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Beginning i)=!U>B_0
1. In this paper, we focus on the need for jz(}P8
2. This paper proceeds as follow. b$)b/=2
3. The structure of the paper is as follows. xb$eFiQ
4. In this paper, we shall first briefly introduce fuzzy sets and related ma.yI};$
concepts OV ~|@{6T
5. To begin with we will provide a brief background on the "2:]9j
Introduction k6-.XW
1. This will be followed by a description of the fuzzy nature of the 44_
7gOZ
problem and a detailed presentation of how the required A7@5lHMF
membership functions are defined. 3Tv;<hF
2. Details on xx and xx are discussed in later sections. /N(L52mz
3. In the next section, after a statement of the basic problem, various ]l.y/pRP5[
situations involving possibility knowledge are investigated: first, an l%]S7|PKx
entirely possibility model is proposed; then the cases of a fuzzy >
(+g:p
service time with stochastic arrivals and non-fuzzy service rule is F aO=<jYi
studied; lastly, fuzzy service rule are considered. ;\yY*
Review qXO@FW]
1. This review is followed by an introduction. ImQ?<g8$
2. A brief summary of some of the relevant concepts in xxx and xxx is v~i/e+.h>y
presented in Section 2. r<4FF=
3. In the next section, a brief review of the .... is given. <wV?B9j
4. In the next section, a short review of ... is given with special regard dX|(n.}
to ... 3D>syf
5. Section 2 reviews relevant research related to xx. }Jkz0 JY~
6. Section 1.1 briefly surveys the motivation for a methodology of Kc~h
action, while 1.2 looks at the difficulties posed by the complexity of 9')
systems and outlines the need for development of possibility lN"%~n?
methods. "e<Z$"7i
Body )Cl!, m)~
1. Section 1 defines the notion of robustness, and argues for its ZaYux-0]kF
p%A
s6
.
importance. ab4(?-'-
2. Section 1 devoted to the basic aspects of the FLC decision-making OL|_@Fv`A
logic. QfjgBJo%
3. Section 2 gives the background of the problem which includes xxx Z%_"
-ENT
4. Section 2 discusses some problems with and approaches to, 2t'^
natural language understanding. 1I< <`7'
5. Section 2 explains how flexibility which often ... can be expressed 9AQMB1D*v4
in terms of fuzzy time-window 04{*iS95J
6. Section 3 discusses the aspects of fuzzy set theory that are used in b?D
hhf
the ... \[</|]'[
7. Section 3 describes the system itself in a general way, including R_iQLBrd
the ….. and also discusses how to evaluate system performance. oJ}!qrrH
8. Section 3 describes a new measure of xx. IK~'ke
9. Section 3 demonstrates the use of fuzzy possibility theory in the UzZzt$Kw
analysis of xx. V2-fJ!
10. Section 3 is a fine description of fuzzy formulation of human ,CACQhrng
decision. Ak(_![Q:q\
11. Section 3 is developed to the modeling and processing of fuzzy Bn>"lDf,
decision rules OhUEp g[
12. The main idea of the FLC is described in Section 3 while Section 4 ico%_fp
describes the xx strategies. }"k+e^0^
13. Section 3 and 4 show experimental studies for verifying the ?"oW1a\
proposed model. <\i}zoPO
14. Section 4 discusses a previous fuzzy set-based approach to cost Vgzw ['L}
variance investigation. Qoa gy L
15. Section 4 gives a specific example of xxx. 1eiV[z$?
16. Section 4 is the experimental study to make a fuzzy model of v/ dyu
memory process. Mf [v 7\
17. Section 4 contains a discussion of the implication of the results of ;IklS*p]
Section 2 and 3. rof&
O
18. Section 4 applies this fuzzy measure to the analysis of xx and (N63k1M
illustrate its use on experimental data. z
D&5R/I
19. Section 5 presents the primary results of the paper: a fuzzy set 3awh>1N2W
model .. !VNLjbee.
a;},y|'E
20. Section 5 contains some conclusions plus some ideas for further ssdpwn'
work. cT8b$P5w
21. Section 6 illustrates the model with an example. 2?=R_&0Q
22. Various ways of justification and the reasons for their choice are y]1:IJL2;
discussed very briefly in Section 2. ^Rgm3?7
23. In Section 2 are presented the block diagram expression of a :wlX`YW+e
whole model dy>iIc>
of human DM system 014p = W
24. In Section 2 we shall list a collection of basic assumptions which oH;0_!
a ... scheme must satisfy.
