-There are many methods and models for analyzing of production processes and the need for their adaptation to and managing complex systems. They differ in both the degree the changing nature of the problem area. oMf actohmemplaetxicitayl amnoddtehlse dofegbreuesinofesdsetpariolcoefsstehse adreescrviebreyd hoabrjdecttso. The industry-accepted standards of the industrial methodolimplement. They do not consider multiple external and internal ogy are used to represent aircraft manufacturing and capacity influences o n t he p roduction, w hich m akes s uch m odels lemssanagement. The industrial methodology is formed based effective. on averaged indicators in the industry, which leads to the An alternative way to solve the production management following problems [4], [5]: problem is to introduce some parameterized algorithms as a simplified f orm o f m athematical m odels. S uch a lgorithms are 1) A large number of statistical factors and assumptions are usually expressed in the form of instructions, which are based on used for production control. the analyzed statistics. The disadvantage of this approach is the 2) Absence of methods for an objective evaluation of the significant averaging of the values of indicators and parameters of current state of production. tohfesmimoidlaerle dinodbujsetcrties.s,Maentdhotdhseyarearfeorumnusluaitteadblfeorfoar wthheolespreacnifigce 3) Absence of methods for identifying problems and deviconditions of each enterprise. ations in production processes. It is necessary to create data analysis methods and process 4) Automation of production processes does not imply an models that are adaptable to specific p roduction conditions. evaluation of the complex state of the enterprise leads Data from the information systems of various manufacturing to: enterprises can be analyzed to determine the states and conditions of production. The important knowledge for production management is extracted as a result of such analysis. The article describes a hybrid approach for analyzing the dynamics of production indicators and forming linguistic recommendations to increase the efficiency and quality of decision making. Hybridization means the usage of ontological engineering methods to describe the characteristics of production in the context of production indicators represented by time series models.
The main goal of the study is to reduce the degree of
uncertainty in the capacity management process of complex
production. Each production has various characteristics. Also,
complex production is an unconventional object of
management in the concept of the situational control theory [
The capacity management includes next steps: developing technical passport of the enterprise; calculation of capacities for each production unit and the enterprise as a whole; development of shortage control strategy; generation of a consolidated report with the forecast for the implementation of the product program; calculation of consolidated capacity balance.
The input parameter vector W from situational control includes such indicators as the fund of working time, equipment usage, the useful annual fund of equipment time, and others. These indicators have a great influence on the evaluation of total production productivity. The inability of the DM to set the values of these indicators severely limits the efficiency of decisions.
Thus, the following research objectives must be solved:
data collection of production state through integration
with enterprise information systems (data consolidation,
ETL) [
Type 2 fuzzy sets A~ in the universum U can be defined using type 2 membership function. Type 2 fuzzy sets can be represented as:
A~ = ((x; u); A~(x; u))j8x 2 U; 8u 2 Jx [0; 1] where x 2 U and u 2 Jx [0; 1] in which 0 A~(x; u) 1.
The main membership function is in the range from 0 to 1, so the appearance of the fuzzy set is expressed as: Z Z
A~(x; u)=(x; u)Jx where the operator R R denotes the union over all incoming x and u.
Time series modeling needs to define interval fuzzy sets and their shape. The fig. 2 shows the appearance of the sets. where A~iU and A~iL is a triangular type 1 fuzzy sets; aiu1; aiu2; aiu3; ali1; ali2; ali3; is reference points of type 2 interval fuzzy set A~i, h is the value of the membership function of the element ai (for the upper and lower membership functions, respectively).
An operation of combining type 2 fuzzy sets is required in the process of working with a rule base build on the values of a time series. The combining operation defined as follows: ~ A1
A~2 = (A~1U ; A~1L)
(A~2U ; A~2L) = = ((a1u1 + a2u1; a1u2 + a2u2; a1u3 + a2u3; min(h1(A~1U ); h1(A~2U )A~1U )); min(h2(A~1U ); h2(A~2U )); ); (al11 + al21; al12 + al22; al13 + al23; min(h1(A~1L); h1(A~2L)); min(h2(A~1L); h2(A~2L)));
The proposed algorithm for smoothing and forecasting of time series based on type 2 fuzzy sets can be represented as a sequence of the following steps: 1) Determination of the universe of observations. U = [Umin; Umax], where Umin and Umax are minimal and maximal values of a time series respectively. 2) Definition of membership functions for a time series M = f 1; : : : ; lg; l n, where l is the number of membership functions of fuzzy sets, n is the length of a time series. The number of membership functions and, accordingly, the number of fuzzy sets is chosen relatively small. The motivation for this solution is the multi-level approach to modeling a time series. To decrease the dimension of the set of relations it is necessary to reduce the number of fuzzy sets at each level. Obliviously, this approach decrease the approximation accuracy of a time series. However, creating the set of membership functions at the second and higher levels increase the approximation accuracy with an increase in the number of levels. 3) Definition of fuzzy sets for a time series. The superscript defines the type of fuzzy sets in that case. A1 = fA11; : : : ; Al1g; A2 = fA21; : : : ; A2mg, where l is the number of type 1 fuzzy sets, m is the number of type 2 fuzzy sets. 4) Fuzzification of a time series by type 1 sets. 8xi y~i =
5) Fuzzification a time series by type 2 sets. 6) Creation of relations. The rules for the creation of relations are represented in the form of pairs of fuzzy sets in terms of antecedents and consequents, for example: A11A21 : : : ! A12A21. 7) Forecasting for the first and second levels based on a set of rules. The forecast is calculated by the centroid method, first on type 1 fuzzy sets A1 = fA11; : : : ; Al1g, then on type 2 fuzzy sets.
