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Beginning CnxK+1n l
1. In this paper, we focus on the need for r^?)F?n!
2. This paper proceeds as follow. ;k9
?
3. The structure of the paper is as follows. \4[c}l
4. In this paper, we shall first briefly introduce fuzzy sets and related )2iM<-uB
concepts .OVW4svX
5. To begin with we will provide a brief background on the l=oN X"l=
Introduction <_##YSGh,
1. This will be followed by a description of the fuzzy nature of the )e4WAlg8c
problem and a detailed presentation of how the required i /O1vU#
membership functions are defined. 4+ASwN9
2. Details on xx and xx are discussed in later sections. LydbP17K}
3. In the next section, after a statement of the basic problem, various Z!C`f/h9
situations involving possibility knowledge are investigated: first, an t_[M&
entirely possibility model is proposed; then the cases of a fuzzy #6Efev
service time with stochastic arrivals and non-fuzzy service rule is &{-oA_@
studied; lastly, fuzzy service rule are considered. eT7!a']x
Review 6%\7.h
1. This review is followed by an introduction. (Sg
Et
2. A brief summary of some of the relevant concepts in xxx and xxx is 47)+'`
presented in Section 2.
{AU` }*5
3. In the next section, a brief review of the .... is given. Nz(c"3T;
4. In the next section, a short review of ... is given with special regard %Y)PH-z
to ... baUEsg[~V
5. Section 2 reviews relevant research related to xx. "_ PH "W
6. Section 1.1 briefly surveys the motivation for a methodology of d-6sC@PB
action, while 1.2 looks at the difficulties posed by the complexity of `^XRrVX<
systems and outlines the need for development of possibility rh:s
7
methods. EmtDrx4!(f
Body F]K$u<U
1. Section 1 defines the notion of robustness, and argues for its SeRK7Q&_
^]#Ptoz^(l
importance. Nt`F0
9S
2. Section 1 devoted to the basic aspects of the FLC decision-making L:t)$iF5+
logic. Z`-)1!
3. Section 2 gives the background of the problem which includes xxx 'NQMZfz
4. Section 2 discusses some problems with and approaches to, :,h=2a_ 8
natural language understanding. Ak\D6eHcB
5. Section 2 explains how flexibility which often ... can be expressed 3X-{2R/ 3
in terms of fuzzy time-window /?.r!Cp
6. Section 3 discusses the aspects of fuzzy set theory that are used in dyQ<UT
the ... haEZp6Z
7. Section 3 describes the system itself in a general way, including i#@ v_^ q
the ….. and also discusses how to evaluate system performance. M\Uc;:) H
8. Section 3 describes a new measure of xx. )9A<fwpN
9. Section 3 demonstrates the use of fuzzy possibility theory in the N8DiEB3~
analysis of xx. 8^P2GG'+-
10. Section 3 is a fine description of fuzzy formulation of human ]Vf8mkDGO
decision. eu}:Wg2
11. Section 3 is developed to the modeling and processing of fuzzy UijuJ(Tle
decision rules ySr091Q
12. The main idea of the FLC is described in Section 3 while Section 4 5H'b4Cyi`
describes the xx strategies. Gpxb_}P
13. Section 3 and 4 show experimental studies for verifying the ?v )"%.
proposed model. =XRgT1>e
14. Section 4 discusses a previous fuzzy set-based approach to cost TeGLAt
variance investigation. WoClTb>F
15. Section 4 gives a specific example of xxx. ZaNyNxbp>z
16. Section 4 is the experimental study to make a fuzzy model of ;8%@Lan
memory process. RBv=
17. Section 4 contains a discussion of the implication of the results of ',J%Mv>Yf
Section 2 and 3. YV ZSKU
18. Section 4 applies this fuzzy measure to the analysis of xx and +NzD/.gq
illustrate its use on experimental data. W(PW9J9
19. Section 5 presents the primary results of the paper: a fuzzy set )qe$rD;N
model .. 93Ci$#<y
gE6y&a
20. Section 5 contains some conclusions plus some ideas for further kGBl)0pr`x
work. k. ?
