 FDLsrc I dilation 1114 I MNCOM dstsrcsrc I max-min comwsi tion

1181 FPOPsrc I DOD ut of stack ITable 1 The instruction set.

IV. HARDWARE DESIGN

A. Algorithm of the fun y operationsAt fist, the architecture of the ALU is presented asFig.2.

Figure 2 ALU of the Fuzzy processor.

In the following, the algorithmsof fuzzy easoning, inferenceprocess and fuzzy arithmetic in the ALU will be described. Wepresent the data flow of the multiplication in Fig.3.

Algorlthm of the reasoning and inference

Stepl. Constract the relation. (reasoning)

The relation is based on the ratio of the margins.Load the margins of two registers. Execute the division,then store to bofl and bun.Exchange two values of margin. Execute the division,and put it to V1 and M1.

a

b

Step2. Max-min composition. (inference)

a.b.

c.

Load the A’, inferring, store results to registers.Change the other pair of ratio (other side), inferring,store results to register.Load the temporal results, choose the minimum valueon the left side, choose the maximum value on the rightside.

Update the result to data format..

Algorithm of Add ition/ Subtraction/ MultipliicationiDivision/ Maximum/ MinimumAssume dst= A , B , a, b) src= (C,D, , d ) .

Stepl. Load the main values of two registers.

if operation = Subtraction or Division, exchange thepositions of C and D in loading.

Step2. Execute the operations.Step3. Load the margin value of two registers.

if operation = Subtraction or Division, exchange thepositions of c and d in loading.

If operation = Multiplication or Division then us e bufland buf2 to save the temporal values and reload marginvalues again to execute the operation.else execute the operation.

Step4.

loadc lmd d ,;npur bru ........................

4 i

4...........OU!+Ul

b u s -- ....... ~ ..........A X 2 W D

inplthp ...................- 1

maatM I+ iBd

Figure 3 Data flow of multiplicaiton ofthe margin values. (Continued . . .

617



A. inference

In our experiences, it is known that the distance, the rainfalland the vertical height will influence the time of our travel and wewill use the result to decide the path that can satisfy the low cost of

investment with the large amount of interest received. The detailsof the inference procedure and the result are in Fig5 and Fig.6.Fuzzy inference of the parameterized fuzzy number is proved to

be like human thinking.

loadc loaddm p t b.oa . ... .-t t t I 4

euzzy numbcr

Figure 3 Data flow of multiplicaiton of the margin values.

Anferencend the other operations are similar to these described above.We can get them by the similar process.

B. The F u u y Processor

The configuration of the whole system is shown in FigA.

MNCoM IFZF IFADDFMUL I

Pind the linguisticvaiabls for he

mix rcault ofoutputsI ITST I-ontinue‘M’

Figure 5 One stage of the given inference procedure.

htann c

lddreaa

m a

control

signal

Figure 4 Architecture of the proposed processor. -410

P IDue to the data format, the structure of the processor is level-

by-level and regular. So, it is extensible for the multi-parameterfuzzy number just only rearranging the control signal instead ofchanging the whole structure.

-t

V. APPLICATIONS

Based on the development described above, we have ap-plied to some examples, e.g. human inference, fuzzy control anddecision-making. And, in this section, we will propose two ofthem to describe the applicaions - nference and fuzzy control. Figure 6 Result of the given inference procedure.

618



B . F u u y control for heat processInstead of the complicated mathematical model, we can ma-

nipulate fuzziness and achieve control objectives by incorporatinglinguistic control rules and the fuzzy number.

The flow chart of the process is described in Fig.7. Andthe results are shown in Fig.8. The final temperature has fit thedesired. So, the purpose of the instruction is proved again.

21

' The processed system

* Heat loss =AT'~K*/~AT'-water temp - r o o m ern1

AT= increasing temp.

A =Watcr tcmp. - target tcmp.