8) Errors evaluation.
IV. ONTOLOGY-BASED LINGUISTIC SUMMARIZATION OF A
TIME SERIES FORECAST
Linguistic Summarization of the time series forecast allows
the decision-maker to react to changes in the production state
more operatively. The rule base in the form of the following
ontology is used to get linguistic summarization of the time
series forecast [
O = hI; E; S; A; R; F i; (1) where I = fI1; I2; : : : ; Ing is a set of indicators that determine the state of the production capacities at some point in time; E = fBad; Good; High; M iddle; Lowg is a set of linguistic labels for linguistic summarization of the values of production indicators; S = fStateHigh; StateM iddle; StateLowg is a set of textual representations of linguistic labels from the set E; A = fhI1; Badi; hI1; Goodi; hI2; Badi; hI2; Goodi; : : : ; hIn; Badi; hIn; Goodig is a set of textual representations of recommendations for each production indicator that depends on various evaluation of its condition: Good (within the norm) and Bad (deviation from the norm); R is a set of ontology relationships:
R = fRE S; RE A; RI Eg;
where RE S is a set of relationships between a linguistic label
and its textual representation;
RE A is a set of relationships between a linguistic label and a
textual representation of a recommendation;
RI E is a set of relationships between a value of production
indicator and its linguistic label. This type of relationship is
formed in the process of linguistic summarization of the values
of production indicators using the reasoner and the set of rules
in the SWRL language [
The ALCHF (D) [
O = T Box [ ABox; where T Box is the terminological box; ABox is the assertional box.
The T Box contains statements describing concept hierarchies and relations between them. The ABox contains axioms defined as a set of individuals and relations between individuals and concepts.
A. Terminological box T Box
I v >
where E is a concept representing a linguistic label of ontology; Bad, Good, High, M iddle, Low are concepts representing linguistic labels for linguistic summarization of values of production indicators; I is a concept representing a production indicator; S is a concept representing a linguistic label; A is a concept representing ontology recommendations;
ing the state of production capacities; Recommendation is a concept representing linguistic labels and recommendations in textual form; v is the concept inclusion axiom; hasResume is a role to set the correspondence between the recommendation and the production indicator; hasState is a role to set the correspondence between a linguistic label and a production indicator; hasV alue is a role to set a value (in Double) of production indicator; hasDescription is a functional role to specify a textual description (in String) of a linguistic label or recommendation. B. Assertional box ABox i1 : I i1 : High s1 : StateHigh a1 : A (i1; value1 : Double) : hasV alue (i1; s1) : hasState (a1; value2 : String) : hasDescription (i1; a1) : hasResume C. Linguistic summarization of production indicators
Suppose that at some enterprise two indicators of production capacities are used: 1) Power in man-hours per 1 month (EP ). 2) Power in machine hours per 1 month (T P ).