,k% \f]a
25. In Section 2 of this paper, we present representation and Qi&!Ub]
uniqueness theorems for the fundamental measurement of fuzziness 'A#`,^]uLF
when the domain of discourse is order-dense. hXxgK
i%
26. In Section 3, we describe the preliminary results of an empirical ^F5Q(A
study /^#8z(@B
currently in progress to verify the measurement model and to e1*<9&S
construct membership functions. {Q/XV=
27. In Section 5 is analyzed the inference process through the two K YSyz)M}
kinds of inference experiments... cmw2EHTT<
This Section !/1aot^(
1. In this section, the characteristics and environment under which (}$pf6s
MRP is designed are described. }|MPQy
2. We will provide in this section basic terminologies and notations )qgcz<p?W
which are necessary for the understanding of subsequent results. $L~?!u&N
Next Section U"Gg
,
2. The next section describes the mathematics that goes into the
@P1#)
computer implementation of such fuzzy logic statements. 6 WD(
3. However, it is cumbersome for this purpose and in practical g{t)I0xm
applications the formulae were rearranged and simplified as S4r-s;U-v/
discussed in the next section. W%3<"'eP
4. The three components will be described in the next two section, (\CT
"u-
and an example of xx analysis of a computer information system will X:aLed_{f
~OuK ewr\
then illustrate their use. .7h:/d
Y:
5. We can interpret the results of Experiments I and II as in the \Vc-W|e
following sections. xWZ87
6. The next section summarizes the method in a from that is useful /QA:`_</oh
for arguments based on xx ?3f-"K_r
Summary =Nyq1~
1. This paper concludes with a discussion of future research mes/gqrJ1I
consideration in section 5. \`FpBE_e)
2. Section 5 summarizes the results of this investigation. 3RwDIk?>%
3. Section 5 gives the conclusions and future directions of research. oS2L"#
4. Section 7 provides a summary and a discussion of some extensions E%
B:6
of the paper. !x%$xC^Iz
5. Finally, conclusions and future work are summarized 3lkz:]SsE
6. The basic questions posed above are then discussed and E46+B2_~zk
conclusions are drawn. Kd<c'!
7. Section 7 is the conclusion of the paper. p!b_tyJ
Chapter 0. Abstract lk<}`#( g
1. A basic problem in the design of xx is presented by the choice of a C(4r>TNm
xx rate for the measurement of experimental variables. <k
41j=d
2. This paper examines a new measure of xx in xx based on fuzzy cft'% IEs
mathematics which overcomes the difficulties found in other xx JemB[
measures. M5C%(sQ$
3. This paper describes a system for the analysis of the xx. 2^V/>|W>w
4. The method involves the construction of xx from fuzzy relations. y3^>a5z!x
5. The procedure is useful in analyzing how groups reach a decision. UWf@(8
6. The technique used is to employ a newly developed and versatile ZQ MK1
xx algorithm. q'% cVM
7. The usefulness of xx is also considered. r_p4pxs
8. A brief methodology used in xx is discussed. *(w#*,lv
9. The analysis is useful in xx and xx problem. kuQ+MQHs
10. A model is developed for a xx analysis using fuzzy matrices. dXBXV>rbB
11. Algorithms to combine these estimates and produce a xx are EN\
uX!