. . -. ~ .....- ... .. . _ -. -. . -.. :. . . ._

AH

I fuzzify IFZFFMOV

Idefuzzify 1FMN

[ -2Z5Jn e ule is

W & is m,A~ i sL.

and, update me fuzzy dataNL,PL

accordingto he absolute value of&

MNCOM

Figure 7 Flow chart of the designed heat process.

32

315 ~ .... ..... )..._ i.-

Figure 8 Two results of the designed heat process.

619

Based on the result, we believe that these instructions can beused to many other fields of the applications. Combined with theH/W in the previous section, not only the fast processing speedit has, but also the general purpose for applications it approaches.More comprehensive information about the PFP, a related thesis[15] should be further read.

VI. CONCLUSION

This paper has described a parameterized fuzzy processor(PFP), fuzzy instruction set and its applicaions. Based on thelinguistic operations, the algorithms of the instructions and theoutline of the PFP areproposed. And in the successive experiment,we comlirm the feasibility of these instructions. We conclude thatthe PFP does really have the powerful capability for performing thehuman-thinking and it can overcome the trouble of the interactionbetween people and machine. So PFP is very suitable for playingthe role of man-machine interface.

AcknowledgementThis research has been supported by a grant #NSC 814408-

E007-15 from National Science Council, R.O.C.

REFERENCES

[1]L A. Zadeh, "Fuzzy set," Inform. and Control, vol. 8, pp. 338-353,1965.

[2]L A. Zadeh, "Outline of a new approach to the analysis of complexsystems and decision process," IEEETrans.Syst., Man, Cybern ..vol. 3,pp. 2 W , an. 1973.

[3]L. A. Zadeh, "A fuzzy-algorithmicapproachto the definition of complexor imprecise concepts," Int.,J.,Man-Machine Studies. vol. 8, pp. 249-291, 1976.

[4]D. Dubois and H. Prade, "Outline of fuzzy set theory : n ntroduction,"in Advances in fuzzy set theory and application (R. M.M. Gupta andR.R. Yager, eds.), pp. 27-48. Amsterdam: North-Holland, 1982.

[5]M. Mizumoto and H.-J. Zimmermann,"Comparison of fuzzy reasoningmethods." Fuzzy Sets and System, vol. 8, pp. 253-283, 1982.

[6]M. Miannoto, "Fuzzy inference using maxdrastic composition in thecompositional rule of inference," in Approximute Reasoning in DecisionAnulysis (M.M. Gupta and E. Sanchn,eds.), pp. 67-76, Amsterdam:

[7]S. Fukami, M. Minunoto, and K. Tanaka, "Some considerations onfuzzy conditional inference," Fuzzy Sets and Systems, vol. 4, pp. 243-

[8]A. Kaufmann. Introduction to the Theory of Fuzzy Subsetr. Florida:Academic Press, 1975.

[9]A. Kaufmann y d M.M. Gupta, Introduction to Fuzzy Arithmetic :Theory and Applrcutton. New York: Van Nostrand Company, 1985.

[10]B.R.Gaines, "Foundations of fuzzy reasoning," Int.,J. , Man-MachineStudies, vol. 8, pp. 623468, 1976.

North-Holland, 1982.

273. 1980.

[11]James J. Buckley, "Fuzzy i/ o controller,"Fuzzy setsandsystem, vol. 43,p ~ .27-137, 1991.

[12]Chiou-Fang Wu. A Generalized Fuzzy Machine. Instituteof ElectricalEngineering, National Tsing Hua University, Hsinchu, Taiwan, R.0.C:M.S. 'Thesis, 1990.

(13lF.DiCesare.Z.Sahnoun, and P.P.Bonissone, "Linguistic summarization

of fuzzy data," Information Science, vol. 52, pp. 141-152, 1990.

[14]H.-JZimmemann, Fuzzy Set Theory - and If.s Applications. Boston:Kluwer-Nijhoff Publishing. 1985.

[lS]Bor-Tow Chen, Design and Simulation of A Fuzzy Processor. Instituteof Electrical Engineering, National Tsing Hua University, Hsinchu,Taiwan, R.0.C: M.S. Thesis, 1991.

parameter is ed fuzzzy number

Documents