=Paper=
{{Paper
|id=Vol-2711/paper2
|storemode=property
|title=Multi-level Computing With Words Model to Autonomous Systems Control
|pdfUrl=https://ceur-ws.org/Vol-2711/paper2.pdf
|volume=Vol-2711
|authors=Anatolii Kargin,Tetyana Petrenko
|dblpUrl=https://dblp.org/rec/conf/icst2/KarginP20
}}
==Multi-level Computing With Words Model to Autonomous Systems Control ==
https://ceur-ws.org/Vol-2711/paper2.pdf
Multi-level Computing With Words Model to
Autonomous Systems Control
Anatolii Kargin1[0000-0003-2885-9071], Tetyana Petrenko2[0000-0001-6305-7918]
Ukrainian State University of Railway Transport, 61050, Feuerbach sq., 7, Kharkiv, Ukraine
1kargin@kart.edu.ua, 2petrenko_tg@kart.edu.ua
Abstract. An autonomous system which must react to unforeseen situations is
considered. The control task of such system is characterized by the processing
of data from large number of sensors, uncertainty and dynamics. The traditional
automation approaches cannot be used to create control system that satisfies
these conditions. Fuzzy logic solves this problem due to ability to data general-
ize and take into account uncertainty, but only for simple applications presented
by a small amount of data from sensors. L. Zadeh Computing with Words
(CWW) approach overcome the problem of large dimensionality if the situation
description is presented by a small number of words, but a high level of abstrac-
tion. However, the problem remains how numerical data from sensors to con-
vert into the words representing the meaning of these data at a high level of ab-
straction. Three-phases CWW model is proposed to solve this problem. At the
first phase, granular computing engine reveal the meaning of data from sensors
and represents its by words of zero-level abstraction. Then abstracting with
words engine maps its words into words of higher abstraction level representing
the meaning of complex dynamic situations. And in the end, CWW engine ob-
tain control decisions using as fuzzy inference inputs the meaning of the words
of high levels abstraction. Such word-based processing of data from sensors is
based on the proposed fuzzy models of the external and internal meanings of
the word. An example of signal switching control of a smart traffic light is giv-
en.
Keywords: autonomous systems, computing with words, abstracting with
words, data from sensors, fuzzy systems.
1 Introduction
Robotics, Internet of Things, smart machines, as automation applications, are design-
ing based on Autonomous Systems (ASs) principles [1-3]. Since ASs leave ordered
environments, for autonomous functioning in more complex, natural conditions, they
have to react to unforeseen situations. In order to ensure autonomous, the AS Control
System (CS) should be real-time decisions making based on the analysis of a complex
situation, which is represented by a spatio-temporal set of data from sensors. Thus, the
control task that AS solves is characterized by the processing of data from a large
number of sensors, uncertainty and environment dynamics. The main restrictions of the
traditional automation approaches are characterized by predefined abilities [4, 5]. The
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons
License Attribution 4.0 International (CC BY 4.0). ICST-2020
CS can only respond to expected situations and according to a pre-programmed action
plan [6], which does not allow to fully realize autonomous behavior in the broad sense.
Alternatively, AI can be used to control autonomous systems. This is one of the main
tasks of the future AI, on the creation of which leading research teams are working
today [7]. On this way, the problem of choosing an AI model that provides decisions
making in the above AS conditions is arise.
The AI model, first of all, should satisfy the requirements for embedded real-time
systems. Secondly, AI model should make decisions in the face of uncertainty
(knowledge incompleteness and data ambiguity, fuzziness and aging) [8, 9]. Thirdly,
the AI model should make decisions based on a large amount of data from sensors
(dimension problem). Fourth, the AI model must scale solutions to adapt to dynamic
changes in the situation (scalability problem) [8].
Models and approaches on the basis of which it is possible to develop AI that meets
the formulated requirements can contingently be divided into two groups: 1) oriented
to the data from sensors processing and 2) oriented to the knowledge processing.
The first group includes such approaches as intelligence analyzing, extracting
knowledge from data streams, generation of informational patterns, aggregation of
heterogeneous data from different sources in order to obtain, for example, the complex
description of situation. All of them are directly addressed in works on information
fusion processes [10, 11]. They are not suitable for automation of decision-making
based on the analysis of complex sophisticated situations.