}O7!>T
presented and justified. V1d{E 0lM
12. The use of the method is discussed and an example is given. d i;Fj
13. Results of an experimental applications of this xx analysis It@1!_tO2
procedure are given to illustrate the proposed technique. fxcCz 5
14. This paper analyses problems in $Fr>'H+i
15. This paper outlines the functions carried out by ... xO` `X<
16. This paper includes an illustration of the ...
Y/Dah*
17. This paper provides an overview and information useful for
f:!b0j
approaching ej^pFo
18. Emphasis is placed on the construction of a criterion function by {~=Z%Cj2Q
which the xx in achieving a hierarchical system of objectives are 6M)
4v{F
evaluated. \c .^^8r
19. The main emphasis is placed on the problem of xx `;\<Fr
20. Our proposed model is verified through experimental study. -Y:^<C^^&8
21. The experimental results reveal interesting examples of fuzzy 4Ww.CkRG
phases of: xx, xx Gd:fh5u':
22. The compatibility of a project in terms of cost, and xx are likewise 7c7:B2Lq
represented by linguistic variables. :TTZ@ q
23. A didactic example is included to illustrate the computational 'U%L\v,
procedure V+y yy-/
Chapter 1. Introduction /P}Wp[)u
Time +bC=yR
1. Over the course of the past 30 years, .. has emerged form intuitive #sg^l
>/*
2. Technological revolutions have recently hit the industrial world {rE]y C^
3. The advent of ... systems for has had a significant impact on the E#I^D/0
4. The development of ... is explored /#]4lFk:h
5. During the past decade, the theory of fuzzy sets has developed in a
}@'Zt6+tS
variety of directions ~ v21b?
6.The concept of xx was investigated quite intensively in recent years ,vE)/{:d
7. There has been a turning point in ... methodology in accordance YlP8fxS
with the advent of ... N %K%0o-
8. A major concern in ... today is to continue to improve... <dA D-2O+
9. A xx is a latecomer in the part representation arena. cf7UV6D g
PE7D)!d
T
10. At the time of this writing, there is still no standard way of xx 7yDWc m_y
11. Although a lot of effort is being spent on improving these P+j5_ V{\b
weaknesses, the efficient and effective method has yet to be ,^#{k!uaC{
developed. U<"@@``+N
12. The pioneer work can be traced to xx [1965]. v[UrOT:
13. To date, none of the methods developed is perfect and all are far ^o@N.+`&<
from ready to be used in commercial systems. Vw~st1",[
Objective / Goal / Purpose s;[OR
1. The purpose of the inference engine can be outlined as follows: #3WKm*T/
2. The ultimate goal of the xx system is to allow the non-experts to j4fv-{=$
utilize the existing knowledge in the area of manual handling of loads, 6bXP{,}Gp
and to provide intelligent, computer-aided instruction for xxx. nR2pqaKc
3. The paper concerns the development of a xx 8M DX()Bm
4. The scope of this research lies in 1m5=Nu
5. The main theme of the paper is the application of rule-based GqT0SP
decision making. +"HLx%k
6. These objectives are to be met with such thoroughness and [|)Eyd[G
confidence as to permit ... oieZopYA
7. The objectives of the ... operations study are as follows: 8>KBh)q
8. The primary purpose/consideration/objective of ZI0C%c.~
9. The ultimate goal of this concept is to provide pg4J)<t#
10. The main objective of such a ... system is to I5$@1+B
11. The aim of this paper is to provide methods to construct such <Z -d5D>
probability distribution. l1utk8'-
12. In order to achieve these objectives, an xx must meet the mK>c+ u)
following requirements: 4 )U,A~!