T.9
21. Section 6 illustrates the model with an example. t#D\*:Xi
22. Various ways of justification and the reasons for their choice are {7pE9R 5
discussed very briefly in Section 2. Bu>yRL=*
23. In Section 2 are presented the block diagram expression of a )Ido|!]0d
whole model 5f`XFe$8
of human DM system 6 peM4X
24. In Section 2 we shall list a collection of basic assumptions which T=f;n;/>
a ... scheme must satisfy.
B|q3;P
25. In Section 2 of this paper, we present representation and Vp-OGX[
uniqueness theorems for the fundamental measurement of fuzziness E6^S2J2
when the domain of discourse is order-dense. S>ylA U;N
26. In Section 3, we describe the preliminary results of an empirical CyBM4qyH
study WbD C
currently in progress to verify the measurement model and to Mb/6>
construct membership functions. . =foXN
27. In Section 5 is analyzed the inference process through the two r0$9c
kinds of inference experiments... y88}f&z#5
This Section W 9:{pQG
1. In this section, the characteristics and environment under which Ynh4oWUp
MRP is designed are described. N n-6/]d#
2. We will provide in this section basic terminologies and notations [\M?8R$)
which are necessary for the understanding of subsequent results. {R8P $
Next Section BRok 89
2. The next section describes the mathematics that goes into the .N><yQ-j3'
computer implementation of such fuzzy logic statements. ToXFMkwY
3. However, it is cumbersome for this purpose and in practical <.%8j\j(
applications the formulae were rearranged and simplified as 9DAwC:<r
discussed in the next section. Pg
8=
4. The three components will be described in the next two section, _nFvM'`<
and an example of xx analysis of a computer information system will \C\y'H5
S@2Jj>3D?
then illustrate their use. ~S{\wL53
5. We can interpret the results of Experiments I and II as in the )PN
H| h
following sections. a|{<#<6n(
6. The next section summarizes the method in a from that is useful "ZB`fNE
for arguments based on xx x3F L/^S
Summary r|BKp,u9
1. This paper concludes with a discussion of future research l fhKZX
consideration in section 5. ?-v?SN#
2. Section 5 summarizes the results of this investigation. eOO*gM=
3. Section 5 gives the conclusions and future directions of research. ;j\$[4W.i
4. Section 7 provides a summary and a discussion of some extensions |N.q[>^R
of the paper. aZ3 #g
5. Finally, conclusions and future work are summarized }nERQq&A
6. The basic questions posed above are then discussed and tD482Sb=
conclusions are drawn. @9
tvN}
7. Section 7 is the conclusion of the paper. ! r\ktX
Chapter 0. Abstract 0# GwhB
1. A basic problem in the design of xx is presented by the choice of a j~>
#{"C
xx rate for the measurement of experimental variables. 2*E<G|-F
2. This paper examines a new measure of xx in xx based on fuzzy j-E>*N}-_
mathematics which overcomes the difficulties found in other xx Nxk'!:
measures. 2;7GgO~
3. This paper describes a system for the analysis of the xx. / UBA
Q8TR
4. The method involves the construction of xx from fuzzy relations. *#9kFz-
5. The procedure is useful in analyzing how groups reach a decision. "2j~3aWj
6. The technique used is to employ a newly developed and versatile !-Q!/?
xx algorithm. 5WG@ ;K%
7. The usefulness of xx is also considered. Li$k<AM
8. A brief methodology used in xx is discussed. #>NZN1
9. The analysis is useful in xx and xx problem. zOp"n\
10. A model is developed for a xx analysis using fuzzy matrices. K",]_+b
11. Algorithms to combine these estimates and produce a xx are Kwau:_B
P3>2=qK"E(
presented and justified. m>:ig\
12. The use of the method is discussed and an example is given. EFO Q;q
13. Results of an experimental applications of this xx analysis 0nn#U
procedure are given to illustrate the proposed technique. >r Glj
14. This paper analyses problems in Etk<`GRfA
15. This paper outlines the functions carried out by ... 4K%
YS
16. This paper includes an illustration of the ... .=D6<4#t
17. This paper provides an overview and information useful for jlZNANR3
approaching ?+_"2XY
18. Emphasis is placed on the construction of a criterion function by >X,6
which the xx in achieving a hierarchical system of objectives are Kep?=9r4+
evaluated. {[dqXG$v `
19. The main emphasis is placed on the problem of xx **[p{R]8o
20. Our proposed model is verified through experimental study. BC+qeocg
21. The experimental results reveal interesting examples of fuzzy ~yg9ZM
phases of: xx, xx umYdr'p!v
22. The compatibility of a project in terms of cost, and xx are likewise lnUy?0(
represented by linguistic variables. Kxn=iv^Ir
23. A didactic example is included to illustrate the computational %0'f`P6
procedure s,=^V/c
Chapter 1. Introduction FeJ5^Gh.
Time a1&^P1.
1. Over the course of the past 30 years, .. has emerged form intuitive mbK$Wp#
2. Technological revolutions have recently hit the industrial world
P7!Sc
3. The advent of ... systems for has had a significant impact on the |ipppE=
4. The development of ... is explored *@Z'{V\
5. During the past decade, the theory of fuzzy sets has developed in a A_+WY|#M
variety of directions xYq8\9Qb
6.The concept of xx was investigated quite intensively in recent years 1
['A1,
7. There has been a turning point in ... methodology in accordance SE1 tlP
with the advent of ... Y;WrfO$J
8. A major concern in ... today is to continue to improve... X,b}d#\
9. A xx is a latecomer in the part representation arena. ueOvBFgZ
9cQSS'`F
10. At the time of this writing, there is still no standard way of xx JqO( ]*"Hi
11. Although a lot of effort is being spent on improving these ?bEYvHAzg
weaknesses, the efficient and effective method has yet to be -MZ Eli g
developed. gDrqs>8
12. The pioneer work can be traced to xx [1965]. aVlHY E
13. To date, none of the methods developed is perfect and all are far F&\o1g-L
from ready to be used in commercial systems. Kj7Osqu2bE
Objective / Goal / Purpose C o M8
1. The purpose of the inference engine can be outlined as follows: xFJ>s-g*
2. The ultimate goal of the xx system is to allow the non-experts to LImD]e`
utilize the existing knowledge in the area of manual handling of loads, Mm5l> D'c
and to provide intelligent, computer-aided instruction for xxx. v-kH7H"z
3. The paper concerns the development of a xx NO&OuiN
4. The scope of this research lies in 6*e:ey U
5. The main theme of the paper is the application of rule-based }E=mZZ)
decision making. </fnbyGR
6. These objectives are to be met with such thoroughness and f?]cW h%
confidence as to permit ... 0YS*=J"7z
7. The objectives of the ... operations study are as follows: cc>h=%s`
8. The primary purpose/consideration/objective of 2`z+_DA
9. The ultimate goal of this concept is to provide $R^"~|m3M
10. The main objective of such a ... system is to H=dj\B
r`
11. The aim of this paper is to provide methods to construct such -~5yl}
probability distribution. 5=dg4"b]
12. In order to achieve these objectives, an xx must meet the m?csake.Me
following requirements: GVg0)}