The knowledge-based AI approach belonging to the second group known as rules-
based systems [12, 13] allow to implement the decision making tasks, taking into ac-
count the above features. Decision making in robotics, internet of things, smart ma-
chines domains carries out Rules Engine (RE) by searching among large number of
situations and, possibly, involving heuristics [8, 13]. The RE widely used in embedded
real-time systems [1, 2, 8, 14], however, the problem of the task dimensionality re-
mains relevant. Thus, for crisp models the prototype of situation is associated with
control decisions by the if-then rules. Since AS inputs are data from sensors, then situa-
tion prototype (condition in the if part of rule) should be built directly on a set of heter-
ogeneous data from sensors. This require large number of rules to represent all possible
situations in which AS must make decisions [15-18]. Using the Fuzzy Logic System
(FLS) as an AI for autonomous systems is problematic for the following reasons, also.
Firstly, among specialists in fuzzy systems there is a belief that it is possible to really
configure or tune a fuzzy system for the not complicated tasks with the number of
input variables not exceeding 5-7 [16, 19]. This circumstance limits using FLS in its
“pure” form for such domains as modern robotics and the Internet of Things, in which
data from sensors are used as input. Secondly, FLS does not have the property of
scalability [8, 15]: adding new input numerical variables or changing the number or
definition of linguistic variables terms requires changing the existing knowledge base
(changing fuzzy rules).
Problems of dimensionality and uncertainty can be solving by words-based data
processing approach thanks to ability of natural language words to generalize and ab-
stract [17, 18]. However, the L. Zadeh Computing with Words (CWW) approach sug-
gests that the words, and not the data from the sensors, come to the inputs of the CWW
model. To use this approach, it is necessary to bridge the gap between the two “data
from sensors” and “word” paradigms.
The purpose of this article is to propose an AI approach and model that solve this
problem. AI model, by analogy with a human thinking, solves three tasks. First, in real
time, AI maps the spatio-temporal stream of data from sensors into natural language
words that reveal the meaning of this data. Second task is abstracting with words.
Based on the words describing the local data sets, the AI should get a description of the
meaning of the whole situation using words of a high level of abstraction. And, thirdly,
according to CWW approach, control is making by fuzzy inference using the meaning
of the words of high levels abstraction.
2 Background
The methodological basis of the AI model is Lotfi A. Zadeh restriction-centered theory
of truth and meaning [20]. In accordance with the stated theory, in this paper we intro-
duce External Meaning of the Word (EMW) and Internal Meaning of the Word (IMW)
formal models. The decision-making process based on data from sensors is divided
into three phases. In the first phase, the spatio-temporal segment of data from the
sensors is transformed into a verbal description in the form of a set of IMWs. Data
meaning presentation by the IMWs is proposed to be implemented based on the
concept of information granule [19] and Granular Computing (GC) [22, 23]. Based on
this concept a “bridge” between data from sensors and knowledge in an IMWs form is
created. The second phase is the reasoning by abstraction and generalization method
[12]. The Abstracting with Words (AW) Engine compute the IMWs, sequentially,
starting from the IMWs received in the first phase, moving up to the words represent-
ing the situation at a high level of generalization. The AW Engine (AWE) inference
based on knowledge in the form of EMW. In this work, we use the AWE model pro-
posed in [8, 15, 24]. This model works with the IMW and EMW represented by fuzzy
certainty factor. The third phase is obtaining IMWs of words which describes the con-
trol decision by logical inference according to the IF - THEN rules. The traditional
Computing With Words (CWW) model [25] developed on the basis of Type-1 Fuzzy
Sets (T1 FS) or Perceptual Computing [24] developed on the basis of interval Type-2
FS (T2 FS) [19, 27] is used in this phase. AWE and CWW Engine (CWWE) are con-
sistent on inputs and outputs due to the fact, that CWW fuzzy sets are defined on the
same universe (certainty factor) as an IMW. Fig. 1 shows three possible options for
implementing computing with words methodology.
For the first option of the data processing based on the CWW approach the input
and output are numerical data. Fig. 1 shows that initially a fuzzifier maps numerical
(crisp) data into a FS which is used as input to the CWWE. Тhen, the CWWE performs
fuzzy inference according to IF-THEN rules. The output of the CWWE is again the
corresponding FS. And in the final phase of the computing, Defuzzifier maps the re-
sulting FS into numerical data. The FSs at the input, output and belonging the rules
represent the words of the lowest level of abstraction, which reflect the meaning of the
directly data. Therefore, dimension problem (the number of input variables and rules in
the knowledge base) is not completely solved. This circumstance limits using in “pure”
form of this CWW technology in AS.
For the second option Fig. 1 shows that the inputs are natural language words for
which Encoder matches either T1 FS or T2 FS [25, 26]. The output of the model is also
the word. The CWWE performs fuzzy inference according to IF-THEN rules. The
rules use words as inputs from a pre-prepared Word Vocabulary (WV), respectively, in
the form of T1 FS or T2 FS. The output of the CWWE is again the corresponding FS.