13. In order to take advantage of their similarity \en}8r9cy
14. more research is still required before final goal of ... can be h ?Ni5
completed ,vn
HEY&
15. In this trial, the objective is to generate... $<~o,e-4
16. for the sake of concentrating on ... research issues {);S6F$[3
17. A major goal of this report is to extend the utilization of a recently W_C#a'$
developed procedure for the xx. C]xKdPQj%
,dG2[<?o
18. For an illustrative purpose, four well-known OR problems are bi^Xdu
studied in presence of fuzzy data: xx. OjUZ-_J
19. A major thrust of the paper is to discuss approaches and has \W\(
strategies for structuring ..methods %pR:.u|
20. This illustration points out the need to specify vuOixAkw
21. The ultimate goal is both descriptive and prescriptive. $eI=5
22. Chapter 2. Literature Review sI7<rI.t){
23. A wealth of information is to be found in the statistics literature, ?0U.1N
for example, regarding xx xw)$).yc
24. A considerable amount of research has been done .. during the #K5)Rb-H
last decade ";&5@H|
25. A great number of studies report on the treatment of D]{#!w(d
uncertainties associated with xx. :z^VI M
26. There is considerable amount of literature on planning /MErS< 6
27. However, these studies do not provide much attention to }i"\?M
uncertainty in xx. h=fzX.dt
28. Since then, the subject has been extensively explored and it is u; c)Tt
still under investigation as well in methodological aspects as in Jvk!a~e
concrete applications. y rSTU-5u
29. Many research studies have been carried out on this topic. Y"x9B%e
30. Problem of xx draws recently more and more attention of system C6$F.v
analysis. jJ}3WJ
31. Attempts to resolve this dilemma have resulted in the ?!h
jI;_&
development of ]dx6E6A,
32. Many complex processes unfortunately, do not yield to this IfK%i/J
design procedure and have, therefore, not yet been automated. XS L*e
33. Most of the methods developed so far are deterministic and /or ku@sQn
probabilistic in nature. -v'|#q
34. The central issue in all these studies is to BrWo/1b
35. The problem of xx has been studied by other investigators, YA";&|V
however, these studies have been based upon classical statistical #
s 4v0auK
approaches. 7S
+YQ$_
36. Applied ... techniques to b3>`%?A
37. Characterized the ... system as V Z#@7t
*J ]2"~_.
38. Developed an algorithm to F5hOKUjv
39. Developed a system called ... which R\^n2gK
40. Uses an iterative algorithm to deduce lURL;h
41. Emphasized the need to 8?YWE62
42. Identifies six key issues surrounding high technology ,#NH]T`c1
43. A comprehensive study of the... has been undertaken I;Sg9`k=
44. Much work has been reported recently in these filed >=T\=y
45. Proposed/Presented/State that/Described/Illustrated/ @@?P\jv~
Indicated/Has shown / showed/Address/Highlights (jV_L1D
46. Point out that the problem of p$qp
C$F
47. A study on ...was done / developed by [] 55mDLiA
48. Previous work, such as [] and [], deal only with m(B,a,g<
49. The approach taken by [] is
+d$
l1j
50. The system developed by [] consists YH:murJMZ
51. A paper relevant to this research was published by [] w2o%{n\L
52. []'s model requires consideration of... `egyk)"aM
53. []' model draws attention to evolution in human development A9?h*/$
54. []'s model focuses on... O%
>FKU>(?
55. Little research has been conducted in applying ... to 3U_,4qf
56. The published information that is relevant to this research... 7%%FYHMO:
57. This study further shows that zFR=inI
58. Their work is based on the principle of )\!-n]+A
59. More history of ... can be found in xx et al. [1979]. zUe)f~4
60. Studies have been completed to established .y)Y20=o!
61. The ...studies indicated that %Ob#GA+
62. Though application of xx in the filed of xx has proliferated in Nydhal00
recent years, effort in analyzing xx, especially xx, is lacking. kW
7$
Problem / Issue / Question o:.6{+|N
63. Unfortunately, real-world engineering problems such as b{Qg$Z
JeR
manufacturing planning do not fit well with this narrowly defined *<5zMSZO
model. They tend to span broad activities and require consideration p5`d@y\hj
of multiple aspects. " iKX-VIl
64. Remedy / solve / alleviate these problems /IkSgKJiz\
67. ... is a difficult problem, yet to be adequately resolved Xyf7sHQ
W{{{c2 .