13. In order to take advantage of their similarity 'HC4Q{b`
14. more research is still required before final goal of ... can be jQc0_F\
completed H1X6f7`
15. In this trial, the objective is to generate... NZl0sX.:
16. for the sake of concentrating on ... research issues Oz+>I^Q
17. A major goal of this report is to extend the utilization of a recently hGpaHY>My
developed procedure for the xx. eVy,7go h
$`uL^ hlj]
18. For an illustrative purpose, four well-known OR problems are !6kLg1
studied in presence of fuzzy data: xx. LO
QEU?z
19. A major thrust of the paper is to discuss approaches and %9M_*]
strategies for structuring ..methods S]<Hx_[}
20. This illustration points out the need to specify 9@!`,Co
21. The ultimate goal is both descriptive and prescriptive. Ly^r8I
22. Chapter 2. Literature Review iR_X,&p
23. A wealth of information is to be found in the statistics literature, {AB0 PM;-
for example, regarding xx nY6^DE2f
24. A considerable amount of research has been done .. during the 1(m89C[
last decade ATwPfo8jx@
25. A great number of studies report on the treatment of 0"ZRJl<)[I
uncertainties associated with xx. .i&]VGv
26. There is considerable amount of literature on planning Peb;XI
27. However, these studies do not provide much attention to ?-6oh~W<
uncertainty in xx. `,xKK+~YG-
28. Since then, the subject has been extensively explored and it is 0kmZO"K#e
still under investigation as well in methodological aspects as in nq
r[HFWs
concrete applications. 1{_;`V
29. Many research studies have been carried out on this topic. D;m>9{=
30. Problem of xx draws recently more and more attention of system U"/":w ~
analysis. yw2sK7
31. Attempts to resolve this dilemma have resulted in the w;)@2}
development of 85
-00m ~
32. Many complex processes unfortunately, do not yield to this }ufH![|[r
design procedure and have, therefore, not yet been automated. tK0?9M.)
33. Most of the methods developed so far are deterministic and /or EE-jU<>|
probabilistic in nature. RP!X5
34. The central issue in all these studies is to NZCPmst
35. The problem of xx has been studied by other investigators, ~:v" TuuK
however, these studies have been based upon classical statistical K8f;AK
approaches. SCZtHEl9
36. Applied ... techniques to p%ek)tT
37. Characterized the ... system as n}}$-xl
8 Zhx&
38. Developed an algorithm to .3M=|rE
39. Developed a system called ... which C,HKao\
40. Uses an iterative algorithm to deduce ,p {|f}0
41. Emphasized the need to bC&*U|de
42. Identifies six key issues surrounding high technology OLg=kF[[
43. A comprehensive study of the... has been undertaken ha&2V=
44. Much work has been reported recently in these filed /J9|.];%r
45. Proposed/Presented/State that/Described/Illustrated/ {d|e@`"T
Indicated/Has shown / showed/Address/Highlights ^Cs?FF@P
46. Point out that the problem of 76Ho\}-U">
47. A study on ...was done / developed by [] 3\JEp,5
48. Previous work, such as [] and [], deal only with j]~;|V5Z
49. The approach taken by [] is gn4+$ f~w
50. The system developed by [] consists 'So,*>]63
51. A paper relevant to this research was published by [] ;n`SF~CU
52. []'s model requires consideration of... RzgA;ZC'
53. []' model draws attention to evolution in human development 3g
ep_aC
54. []'s model focuses on... 3V2dN)\
55. Little research has been conducted in applying ... to X?kw=x{2P
56. The published information that is relevant to this research... U|yXJ.Z3
57. This study further shows that QmxI;l
58. Their work is based on the principle of 'ONCz
59. More history of ... can be found in xx et al. [1979]. #s%_ L
60. Studies have been completed to established jAXKp
b
61. The ...studies indicated that e,V @t%
62. Though application of xx in the filed of xx has proliferated in N5K\h}'%
recent years, effort in analyzing xx, especially xx, is lacking. csK;GSp}
Problem / Issue / Question 3&`LVhx
63. Unfortunately, real-world engineering problems such as v_G1YC7TU
manufacturing planning do not fit well with this narrowly defined GoSdo
model. They tend to span broad activities and require consideration 9fQ[:Hl"