And in the final phase Decoder maps FS to words, words ranks, or words classes. In
this case the FSs at the input, output and belonging the rules can represent the words of
the different level of abstraction including high. The main reason that makes difficult
to use this technology in AS is that data from sensors cannot be automatically
converted to words (FS). A human implements the function of perceiving the
environment and converting his perceptions into words, which are then the Encoder
input.
Fig. 1. Computing with words model options
In this article, we propose the third option, when the data processing from the
sensors is carried out sequentially first by AWE, and then by CWWE. Fig. 1 shows
that the AWE input is the data from sensors. The AWE in real time performs the first
and second phases of data from sensors processing, automating such human function
as sensation and perception [24]. The AWE maps the input data from sensors into
IMW. The IMW is represented in the form of FS. The CWWE implements fuzzy rea-
soning with words that are the AWE output words (IMWs in the form of FS). Due to
the fact that AWE creates a description of data from sensors in the form of words of a
high level of abstraction, in CWWE decision-making is based on words that at a high
level of generalization represent knowledge about solving a problem. It is significantly
reduce the task dimension. Thus, the three-phases CWW model (GC → AW → CWW)
satisfies the requirements for the AI model of AS. Call this model as expanded CWW
(eCWW) model.
3 Abstracting With Words Model
3.1 Representation of the External Meaning of the Word
In semiotics, at the conceptual level, the word is represented by the triangle: firstly, the
word is an element of the sign system; secondly, the word is a denotation of the
sensation or perception of the real world essence, thirdly, the word has a designation
giving the concept to the sign. Accordingly, three models of word are considered: sign
model of the word, model of the internal meaning of the word and model of the
external meaning of the word. To formalize AW, the last two of the three mentioned
word models were used. A sign model in the form of a word representation in a natural
language or a words combination or sentence or even a group of sentences is a
component of the EMW model.
A graphic illustration of the word models is shown in Fig. 2. The Fig. 2 shows both
models: EMW and IMW. The EMW model defines the meaning of a word N through
the meaning of other words. Formally, this is a graph representing a semantic rela-
tionship: the vertex N of the graph is connected to the vertices Mi, which depict the
corresponding words, through which the meaning of the word N is revealed [28]. The
arcs of the graph indicate the parameters that determine the type of semantic relation-
ship. The cloud around N, denoted by knowledge about word, depicts the representa-
tion in natural language of the word sign model. The WV is represented by set of
knowledge portions in the form of Fig. 2. In WV the words are organized as a multi-
level structure. Fig. 2 and Fig. 3 show that the meaning of the word N is an abstrac-
tion of a higher level compared to the meaning of the words {Mi, i=1, 2,...,k}, through
which the EMW of the word N is revealed. In turn, the meaning of each of the words
of the lower level, for example, Mi, is also represented through the words {Wij, j=1,
2,...,p} of a more lower levels. This EMW definition continues, going down the ab-
straction levels to words whose meaning is determined directly by the data from sen-
sors. The WV lth level includes lth abstraction level words for which the EMW defi-
nition is given through the words l-1, l-2, ..., 0 abstraction levels.
As mentioned earlier, the EMW model is based on semantic relationships. In [8,
16] the choice of four semantic relationships “object-property” (consist_of); “whole-
part” (part_of); “genus-species” (is_а); “action object-action-subject of action” (be-
fore) is founded. The first three relationships are used in knowledge representation
model of traditional semantic network. The last relationship is introduced to represent
knowledge about dynamical situations, processes passing in time including time
events and actions.
Fig. 2. Word meaning models Fig. 3. Multilevel structure of the EMW
Relationships are parameterized. The following EMW model parameters are
introduced. There are certainty (a), temporary delay (b), information aging rate (v) and
information completeness (g). The EMW presentation base model is given below.
, Mi ϵ ΩN}>, (1)
where N is a word identifier; know is a signs word model; ΩN = {Mi}i=1, 2,...,k is a set of
words of the lower levels of abstraction, which are used for the definition of the
meaning of the word N; Mi is a low-level word identifier; (ai, bi, vi, gi) are the parame-
ters.
The word N, according to Mendel’s theory [18], has a different meaning (means
different things) for different people. Therefore, the expert (group of experts) have
different beliefs that the word Mi, can be used to explain the meaning of the word N.