68. Two major problems have yet to be addressed =`
%iv|>r0
69. An unanswered question ]h`<E~
70. This problem in essence involves using x to obtain a solution. 2".^Ma^D!
71. An additional research issue to be tackled is .... w|;kL{(W
72. Some important issues in developing a ... system are discussed EE^
N01<"\
73. The three prime issues can be summarized: jDaWmy<ha
74. The situation leads to the problem of how to determine the ... (t{m(;/
75. There have been many attempts to v)TFpV6b{p
76. It is expected to be serious barrier to Rzolue 8
77. It offers a simple solution in a limited domain for a complex gA&+<SK(
problem. oI!L2
1. There are several ways to get around this problem. E@f2hW2
2. As difficult as it seems to be, xx is by no means new. !.[N(%"
3. The problem is to recognize xx from a design representation. q*h1=H52
4. A xx problem can trace its roots to xx. r%QnV0L^
5. xx [1987] used a heuristic approach to simplify the complexity of g.cD3N
the problem. vE9M2[TJA
6. Several problems are associated with them. X1P_IB
7. Although some progress has been made in this area, at least two $p}
/&
major obstacles must be overcome before a fully automated system `wyX)6A|bt
can be realized. Ix"hl0Kh
8. Most problems in practice are complicated ${/"u3a_
9. More problem surface here. &|:T+LVv$+
10. Hamper effort toward a xx system ""dX4^gtU
11. In order to overcome the limitations due to incomplete and BBub'
imprecise xx knowledge, a xx program has been developed, which "/EE$eU
bases its knowledge upon the statistical analysis of a sample bEXm@-ou
population of xx QSn%~o05
12. The above difficulties are real challenges faced by researchers t*fG;YOg
attempting to develop ")q{>tV
13. This type of mapping raises no controversy to the issue of .>(?c92
membership function determination. 4b" %171
14. However, attempts to quantify the xx have met both theoretical T4W"!4[
and empirical problems. doCWJ
IZm_/
15. It has become apparent that in order to apply this new !U,^+"l'GP
methodological framework to real-world problems and data, we have /nK)esB1L
to pay attention to the problems of xx and xx. XsldbN^6
Chapter 3. Proposed methodology ^J8sR4p#
Assumption X^tVq..0
1. In the case when the assumption of a xx seems to be too AUloP?24
restrictive or inadequate, the formulation with Fuzzy termination e JMD8#
time, i.e. given by a fuzzy set in the space of control stages, may be )shzJ9G
applied. w8t,?dY
2. We assume here the fuzzy constraints to be state-dependent, and hT&,5zaWdv
the fuzzy goal to be the same for all the control states, xx, which &gkGH<oaX
stems from the problem's nature. :E|HP#iwu
3. An approach to the solution of this problem is presented under the UarU.~Uqi
assumption that the sampling rate Decision can be made prior to the (}Ql#q
K
execution of the experiment, as opposed to being made while the (/&IBd-
experiment is in progress. n:?fv=9n
4. Another assumption made above is that there are precise odds at ]JX0:'x^
which the expert is indifferent. {
~yj]+Im
5. Main simplifying assumptions are: D[)")xiG
6. This, in our view, is a questionable assumption. j.$#10*:
Outline / Structure / Module 7N^9D
H{`
1. An outline of the research 0fvQPs!O
2. Information is incorporated within the scheme #&.&Uu$
3. Is built into ... structure O6P0Am7s
4. A nice modular structure. BRP
9j
y
5. The principles of ... are applied as modularized criteria dtQ>4C"N
Classification ^*C+^l&J!
