To reduce a fuzzy automaton into equivalent minimal automaton is a challenging issue related to fuzzy finite automata theory. The state minimization and state reduction techniques are used to convert fuzzy automata into equivalent fuzzy automata. For state minimization of fuzzy automaton, two identical states are merged to obtain a smaller equivalent automaton and for state reduction indistinguishable states are merged to find a relative smaller automaton. This paper reviews different methods used for state minimization and state reduction of fuzzy automata over complete residuated lattice.

1.
L. A.
Zadeh
,
Information and Control
,
8
,
338
353
(
1965
).
M.
Mizumoto
,
Info. Cont.
,
48
,
30
48
(
1981
).
2.
M.
Mizumoto
and
K.
Tanaka
,
Info. Cont.
,
50
(
2
),
160
174
(
1981
).
3.
W. G.
Wee
, “
On generalizations of adaptive algorithm and application of the fuzzy sets concept to pattern classification
”, Ph.D. dissertation,
Purdue Univ.
,
West Lafayette, IN,USA
,
1967
.
4.
E.T.
Lee
and
L.A.
Zadeh
,
Info. Sc.
,
1
(
4
),
421
434
(
1969
).
5.
G. D.
Bruce
and
K. S.
Fu
, “
A model for finite-state probabilistic systems
”,
Proceedings of 1st Annual Allerton Conference on Circuit and Systems Theory
,
1963
.
6.
K. S.
Fu
and
R. W.
McLaren
, “An application of stochastic automata to the synthesis of learning systems”,
School of Elea. Engg., Purdue University
, Tech. Rept. TR-EE65-17, April
1965
.
7.
E. S.
Santos
,
Info. Cont.
,
12
,
367
377
(
1968
).
8.
E. S.
Santos
,
J. Math. Anal. App.
,
37
,
677
686
(
1972
).
9.
E. S.
Santos
,
Info. Sc.
,
10
,
193
197
, (
1976
).
10.
D.W.
Qiu
,
Science in China (Series F)
,
44
(
6
),
419
429
(
2001
).
11.
D.W.
Qiu
,
Science in China (Series F)
,
45
(
6
),
442
452
(
2002
).
12.
Y.M.
Li
and
W.
Pedrycz
,
Fuzzy Sets and Systems
156
,
68
92
(
2005
).
13.
Rahul Kumar
Singh
 et al,
Fuzzy Automata: Int. J. Future Rev. Comp. Sci.Comm. Engg.
,
3
(
7
),
11
17
, (
2017
).
14.
M.
Mizumoto
,
J.
Toyoda
,
K.
Tonaka
,
J. Comput. System Sci.
,
3
,
409
422
(
1969
).
15.
D.S.
Malik
,
J. N.
Mordeson
 et al,
Info. Sc.
,
113
,
323
330
(
1999
).
16.
N.C.
Basak
and
A.
Gupta
,
Fuzzy Sets and Systems
,
125
,
223
229
(
2002
).
17.
W.
Cheng
and
Z. W.
Mo
,
Fuzzy Sets and Systems
,
141
,
439
448
(
2004
).
18.
Y.M.
Li
and
W.
Pedrycz
,
Fuzzy Sets and Systems
,
158
(
13
),
1423
1436
(
2007
).
19.
H.
Lei
and
Y. M.
Li
,
Inf. Sci.
,
177
,
1413
1421
(
2007
).
20.
Wu
and
Qiu
,
Fuzzy Sets and Systems
,
1761
,
1635
1656
(
2010
).
21.
A.
Choubey
and
K. M.
Ravi
,
Iranian Journal of Fuzzy Systems
,
10
(
1
),
75
88
(
2013
).
22.
A.
Choubey
and
K. M.
Ravi
,
J. Appl. Math. Informatics
,
27
(
1-2
),
409
417
(
2007
).
23.
A.
Choubey
and
K. M.
Ravi
,
Adv. Fuzzy Maths
,
4
(
2
),
147
165
(
2009
).
24.
S.
Moghari
and
M. M.
Zahedi
,
J. Fuzzy Set Valued Anal.
,
2014
,
1
18
(
2014
).
25.
S.
Moghari
and
M. M.
Zahedi
,
J. App. Math. Compu.
,
50
(
1-2
),
417
43
(
2016
).
26.
L.
Li
and
D.
Qiu
,
IEEE Trans. Fuzzy Sys.
,
23
(
2
),
434
443
(
2015
).
27.
V.
Topencharov
and
K.
Peeva
,
J. Math. Anal. Appl.
,
84
(
1
),
270
281
(
1981
).
28.
K.
Peeva
,
Theor. Comp. Sc.
,
88
,
269
285
(
1991
).
29.
L.
Ilie
and
S.
Yu
,
Theor. Comp. Sc.
,
306
,
373
390
(
2003
).
30.
L.
Ilie
,
G.
Navarro
, and
S.
Yu
, “On NFA reductions, in
Theory is Forever (Lecture Notes in Computer Science)
”. Vol.
3113
,
New York, NY, USA
:
Springer
, pp.
112
124
,
2004
.
31.
M.
Ćirić
,
A.
Stamenković
,
J.
Ignjatović
, and
T.
Petković
,
J. Computer Syst. Sc.
,
76
,
609
633
(
2010
).
32.
A.
Stamenkovic
 et al,
Fuzzy Sets and Systems
,
333
,
124
139
(
2018
).
33.
H.
Comon
,
M.
Dauchet
,
R.
Gilleron
, et al 
Tree automata: techniques and applications
,
2007
.
34.
Y.M.
Li
and
W.
Pedrycz
,
Fuzzy Sets and Systems
,
156
,
68
9
(
2005
).
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