The quantitative assessment of certainty based on the Stanford theory of Certainty
Factor (CF) [13]. In (1), the parameter −1.0 ≤ a ≤ +1.0 is the certainty. If it is neces-
sary to indicate the presence or absence of a word Mi to determine meaning of the
word N, then the certainty close to ai = +1.0 or vice versa ai = −1.0, respectively. The
parameter b in (1) is a dynamic characteristic of the situation that the word N repre-
sents. The dynamic parameter 0 ≤ b < ∞ (time interval) is used to determine word
that, in the sense, describe temporary event and process. For example, if in explaining
the meaning of the word N it should be noted that the situation represented by the
word Mi should appear later by τ time units than the situation whose meaning repre-
sents the word Mj, then in (1) bi = 0, bj = τ. The information aging rate 0.0 ≤ vi ≤ 1.0
indicates how fast the relevance of information about situation presented by the word
Mi have been lost. If the situation is a fast process, then the aging rate is close to vi =
1.0. For static situation, the aging rate is vi = 0.0. A parameter of the information
completeness 0.0 ≤ gi ≤ 1.0 is characterization of the missing information to deter-
mine the meaning of the word N based on only the one Mi word. When the definition
of the word N is given by enumeration of its representatives {Mi, i=1, 2,...,k}, then gi
= 1.0 for the each Mi. In the case when the word N definition needs a certain set of
words, for example, {Mi, i=1,2,...,k}, then the parameters of information complete-
ness for individual word Mi must satisfy the condition g1 + g2 + + gk ≥1.0. Based on
the model (1), it is possible to represent any of the consist_of, part_of, is_a or before
relationships [24]. On the base of that relationships set, it is possible to represent ex-
ternal meaning of a word which on arbitrary level generalize the data from sensors.
The following is an example of such a representation.
In this article, the eCWW model application is considered by the example of Smart
Traffic-Light (STL). The EMW presentation in the form (1) is considered on the ex-
ample of one of the criteria, namely, pedestrian comfortable conditions. In (2), an
example of the EMW definition is given.
1. <5.PC, pedestrian comfort, {<3.WC, (0.95, t, 0.01, 0.4)>, <1.AP, (0.9, t, 0.5, 0.35)>, <4.F2,
(1.0, t, 0.5, 0.25)>}>;
2. <4.F2, factors of the 2nd degree of importance, {<0.Il, (0.75, t, 0.01, 0.4)>, <0.Ni, (0.9, t, 0.5,
0.35)>, <3.F3, (1.0, t, 0.5, 0.25)>}>;
3. <3.WC, weather comfort, {<2.WCs, (0.95, t, 0.01, 1.0)>, <2.WCw, (0.95, t, 0.01, 1.0)>}>;
4. <3.F3, factors of the 3rd degree of importance, {<2.Sl, (−0.75, t, 0.15, 1.0)>, <0.RR, (−0.75, t,
0.15, 1.0)>}>;
5. <2.WCs, weather comfort spring-summer season, {<1.Ss, (0.75, t, 0.01, 1.0)>, <0.Ys, (0.75, t,
0.01, 1.0)>}>;
6. <2.WCw, weather comfort fall-winter season, {<1.Ws, (0.75, t, 0.01, 1.0)>, <0.Yw, (0.75, t,
0.01, 1.0)>}>;
7. <2.Sl, sleet, {<0.Pd, (0.75, t, 0.01, 0.4)>, <0.IT, (0.9, t, 0.5, 0.35)>, <1.IS, (0.75, t, 0.5,
0.25)>}>;
8. <1.AP, air exhaust pollution, {<0.СН, (0.9, t, 0.01, 0.3)>, <0.CO, (0.9, t, 0.01, 0.3)>, <0.NO,
(0.9, t, 0.01, 0.4)>}>;
9. <1.Ss, spring-summer season, {<0.Ps, (0.75, t, 0.01, 0.3)>, <0.Ws, (0.75, t, 0.01, 0.3)>,
<0.WCs, (0.75, t, 0.01, 0.4)>};
10. <1.Ws, fall winter season, {<0.Pw, (0.75, t, 0.1, 0.4)>, <0.Ww, (0.75, t, 0.1, 0.3)>, <0.WCw,
(0.75, t, 0.1, 0.3)>}>;
11. <1.IS, icing, snow sticking, {<0.Pd, (0.75, t, 0.01, 0.45)>, <0.TR, (0.9, 10, 0.5, 0.25)>, <0.IT,
(0.9, 0, 0.001, 0.5)>}>;
12. <0.Ps, precipitation spring-summer, {, }>;
13. <0.Pw, precipitation fall-winter, {}>;
14. <0.Ws, wind spring-summer, {, ,
}>;
15.<0.Ww, wind fall-winter: {, }>. (2)
In (2), the first digit of a word identifier indicates the WV abstraction level to which
this word belongs. A full knowledge fragment is represented by 28 words, distributed
across 5 levels (Fig. 3). At the top 5th level of abstraction, one word is 5.PC
(pedestrian comfort), EMW of which is given using the three words 3.WC (weather
comfort), 1.AP (air pollution) and 4.F2 (factors of the 2nd degree of importance).