1. A xx system comprises three main components: KQ3]'2q
2. Must decompose the original .. into a set of .. >Dpz0v
3. Consists of the following steps: Nt#zr]Fz
4. This is summarized in the following steps: ;$@7iL
(veGztt
5. Can be broadly classified into the following areas: SsDz>PP
6. Can be characterized by its function of effectively processing the $]4^ENkI
7. Can allow further breadth of application of ...into more FG7}MUu
8. The following steps should be followed /-<S F T`
9. xx can be classified by a different ways. i TY4X:x
10. Based on the xx, one may classify xx into the following: [JFmhLP9
11. This catalog may change due to wear, breakage, and purchasing. IpY R
System !*.mcIQT
1. Unlike many conventional program, expert systems do not i]*Wt8~!
usually deal with problem for which there is clearly a right or wrong L,.Ae
i9
answer. [
P2$[|IM
2. The system consists of both ... and ... [AQ6ads)
3. The system has a hierarchical modular architecture organized on UiA\J
three levels. ?:Y{c#w>
4. expert system domains are area of expertise elb|=J`M0
5. To develop a xx system for xx, the following factors must be 8Wid.o-U
considered: KDgJ~T
6. The system has been developed / designed to determine Ae:(_UJz
7. The system has proven to be able to ?ltTJ(Po
8. The domain in which an expert system operates is a particular r#*kx# "
domain >-
]tOH,0
9. The system comprises a ... with KgX~PP>
10. The system is [feature-oriented ] / based on the ... technique 2V_C_5)1
11. The system environment must be relatively stable `h_,I R<
12. The system is utilized to generate, load, store, update and I\PhgFt@O
retrieve ... n[lf==R
13. The development of a xx system has two stages: xx stage and xx C_=! ( @`8
stage. |E0>-\6
14. The most essential part of .. system is the ... MPA<?
15. The successful developments in ESs have made them an 1Vt7
[L*
important tool in the development of 5j1}?0v_
16. An automated system was developed for *qYcb}
]
17. In this case, the system can be considered to be generative. ,i#]&f`c;5
-}1S6dzr
18. An interactive automatic ... system FOgF'!K
19. A …. is commonly thought of as a truly integrated .. system jFpXTy[>
20. Should be capable of being generated from a ... system !YSAQi
;I
21. xx is an important part of the integrated system. G!T)V2y
22. The model consists of four rule bases, each of which addresses a Oyhl*`-*t
separate problem in the hierarchy of scheduling decision. qlD+[`=b
23. The rule bases are linked to each other in a chin-like manner in +r *f2\S
the sense that the consequent of one rule base constitutes a part of kM|akG
the antecedent of the next rule base. Bx
0^?>
24. The rule base consists of all possible combinations of the pL8+gL
linguistic terms associated with the linguistic variable of the ?Q;8D@
antecedent of a rule. r<c yxR
~
Computer System "12.Bi.O"[
1. The system has been implemented using Prolog language in an zI8Q "b
MS-DOS environment. Prolog was chosen because it offers a well *,{. oO9#
known and flexible environment in which fuzzy reasoning may be 1B
w
CJ7?8
easily implemented. 2;r(?ebw
2. The current version of the xx program when compiled with J!O5`k*.C
WATFOR77 results in an executable code of about 270K bytes. YW9 [^
Typical run time, when run on a XX computer (an IBM compatible KL,=Z&.<=
machine) operating at 4.77 Mhz with 640K RAM, ranges from 10 min BRYhL|d~.
to 2h, depending on the size (or complexity) of the problem. -q|K\>tgU
3. Time consuming procedures have been implemented in ~V[pu
C-language and directly linked to the Prolog environment. z
g+78
4. The xx process, once the xx's data has been entered, requires &0SX*KyI
approximately 180 seconds. ]]`hnzJX
5. It should be noted that the computation was done with a 20 Hhz, !}|n3wQ
80386..209;based microcomputer equipped with a 80387 math R}c,ahd
co-processor. @B
%m,Mx
6. The computer programs used for the analyses, one based on the xx XWV
)
method and the other based on the new method, were written in wv<D%nF2|
FORTRAN with a compiler that supports the math co-processor. 8PB(<|}u
7. Lisp, Prolog give maximum flexibility but also maximizes fs+l
`}#(Ze*V:
development time. (f^WC,
l Internal representation is the way a model is represented in the f9u ^/QVS&
computer. eU'DQp*
l An interactive menu-driven procedure is used in this study Er^ijh,
l Shell can be develop very fast at the cost of time fairly severe 2Un~Iy
limitations. j9n3
l While there is no measurable saving of time for the case involving u"XqWLTV
five criteria, the saving is dramatic for the case involving 10 criteria |E-/b6G
-- the computation time reduces from 10 hr 40 min to about 1 min. r,X5@/
l This combination is being implemented in an objected-oriented U1bhd}MoR
programming environment (Smalltalk-80 system) to solve problems DKgwi'R
encountered in construction xxx. m6tbN/EJZ
Method / Approach / Study / Process Model / Equation /Algorithm / l4?o0;:
)
Rule / Formula / Technique Jaz|b`KDj
l A discussion is presented of a problem-solving system N|K,{
p^li
l To improve the efficiency of the method, the following approach ^IGutZov
may be applied. {E1g+><
l In order to an investigation was made to find the causes of the WV}<6r$e
l Although large collections of rules and equations have been 2*Hw6@Jj
complied, none are generally accepted Ac;rMwXk#
l This approach will be explained and discussed thoroughly in the rStfluPL
body of the report. P/snzm|@
l This can be accomplished by Z3?,r
[
l This algorithm to compute the total cost can be described step by //cj$}Rn!