of multiple aspects. {$AwG#kt
64. Remedy / solve / alleviate these problems \k
9EimT}
67. ... is a difficult problem, yet to be adequately resolved b';oFUU>Q
;+;%s D
68. Two major problems have yet to be addressed "WF@T
69. An unanswered question 6> DmcG:.
70. This problem in essence involves using x to obtain a solution. 2e_ m>I
71. An additional research issue to be tackled is .... X^o0t^
72. Some important issues in developing a ... system are discussed yor6h@F1
73. The three prime issues can be summarized: Ie"eqO!
74. The situation leads to the problem of how to determine the ... @h=r;N#/`P
75. There have been many attempts to H3#rFO"C*
76. It is expected to be serious barrier to o$q})!
77. It offers a simple solution in a limited domain for a complex [x[nTIg
problem. 2QIx
~Er
1. There are several ways to get around this problem. >S}^0vNZX
2. As difficult as it seems to be, xx is by no means new. `=%mU/v
3. The problem is to recognize xx from a design representation. !-AK@`i.
4. A xx problem can trace its roots to xx. M!4}B
5. xx [1987] used a heuristic approach to simplify the complexity of vw2yOLRX
the problem. 5}Z_A?gy
6. Several problems are associated with them. 2 Q}^<^r
7. Although some progress has been made in this area, at least two 9
M;k(B!
major obstacles must be overcome before a fully automated system 8," 5z_
can be realized. | K w}S/F
8. Most problems in practice are complicated ;&9wG`
9. More problem surface here. O>,Rsj!e
10. Hamper effort toward a xx system 5H!6m_,w
11. In order to overcome the limitations due to incomplete and A}W}H
;8x
imprecise xx knowledge, a xx program has been developed, which {?uG] G7
bases its knowledge upon the statistical analysis of a sample y^}00Z+l
population of xx I><sK-3
12. The above difficulties are real challenges faced by researchers "w&G1kw5I
attempting to develop dQ-:]T (
13. This type of mapping raises no controversy to the issue of |5g1D^b]s^
membership function determination. <G60R^o
14. However, attempts to quantify the xx have met both theoretical ^3lEfI<pBm
and empirical problems. chszP{-@X
I?X!v6
15. It has become apparent that in order to apply this new T{4Ru6[
methodological framework to real-world problems and data, we have X;QhK] Z
to pay attention to the problems of xx and xx. q3e^vMK
"
Chapter 3. Proposed methodology js F96X{
Assumption ((
{4)5}
1. In the case when the assumption of a xx seems to be too "
"{#~X}
restrictive or inadequate, the formulation with Fuzzy termination EL:Az~]V
time, i.e. given by a fuzzy set in the space of control stages, may be Rdl^-\BV
applied. us >$f20T
2. We assume here the fuzzy constraints to be state-dependent, and !~QmY,R
the fuzzy goal to be the same for all the control states, xx, which aqoxj[V^3L
stems from the problem's nature. <?Y.w1
3. An approach to the solution of this problem is presented under the ;To][
J
assumption that the sampling rate Decision can be made prior to the +&qj`hA-b
execution of the experiment, as opposed to being made while the P<MNwdf(+
experiment is in progress. jQi)pVT^
4. Another assumption made above is that there are precise odds at f{ER]U
which the expert is indifferent. <69Uq8GI
5. Main simplifying assumptions are: /5r!Fhx
6. This, in our view, is a questionable assumption. tY0C& u2
Outline / Structure / Module rF)[ Sed:T
1. An outline of the research Uv%?z0F<C
2. Information is incorporated within the scheme |iGfWJ^+
3. Is built into ... structure ;6/dFOZn
4. A nice modular structure. +X4/l"
|
5. The principles of ... are applied as modularized criteria Ika(ip#]=
Classification Qv/Kb w
N{
1. A xx system comprises three main components: ';Ew
-u
2. Must decompose the original .. into a set of .. THf*<|
3. Consists of the following steps: 3%DDN\q\u
4. This is summarized in the following steps: Hribk[99
_S3qPPo3l]
5. Can be broadly classified into the following areas: ;nZN}&m
6. Can be characterized by its function of effectively processing the OM 4,Sevk
7. Can allow further breadth of application of ...into more :y8wv|m
8. The following steps should be followed w//L2.
9. xx can be classified by a different ways. -$+`v<[r
10. Based on the xx, one may classify xx into the following: 3lT>C'qq
11. This catalog may change due to wear, breakage, and purchasing. 59Lmv
&s
System '/v@q]!