EMW of the last word is also given with the help of three words of a lower level of
abstraction. These are the words 0.Ni (noise), 0.Il (illumination) and 3.F2 (factors of
the 3rd degree of importance). At the bottom zero WV level, pedestrian comfort is
represented by 17 zero-level words that are defined on a set of IGs that represent input
from precipitation, wind, temperature, air pollution, illumination, noises sensors and
season data. The external meaning of 0-level words that are not included in the
fragment (2) of the WV is explained below.These are such words: 0.WCs (wind chill
spring-summer), 0.WCw (wind chill fall-winter), 0.СН (air pollution СН), 0.CO (air
pollution CO), 0.NO (air pollution NOy), 0.Il (illumination), 0.Ni (noises), 0.RR (road
repair work), 0.Pd (precipitation fall-winter drizzling or more intense rain), 0.IT (icing
temperature), 0.TR (temperature reduction), 0.Ys (season of the year, spring-summer),
0.Yw (season of the year, fall-winter). In their definition, there are references to IGs
identifiers. For example, the definition of the word 0.Pw in (2) is given using one IG
dry with identifier d.
In fig. 3 arcs of the graph are bidirectional. This is explained by the following. In
order to obtain EMW of the lth abstraction level, it is necessary to perform a
downward l-step process of revealing the meaning through words of lower levels up to
data from sensors. The converse is also true. In order to calculate IAM of the lth
abstraction level, it is necessary to perform the l-step upward process of abstraction,
starting with the data from the sensors.
3.2 Representation of the Internal Meaning of the Word
In Fig. 2, IMW is represented. This is depicted by shaded arrows inside which indicate
IMW. This view emphasizes that the IMW is the computational meaning of the word.
The IMW expresses the degree of conformity of EMW (1) with the situation
represented by the spatio-temporal data set from the sensors. A numerical estimate of
the IMW of the word N (Fig. 2) depends, firstly, on the parameters by which EMW
was defined in (1), and, secondly, on the IMW of these words {Mi, ϵ ΩN} calculated for
the same spatio-temporal dataset. The [24], an estimate of the closeness of the meaning
of data from sensors to their verbal description was introduced. We use this
characteristic to formally define the IMW. The IMW is a fuzzy L-R number
X : {x | m X ( x), x [−1,+1]} (3)
with Gaussian L-R membership function
mXL ( x) = exp( −( x − ) 2 / 2t L2 , x [−1, ];
(4)
mXR ( x) = exp( −( x − ) 2 / 2t R2 , x [ ,+1];
the parameters of which are the certainty (−1 ≤ α ≤ +1) and the dynamics t=tL+tR (0 ≤
t < ∞), where tL and tR are the time intervals since the last data acquisition from the
sensor and the data change, respectively.
Based on (3), (4), the certainty factor as an IMW crisp characteristic is calculated
cf = k t , (5)
where
mXL ( x) +
mXR ( x)
x[ −1, ] x[ , +1]
kt = 1 − v .
Card ([−1,+1])
3.3 The Internal Meaning of the Word: Computing Model
The inputs and output of the IMW computing model for the example of the word N
are shown in Fig. 2. The IMW of the word N is calculated based on its EMW defini-
tion (1) and IMWM 1 , IMWM 2 ,…, IMWM k .
XN =f( X M1 , X M 2 ,..., X M k ), (6)
where X M1 , X M 2 ,..., X M k are the IMWs of the words M1, M2,…,Mk in the form (3).
The IMW calculation are operations with fuzzy L-R numbers (3), (4). To calculate
IMW in (6), the knowledge presented by the EMW model (1) is used. The essence of
the calculations is the comparison of the ЕMW definition (1) with inputs IMWs. The
computational procedure is divided into three steps: matching is pairwise comparison
of the ЕMW parameters (ai, bi), presented in the ЕMW definition (1), with the
IMWM i of the corresponding input variable; aggregation of similarity estimates ob-
tained in the first step for all input variables; actualization the IMWN parameters.
Matching is the operation of comparing two fuzzy L-R numbers: Xi = (ai, 0, bi), ob-
tained from (1), and the X in i = ( i , t Li , t Ri ) which is the corresponding IMWM i input.