Production indicator values must be specified based on forecast values in the form of following ABox axioms: EP : I T P : I (EP; 3610) : hasV alue (T P; 2700) : hasV alue
The expert is forming the following set of SWRL-rules to produce a linguistic summarization for each production indicator:
ˆ swrlb:lessThanOrEqual(?val, 2000) > Low(?ind) EP(?ind) ˆ hasValue(?ind, ?val) ˆ swrlb:greaterThan(?val, 2000) ˆ swrlb:lessThanOrEqual(?val, 4000) > Middle(?ind) EP(?ind) ˆ hasValue(?ind, ?val) ˆ swrlb:greaterThan(?val, 4000) > High(?ind)
ˆ swrlb:lessThanOrEqual(?val, 1000)
> Low(?ind) TP(?ind) ˆ hasValue(?ind, ?val) ˆ swrlb:greaterThan(?val, 1000) ˆ swrlb:lessThanOrEqual(?val, 3000)
> Middle(?ind) TP(?ind) ˆ hasValue(?ind, ?val) ˆ swrlb:greaterThan(?val, 3000)
> High(?ind)
Each production indicator is associated with a specific linguistic label after the implementation of these rules:
A predefined set of SWRL rules is used to map a linguistic label to its textual representation:
> hasState(?ind, ?state) Middle(?ind) ˆ StateMiddle(?state)
> hasState(?ind, ?state) High(?ind) ˆ StateHigh(?state)
> hasState(?ind, ?state) (EP; StateM iddle) : hasState (T P; StateM iddle) : hasState
Following axioms are added in ABox after executing the set of SWRL rules presented above:
The following rule in SQWRL language [
> sqwrl:select(?ind, ?descr)
Executing a query in the SQWRL language presented above produces the following result:
TP The value of the production indicator is average EP The value of the production indicator is average Linguistic labels are used to forming recommendations for balancing the production capacities of an enterprise. D. Generation of linguistic recommendations for production management
The following set of SWRL rules set by the expert is used to generate recommendations for balancing the production capacities:
EP(?ep) ˆ Low(?ep) > Bad(?ep) EP(? ep) ˆ Middle(?ep) > Bad(?ep) EP(?ep) ˆ
High(?ep) > Good(?ep) TP(?ep) ˆ Low(?ep) > Bad(?ep) TP(? ep) ˆ Middle(?ep) > Bad(?ep) TP(?ep) ˆ
High(?ep) > Good(?ep)
The SWRL rules presented above are based on linguistic labels assigned by the linguistic summarization algorithm and generate the following ABox axioms:
EP : Bad
T P : Bad
The following SWRL rules are used to generate textual recommendations for balancing production capacities based on the attached linguistic labels of production indicators: EP(?ep) ˆ Bad(?ep) ˆEP Bad(?res)
> hasResume(?ep, ?res) EP(?ep) ˆ Good(?ep) ˆ EP Good(?res)
> hasResume(?ep, ?res) TP(?tp) ˆ Bad(?tp) ˆ TP Bad(?res)
> hasResume(?tp, ?res) TP(?tp) ˆ Good(?tp) ˆ TP Good(?res)
> hasResume(?tp, ?res) EP(?ep) ˆ Bad(?ep) ˆ TP(?tp) ˆ Bad(?tp) ˆ EP TP Bad(?res)
> hasResume(?ep, ?res) ˆ hasResume(?tp, ?res) EP(?ep) ˆ Good(?ep) ˆ TP(?tp) ˆ Good(?tp) ˆ EP TP Good(?res)
> hasResume(?ep, ?res) ˆ hasResume(?tp, ?res)
Recommendations for balancing production capacities (EP Bad, EP Good, TP Bad, TP Good, EP TP Bad, EP TP Good) set by the expert and contains some textual representation.
ABox is contained the following axioms after the execution of SWRL rules presented above: (EP; EP BAD) : hasResume (EP; EP TP BAD) : hasResume (T P; TP BAD) : hasResume (T P; EP TP BAD) : hasResume
The following rule in SQWRL language is used to develop recommendations for balancing production capacities of enterprise based on the content of ABox: hasResume(?ind, ?rule) ˆ hasDescription(?rule, ?descr)
> sqwrl:selectDistinct(?ind, ?rule, ?descr)
The following result will be obtained as a result of executing the SQWRL rule presented above: TP TP Bad ”Capacity in machine hours per 1 month is not enough to execute the production program.
Additional equipment is required.” EP EP TP Bad ”Capacity in man hours and machine hours per 1 month is not enough to execute the production program. The following steps must be taken: buy additional equipment, hire additional personnel.” TP EP TP Bad ”Capacity in man hours and machine hours per 1 month is not enough to execute the production program. The following steps must be taken: buy additional equipment, hire additional personnel.” Recommendations generated for different indicators (EP and T P ) and received after the implementation of the same rule (recommendation EP TP Bad) are displayed only once. Recommendations formed by more complex (compound) rules (recommendation EP TP Bad) overlap recommendations of more simplistic rules (recommendations EP Bad, TP Bad). Thus, the user has received the following information as recommendations for balancing the production capacities of the enterprise:
Capacity in man hours and machine hours per 1 month is not enough to execute the production program. The following steps must be taken: buy additional equipment, hire additional personnel.
Data-driven production management is a relevant area of research. The growth of data-driven production management is promoted by both the existing automation systems at enterprises and the volumes of data accumulated in such systems.
This article has proposed an approach to the analysis of the dynamics of production indicators based on time series models. Type 2 fuzzy sets are used for time series modeling. Type 2 fuzzy sets allow modeling objects with a higher degree of uncertainty.
The proposed approach allows to increase the efficiency of decision-making on production management. The proposed approach in contrast to the decision-making process based on an industrial methodology operates not with average production indicators, but with values of production indicators extracted from the information systems of an enterprise.
The proposed approach to the formation of linguistic recommendations allows decision-makers to gain a deeper understanding of the current state of production and respond to changes in production indicators more operatively. The process of forming linguistic recommendations is based on a set of fuzzy and SWRL-rules.
The reported study was funded by RFBR and Ulyanovsk region, projects numbers 18-47-732016, 18-47-730022, 19-47730005, 19-07-00999.