1. Unlike many conventional program, expert systems do not 1GI/gc\
usually deal with problem for which there is clearly a right or wrong 1:VbbOu->V
answer. kZJ.G
2. The system consists of both ... and ... N;.}g*_+}
3. The system has a hierarchical modular architecture organized on "*N=aHsj
three levels. 9e>Dqlv
4. expert system domains are area of expertise [(PD2GO+
5. To develop a xx system for xx, the following factors must be wR*>9LjeG
considered: ~T'Ri=
6. The system has been developed / designed to determine 6|AD]/t^K
7. The system has proven to be able to YN
V4'
8. The domain in which an expert system operates is a particular iw)^;8q
domain M
PI=^rc2
9. The system comprises a ... with Mpu8/i
gX,
10. The system is [feature-oriented ] / based on the ... technique \C eP.,<
11. The system environment must be relatively stable xQK;3b
12. The system is utilized to generate, load, store, update and D<:J6W7]
retrieve ... 1Zj NRg=
13. The development of a xx system has two stages: xx stage and xx H 6~6hg
stage. ? j8S.d~
14. The most essential part of .. system is the ... |A0)-sVZ
15. The successful developments in ESs have made them an oR_qAb
important tool in the development of cN(Toj
'`
16. An automated system was developed for H$o=kQN
17. In this case, the system can be considered to be generative. U81--'@y
&3t[p=
18. An interactive automatic ... system Nt5`F@;B
19. A …. is commonly thought of as a truly integrated .. system aF
(L_
20. Should be capable of being generated from a ... system zXRq) ;s
21. xx is an important part of the integrated system. FC BsC#
22. The model consists of four rule bases, each of which addresses a ]:X# w0UR
separate problem in the hierarchy of scheduling decision.
qV
Df98
23. The rule bases are linked to each other in a chin-like manner in ! O~:
the sense that the consequent of one rule base constitutes a part of h]{V/
the antecedent of the next rule base. k(bDj[0q^
24. The rule base consists of all possible combinations of the v+b#8
linguistic terms associated with the linguistic variable of the .nG14i7C
antecedent of a rule. PDi]zp9>H
Computer System q<Sb>M/\,
1. The system has been implemented using Prolog language in an U-mZO7y!
MS-DOS environment. Prolog was chosen because it offers a well Vhi4_~W3j]
known and flexible environment in which fuzzy reasoning may be rTmVHt
easily implemented. ^_rBEyz@
2. The current version of the xx program when compiled with yPXa
WATFOR77 results in an executable code of about 270K bytes. %UXmWXF4$
Typical run time, when run on a XX computer (an IBM compatible gL(_!mcwu
machine) operating at 4.77 Mhz with 640K RAM, ranges from 10 min , R;k>'.
to 2h, depending on the size (or complexity) of the problem. |
mp~d<&
3. Time consuming procedures have been implemented in dWK"Tkf\
C-language and directly linked to the Prolog environment. GVK c4HGt
4. The xx process, once the xx's data has been entered, requires $c0<I59&|
approximately 180 seconds. @
yj$
5. It should be noted that the computation was done with a 20 Hhz, nd#owjB
80386..209;based microcomputer equipped with a 80387 math L4t(Y7
co-processor. vXLGdv::
6. The computer programs used for the analyses, one based on the xx 6F8TiR&
method and the other based on the new method, were written in `37%|e 3bQ
FORTRAN with a compiler that supports the math co-processor. 4o69t
7. Lisp, Prolog give maximum flexibility but also maximizes #6F|}E
yE_T#FN
development time. 3'zL,W W
l Internal representation is the way a model is represented in the 4L _AhX7
computer. UpSa7F:Uw
l An interactive menu-driven procedure is used in this study U)6Ew4uRxV
l Shell can be develop very fast at the cost of time fairly severe $g&_7SJ@
limitations.