The result of the comparison is the new L-R number Xi'. It is a fuzzy certainty that the
compared fuzzy numbers are close. Calculations on this and following phases are
based on the generalization principle [16].
X i = ( i , t Li = t Li , t Ri = t Ri ) , (7)
where
i = i exp( − i t Li ) MIN (1i , 2i ) , (8)
+ 1, if (−1 i ai or ai i +1), ai 0;
2( i + 1)
i = − 1 +
1
, if − 1 i ai , ai 0; (9)
ai + 1
2( i + ai )
+ 1 + a + 1 , if ai i +1, ai 0;
i
2i = −1 + 2 exp( − i | t Ri − bi |) . (10)
In (7)-(10), the parameters of the ЕMW definition ai, bi, vi and input IMW parame-
ters αi, tLi, tRi. are used. The α'i in (7) is a closeness degree estimate of the input
IMWM i parameters and the ЕMW definition parameters. With small differences,
estimates (9), (10) are close to +1, with maximum differences, estimates tend to –1. If
the estimate is obtained based on the actual data (tLi = 0), then it is not adjusted. For
aged input data, when the parameter tLi > 0, the estimate (8) is corrected in proportion
to the aging rate vi so that α'i→0.
Aggregation of fuzzy closeness estimates obtained during the matching step for
each input variable is carried out as an operation of adding k weighted fuzzy L-R
numbers {Xi'}i=1,2,...,k. The weighting coefficient is the information completeness
parameter gi from the ЕMW definition (1). The operation result is again a fuzzy L-R
number.
X = ( , t L = t Li , t R = t Ri ) , (11)
i =1, 2...k i =1, 2...k
where
2( − 0.5), if +1;
=
+ 1, if +1;
= g1 ( 1 + 1) / 2 + ... + g k ( k + 1) / 2 .
In the last expression (11), the rationing of components on the interval 0.0 ≤
(α'i+1)/2 ≤ +1.0 is performed previously, and then the weighted sum of the normal-
ized numbers is found. The inverse rationing operation is performed, so that –1.0 ≤ α''
≤ +1.0.
Actualization of IMWN value at the output is the final phase of computing. The
operation is as follows. First, on the basis of the found value X'' of the fuzzy L-R
number (11), the cf is calculated by the formula (5). Then this cf value is used to find
the parameters of the L-R number XN, which is the final value of IMWN.
αN = cf, (12)
0, if | cf − − cf | ;
t RN = − (13)
t RN + 1, other wise;
t LN = MAX (t L1 , t L2 ,..., t Lk ) , (14)
−
where t RN , − cf are the parameter values in the previous calculation step;
t L1 , t L2 ,..., t Lk are the IMW parameters of input variables.
4 eCWW Model
As pointed earlier, the eCWW process consist of three phases: GC, AW and
CWW.
In the first GC phase, the spatio-temporal segment of data from sensors is mapped
into the IMWs. This is accomplished by Quantitative Abstraction (QA) and Definitive
Abstraction (DA) [12]. The QA is restrictions on the numerical data from the sensors
based on the requirements for the solution accuracy. The DA maps this quantitative
restriction on the semantic representation in the form of IMW. The eCWW model is
based on the hypothesis that data prototype (a spatio-temporal set of data from sen-
sors) has the meaning that can be expressed by the natural language words. Due to the
word model introduced in this article, the meaning of the data prototype can then be
represented at different levels of abstraction in the form of IMW.
The QA result is the internal meaning of the data granule, which is not yet ex-
pressed in words. This is a “bridge” between the numerical data from the sensors and
knowledge in the form of words. The QA granulation process is based on knowledge
about the granules. This knowledge can be presented in the forms of the numerical
interval with crisp boundaries, fuzzy intervals defined by T1 FS [16] or T2 FS [26]. In
this work, the knowledge about the granules is presented by functional dependence of
certainty α=f(p) on the data, for example, p as shown in Fig. 4.
Fig. 4. IMW calculating at the first phase (quantitative and definitive abstraction)
The QA result is the IG fuzzy characteristic (internal meaning of the granule) in the
form (3) FCig = ( ig , tLig, tRig). Fig. 4 shows an example of a QA for one rain precipi-
tation sensor. The range of possible rainfall values p (universe) is represented by three
granules dry (d), drizzling rain (dr), heavy rainfal (rf). The granules in the Fig.4 are
shaded ovals and marked IGd, IGdr, IGrf, accordingly. The definition of IG (re-
strictions) is given by certainty functions ig on an universe (the abscissa shows the
universe of precipitation p in mm per hour). Certainty values (−1≤ α ≤ + 1) is along
the ordinate axis. For the considered example, the ig are defined by trapezoidal
piecewise linear functions with the parameters given in Table I. The computations of
the internal meaning of the granules are carry out in real time for the input numerical
value from sensor. For example, for the precipitation p*: FCd = ( d ( p ) , tL, tRd),
FCdr = ( dr ( p ) , tL, tRdr), FCrf = ( rf ( p ) , tL, tRrf). The values of tRd, tRdr, tRrf are
found by formula (13). The value of tL is found by formula (15).