step as follows: im{'PgiR
l The above preliminary analysis has provided important z1[2.&9D-
information \U;4\
l Various methods have been proposed for selecting an optimum... 7^,C=2
l These concepts have been applied to WqP>cl2Lm
l On the basis of the concept mentioned above, WGjT06a\
l This can be achieved by {;
0j9rr
l This fact suggests that a new concept y;Xb."e~
l This was accomplished by taking ... W$LaXytmak
f"t\-ux.b
l The preparatory stage is very time consuming process. p6m](Jg
l Test are performed for validity, completeness, and compatibility ^ZnlWZ@r
l There is little hope of achieving successful ... {wMw$Fvf
l There has been an increasing awareness of the potential of using Q!K@
most ..so far made have not taken this approach, with the exception !Cxo4Twg
of 0STtwfTr:
l Only a few studies can be found. =g4^tIYq
l It is a very tedious process to go through 2?YN8
n9n
l It is only when .. has been completed that .. may be effected Awl4*J~
l The entire interpretation process is conducted in one's head. fP>_P#gZ
l These approaches are sometimes very tedious. W
5,e;4/hL
l Several techniques can be used jqq96hP,
l A polynomial parametric model can be written as [the Pk/{~!+
$
following]/[follows]: cF!ygz//
l A xx model is constructed/formulated using xx. t"M&Yy
l A xx model represents an xx by its xx. ~_ss[\N
l A process decision model captures the logic essential to yO Ed8
l From the equation above, xx is equal to the summation of xx Jydz2
zt!
times the ... 5W"&$6vj
l The validity of a xx model can be checked using Euler's formula. ucP
}( $
l Given a model, one can mathematically determine whether ... or ... V`xZ4 i%L
l Equations for xx need to be derived and implemented in the n'R9SnW
system. \jL n5$OW
l A number of heuristic rules have been developed for QX}O{LQR
l Optimum .. techniques can be made more reliable by ... so that x
'Pp!
l An algorithm based on the characteristic ... is used to determine S <~"\<ED
l Euler's formula states the following: U-/-aNJ]U
l The completed model should agree with the formula. lM
]n
l For manufacturing purposes, a detailed and precise model of the ozN#LIM>P
object is necessary *Pj[r
l Engineering design models are very well defined; therefore, ?K,xxH
l To keep the domain narrow enough to be implementable, yet wide 0>hV?A
enough to P,5gaT)
be useful. Wr+?ul*_
9x;CJhX
Point of View nXH U|5.I
l from an implementation standpoint, H9'Y` -r
l From the point of view of this application, ~=HrD?-99p
l From this point of view, Zadeh suggested an inference rule named <P&~k\BuF{
xxx (CRI for short). LASR
*
l Information is the meaningful interpretation and correlation of L
;5R*)t
some aggregation of data in order to allow one to make decisions. -I."= c%
l From a practical point of view, the computational aspects of an ,<iJ#$:
Sx
FLC require a simplification of the fuzzy control algorithm. .b'o}DLa
l The use of a hammer to insert screws, although partly effective, cQ kH4>C~
tends to distort, destroy, and generally defeat the purpose of using a 72rnMHq
screw [Kusiak AI Implications for CIM p.129] E]eVoC
Justification ,G2]3
3Z
l We choose the so called xx in our experiment because it has
]|NwC<
received wide acceptance and can TI
'(
l Prolog was chosen because it offers a well known and flexible Z"spu
a5
environment in which fuzzy reasoning may be easily implemented. OsS5WY0H
l The rationale behind this is that it can be much easier for an H/!_D f
estimator to rate a cost as high than to attempt to place a dollar &YMz3ugI
value on the estimate. yEYlQ= [#
l This strategy has been widely used in fuzzy control applications ?^TjG)e7
since it is natural and easy to implement. z"4UObVs
l A function definition expresses the membership function of a ^kg[n908Nw
fuzzy set in a functional form, typically a bell-shaped function, etc. a.P7O!2Lp
Such functions are used in FLC because they lead themselves to S3cjw9V
manipulation through the use of fuzzy arithmetic. MUo}Qi0K
l It should be noted that in our daily life most of the information on e[txJ*SuO