B".3NQ
l While there is no measurable saving of time for the case involving +|6E~#zklY
five criteria, the saving is dramatic for the case involving 10 criteria E|"QYsi.Ck
-- the computation time reduces from 10 hr 40 min to about 1 min. AK//]
l This combination is being implemented in an objected-oriented "BA&
programming environment (Smalltalk-80 system) to solve problems Egi(z9|Pp
encountered in construction xxx. 2=
)V"lR\
Method / Approach / Study / Process Model / Equation /Algorithm / eHc.#OA&
Rule / Formula / Technique -#`tS
l A discussion is presented of a problem-solving system L~!Lq4]V\g
l To improve the efficiency of the method, the following approach 8E|FFHNK<2
may be applied. ;%mdSaf
l In order to an investigation was made to find the causes of the gg&Dej2{
l Although large collections of rules and equations have been +HF*X~},i
complied, none are generally accepted I|tn7|*-A[
l This approach will be explained and discussed thoroughly in the 49Hgq/uO
body of the report. e/Y&d9`
I
l This can be accomplished by GXwQ
)P5]
l This algorithm to compute the total cost can be described step by g>n1mK|
step as follows: v%)=!T,
l The above preliminary analysis has provided important R_duPaWc@
information uWkuw5;
l Various methods have been proposed for selecting an optimum... 1Ba.'~:
l These concepts have been applied to i|N(=Z
=
l On the basis of the concept mentioned above, Q32GI,M%B
l This can be achieved by zvKypx
l This fact suggests that a new concept x?2y^3<5
l This was accomplished by taking ... ]64?S0p1c!
WZf}1.Mh*
l The preparatory stage is very time consuming process. \SA$:^zO
l Test are performed for validity, completeness, and compatibility bX`VIFc
l There is little hope of achieving successful ... 84y#L[
l There has been an increasing awareness of the potential of using TN.&FDqC9
most ..so far made have not taken this approach, with the exception fHacVjJ
of ILT.yxV
l Only a few studies can be found. ^:]~6p#
l It is a very tedious process to go through i]IZ0.?Y
l It is only when .. has been completed that .. may be effected htHnQ4Q
l The entire interpretation process is conducted in one's head. "uD^1'IW2
l These approaches are sometimes very tedious. Q);^gV
l Several techniques can be used h7[PU^ m
l A polynomial parametric model can be written as [the BCw0kq@
following]/[follows]: y0cB@pWp
l A xx model is constructed/formulated using xx. e]u3[ao
l A xx model represents an xx by its xx. |d=MX>i|G
l A process decision model captures the logic essential to #AUa'qBt
l From the equation above, xx is equal to the summation of xx {9YNv<3
times the ... @G0j/@v
l The validity of a xx model can be checked using Euler's formula. .RxAYf|
l Given a model, one can mathematically determine whether ... or ... \!,qXfTMB
l Equations for xx need to be derived and implemented in the kV3Z
t@+
system. l} UOg
l A number of heuristic rules have been developed for U#1,]a\
l Optimum .. techniques can be made more reliable by ... so that Vq1ve;(8s
l An algorithm based on the characteristic ... is used to determine pm
}!?TL
l Euler's formula states the following: ^PI8Bvs>j
l The completed model should agree with the formula. rg{|/ ;imT
l For manufacturing purposes, a detailed and precise model of the RE}$(T=
object is necessary H}B%OFI \+
l Engineering design models are very well defined; therefore, q/HwcX+[b
l To keep the domain narrow enough to be implementable, yet wide 3erGTa[|q
enough to Ff@Cs0R
be useful. B
M$+r(#t
M;K%=l$NG
Point of View 9WhZ=
Xk
l from an implementation standpoint, G@Y!*ZH*f
l From the point of view of this application, E/_I$<,_y
l From this point of view, Zadeh suggested an inference rule named k(.6K[b
xxx (CRI for short). PhOtSml0
l Information is the meaningful interpretation and correlation of 26Jb{o9Z<
some aggregation of data in order to allow one to make decisions. zs~v6y@
l From a practical point of view, the computational aspects of an WVfwt.Y
FLC require a simplification of the fuzzy control algorithm. kKP<