0, if m(p i ) error;
tL = −
(15)
t Li + 1, if m(p i ) = error.
In (15), the time interval from the moment of the last control is set to zero when the
correct data is received from the sensor.
TABLE I. IG DEFINITION
Input Data IG / ig IG definition ig (p1, p2, p3, p4)
Dry/d 0.0, 0.0, 0.1, 0.4
Precipitation drizzling rain/dr 0.1, 0.4, 0.8, 2.0
heavy rainfall/rf 0.8, 2.0, 8.0, 18.0
The QA computing is the real-time processing of data stream. The problem arising
from stream processing is solved due to the introduction of the time delay bi and aging
rate vi parameters into the EMW model (1). This allows to “blur” in time the time data
segments, so that then fuzzy compare them with the prototypes. The transition from
the processing of a sequence of data segments to one blurred in time prototype al-
lowed us to move away from a regularly discrete time model to event time model.
The DA result is the IMWs of the all 0-level words. The 12-15 lines of the example
(2), the EMW definitions of the zero level is given. It can be seen that the EMW defi-
nition is given in the form (1). The peculiarity is that the definition uses data granules,
not words. In this regard, the DA computing is IMW calculations according to the
computing model (6)-(14).
In the second AW phase, the IMWs of the first, second and so on abstraction levels
are calculate. At each level, for each word belonging to this WV level, the AWE cal-
culates IMW according to the model (6)-(14). Since words in WV are stratified by
abstraction levels, the calculation process is performed from the bottom up rising
sequentially by levels. As a result of the multi-step abstraction procedure, AWE com-
putes IMWs for all WV words. These IMWs are available for CWWE in the next
third processing phase (Fig. 1).
In the third phase, the CWWE performs inference T1 FS according to IF-THEN
rules. Any of the known models (Mamdani, Takagi-Sugeno, Tsukamoto, Larsen) can
be used here. The peculiarity of CWWE is that its rules use words from the WV of
AWE. Namely, the use of α (IMW characteristic), obtained on the second phase, di-
rectly as T1 FS inputs imposes requirements on the IF-THEN rules presentation. Еnу
terms of Linguistic Variables (LV) in IF fields of the rules should be defined on the
universe [−1, +1], on which the IMW crisp characteristic α is defined in (12). Since
the meaning of the α characteristic is certainty, it is possible to use three or more lin-
guistic assessments (terms), for example, HIGH, LOW and UNKNOWN. A hybrid
version of the T1 FS is possible when part of LVs is defined on the [−1, +1] universe
and another on the domain universe.
5 Smart Traffic-light Based on eCWW Model
The creation of urban traffic management systems as an AS is provided for in strategic
plans for the development of smart cities. One of the components of such a system is
Smart Traffic-Light (STL), which consists of a set of autonomous, intelligent, and
wireless low-cost devices [29]. As an example, here we consider the possibility of
using the eCWW model to control the STL installed at the pedestrian crossing. In STL
a pedestrian button for changing a light signal is supposed. The STL model is
developed and tested on the equipment of the IoT&SM training polygon [30].
The task of real-time control STL is set taking into account the following criterions:
1) Safety, 2) Local situation, 3) Pedestrian comfort, 4) Global transport situation, 5)
Emergency cases. To control the STL based on the first four criteria, input from
various sensors is used. For example, to describe safe situation is used data from
ultrasonic, infrared, laser and video sensors: approaching / retreating vehicles, their
distance, speed and acceleration [15, 30]. The EMW representation of the word safe in
the form (1) is given in [15]. This article discusses an example of the EMW
representation and the IMW calculation for STL control according to the one criterion
of pedestrian comfort. Knowledge about granules and EMWs of 0-level WV of the
first GC phase is fragmentarily presented in Fig. 4 and Table I. The EMWs
presentation of the second AW phase is given in (2). The example of fuzzy rule of the
third CWW phase is given below in (16). The example uses the CWWE of the T1 FS
Mamdani model. The CWWE inputs are IMW coming directly from the upper
abstraction levels of WV of an AWE, namely safe, local situation, pedestrian comfort,
global transport situation and emergency case in the form of cf. In addition, two nu-
merical variables are still used, coming directly from the sensors. This is pedestrian
waiting time and traffic light. The CWWE outputs switch light xxxx is numerical cer-
tainty −1 ≤ α ≤ + 1. Fuzzy rules are built on the LVs whose names are the same as the
names of words from WV of the AWE. Input and output LVs are defined on the
universe −1 ≤ α ≤ + 1 and are not related to the domain scale. All LVs have three
terms, each represented by trapezoidal membership functions. The membership
functions parameters set are {LOW (−1.0, −1.0, −0.5, 0.0), UNKNOWN (−0.5, −0.1,
+0.1, +0.5), HIGH (+0.1, +0.5, +1.0, +1.0)}.