which our decisions are based is linguistic rather than numerical in S $wx>715
nature. Seen in this perspective, fuzzy control rules provide a natural |e+8Xz1>
framework for the characterization of human behavior and decisions \
;.W;!*
analysis. z#qlu=
l Many experts have found that fuzzy control rules provide a M%dJqwH5{
HsA4NRF'7
convenient way to express their domain knowledge. This explains ;CbQ}k
why most FLCs are based on the knowledge and experience which c.5?Q>!+
are expressed in the language of fuzzy "if-the" rule. *=
]hc@
Chapter 4. Examples j3j<01rq
Example/ Data /mMRV:pd
l The data used in the following example was taken from an hrfu\cI
experiment in which xx was measured between x and x using a xx eKdF-;
technique. :W'Yt9v)
l The data consists of over xx measurements. F
Qtlo+3
l An example of xx is discussed and the control rules of xx are Uj!3H]d
compared with a xx tb;!2$
l Examples of complex processes to which this technique may be :1Jg;G
applied are xx, xx, etc. Xg>nb1e
l The following example is constructed only for the purpose of HWe?vz$4"
illustrating the computational procedure discussed. @4h{#
l This example clearly demonstrates that the profile of an individual xf1@mi[a
xx, or a very small group of xx, with no enough data to be studied ByR%2_6&
statistically, can be meaningfully analyzed by fuzzy possibilistic :S
Tj
<
methods. jYAD9v%
l There is no space here to go into detail on all these methods, but x!CCSM;q
deserve a mention and the bibliography will point to detailed H38ODWO3
references for those wishing this level of detail. hL:n9G
l Note that the golf ball spotting example is used throughout the ve|:z
paper. 32[ lsU>1
Comparisons xL,;(F\^
l As well, the pros and cons of these representations from a process 98u$5=Z'/
planning point of view will be discussed. V:?exJg9
l The method of using xx to implement xx described by Zadeh `TNWLD@Z
(1973) appeared more suitable TxZ ^zj
l As discussed [in the previous section]/[preciously], %";bgU2Q
sdq8wn
Relation _97A9wHj
l We can not invert F' directly because it defines a many-to-one W
79wz\a
mapping. w i,}sEoM
l The relationships appear very complicate $Z
Sjq
l Lifting tasks involve complex and imprecise relationship between T%kr&XsQX
the task variables and the human operator's characteristics. (UWV#AR
l These methods are based on the relationship between ... and ...
a6AD`| U8
l The fundamental concept of a fuzzy rating language is that we can RY=B>398:
establish a relationship among terms such as high, medium, and low, qx3@]9
and then modify these relationships. m[~fT(NI
l This article will thus mention the latter as well as the former. ~>:uMXyV2t
l The former two bear a close relation to a fuzzy Cartesian product. C*A!`Q?1Y
Importance };5d>#NK,Y
l The emphasis is on an implementation of a general approach to wO6
D\#
rule based decision making. 8PQKB*<dB"
Consideration / Attention +C4UM9
l Careful evaluation is necessary to ensure pSM\(kVKa
l Such a formulation does not change further considerations. ZzZy2.7
l Considerable attention has been paid to xVOoYr>O
l Attention should be paid to an important finding of this SJ(<u2J]
investigation. R-Y07A
l Caution should be exercised in this process to avoid ... k/MrNiC
l Primary consideration is given to ... components, though others X6lkz*M.
can be accommodated neN #Mo'A
l After ... has been defined by ..., a carefully analysis is carried C"`,?K(U
out/performed to determine M^f+R'Q3
l A number of factors such as ...need to be taken into consideration D?yiK=:08`
before making the appropriate decision. aj>6q=R
l It should be noted that XxXMtiZ6
l It is important to point out that ... IGKF&s*;{[
l These considerations have heightened interest in the possibility of W dM?{;
#
providing ... ~.-o*
vwA d6Tm
l We should stress the fundamental importance of the xx S6~&g|T,
Chapter 5. Results. -?T:> *]p
Advantages / Disadvantage ozF173iI
l One of the major advantages of this new measure of xx is that it O7&