IF safe is HIGH and
local situation is UNKNOWN and
pedestrian comfort is LOW and
global transport situation is HIGH and
emergency case is UNKNOWN and
pedestrian waiting time is MIDDLE and
traffic light is GREEN-CAR, RED-PEDESTRIAN
THEN turn on the traffic light: yellow for car and red for pedestrian is HIGH (16)
In conclusion, we give an example of eCWW computing for one time sample of
processing data from sensors. A detailed description of the AWE computing algorithm
can be found in [24]. Here we will focus on the integration of GC with AWE and
CWWE computing. The computing operates in real time. The trigger event model for
STL control is used. Events related to the fulfillment of condition (13) for any of the
IGs activate AWE. After completion of the IMW calculations of all WV words, the
CWWE is initiated. For the example below, it is assumed that changing the
precipitation value led to the fulfillment condition (13). On the QA step, the GC
calculated: FCd = (+0.95,0,0), FCdr = (−0.9,0,0), FCrf = (−1.0,0,0). An example is
considered for the fall winter season. On the DA step, AWE computed: IMW0.Pw =
(0.95,0,0), IMW0.Ps = (0.98,0,0), IMW0.Pr = (−0.95,0,0). The results of these
calculations can be seen in Fig. 4. The another IMWs are: IMW0.Ww = (0.95,0,120),
IMW0.WCw = (0.75,0,120). Then, on AW step, on the basis of EMWs the AWE
sequentially starting from the first level of the WV, then the second and so on
calculated: IMW1.Ws = (0.85,0,0), IMW1.Ss = (0.95,0,0), IMW2.WCss = (−0.75,0,0),
IMW2.WCw = (0.85,0,0), IMW3.WC = (0.85,0,0), IMW5.PC = (0.8,0,0). After completing the
IMW computing of all WV levels, the CWWE wos activated. When processing the
rules, for example, (16) the IMWs numerical characteristics α7.SF = 0.9, α6.LS = −0.35,
α5.PC = 0.8, α3.GTS = 0.6, α5.EC = 0.25 found at the previous phase of the calculations,
and the values from the sensors t=42 sec, TL=(0, 0, 1, 1, 0, 0) as an inputs were used.
After defuzzification of the inference results in CWWE, we obtained a rank of all con-
trol decisions by the certainty criterion, for example, αturn on the traffic light: yellow for car and red for
pedestrian = 0.65.
6 Conclusion
The eCWW model expands the capabilities of the AS, which creates the conditions for
its use in domains where it is required to make control decisions in unforeseen
situations. Such opportunities appeared due to the transition from the concept of data
from sensors processing to the concept of word processing in the form of a three-phase
procedure. In the first, the spatio-temporal segment of data from sensors is mapped into
the words. This allowed preliminary to generalize data from sensors into the words of
higher abstraction levels and after that carry out fuzzy reasoning based on them. This
became possible thanks to the introduction the models of the internal and external
meaning of the word. Secondly, in AS control, the situation dynamic properties are
taken into account and the effect of uncertainty associated with the incompleteness and
aging of data, as well as the uncertainty of the experts in describing the AS behavior, is
reduced. This opportunity appeared due to the presentation of the external meaning of
the word by parametrized semantic relations and the internal meaning by the fuzzy
characteristics of the word. Third, proposed model meets the requirements for real-time
applications that use sophisticated dataset from sensors. The number of fuzzy rules has
been significantly reduced due to the use words of high-level abstraction as CWW
linguistics variables and inputs. Computing time is reduced due to this. Fourth, due to
the WV openness property, the model adaptability and the possibility to evolving are
supported. Therefore, predefined EMWs can subsequently be tuned using well-
established methods for determining fuzzy sets, for example, Enhanced Interval
Approach or an arsenal of evolutionary and bio-inspired methods.
In the future, it is planned to improve proposed eCWW model so that it has the
ability to adapt and tune the parameters of the EMW in the operational mode.
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