application of connected fuzzy models with possibilities of using non standard fuzzy sets in process...
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APPLICATION OF CONNECTED FUZZY MODELS WITH POSSIBILITIES OF USING NON STANDARD FUZZY SETS IN PROCESS OF PLANNING PRODUCTION AND SALES FOR A NEW PRODUCT
Zikrija Avdagić, PhD.,Professor Computer Science Department, Faculty of Electrical Engineering, University of Sarajevo
Admir Midžić, MSc. Information Systems Department, DD BH Telecom Sarajevo,
ESTIMATION MODEL FOR PRICE OF NEW PRODUCT
Production costs
Competition price
Information necessary for making
of profit and coverage of the market
Estimation model for price of new
product
4 Rules
recommended price
0
fuzzy sets
Estimation model for the number of sold
products
1 Rule
Estimated number of sold
products (production planning)
0
fuzzy sets
ESTIMATION MODEL FOR THE NUMBER OF PRODUCTS SOLD
FUZZY MODELS
DEFINITION OF 1. RULE
Cijena konkurencije Troškovi proizvodnje Naša cijena
1
Pr. Premise 1IF any price of competition
Premise 2AND any production costs
ConclusionTHEN must exist fuzzy set HIGH price
R1
R1 Our price must be high(unconditional)(Proposed by financial director)
competition price production costs our price
unit singletons
over
universe of discourse
Troškovi proizvodnje Naša cijena
1
Cijena konkurencije
Pr. Premise 1IF any price of competition
Premise 2AND any production costs
ConclusionTHEN must exist fuzzy set LOW costs
R2
DEFINITION OF 2. RULE
R2 Our price must be LOW(unconditional)(This rule is proposed by director deputy. It is good because of covering products on market. We can notice one special feature of fuzzy systems because we can model conflict expert knowledge (1. and 2. rule).
competition price production costs our price
Ovaj fuzzy skup je nastao transformacijom skalara (22) u pi krivu
1
11
Cijena konkurencije Troškovi proizvodnje Naša cijena
Pr. Premise 1IF any price of competition
Premise 2AND discrete value of production costs (11)
ConclusionTHEN our price must be fuzzy set around value 2*product costs
R3
competition price production costs our price
This fuzzy set was derived using transformation of scalar (2*11=22) into Pi curve
R3 Our price must be around value 2*production costs(unconditional but for concrete value of production cost we can derived fuzzy set in conclusion )(This rule is proposed by manufacture director, making sure covering of manufacturing product costs.)
DEFINITION OF 3. RULE
fuzzy skup nije vrlo visoka
stepen članstva za ulazni parametar
ulazni parametar
Troškovi proizvodnje
Naša cijena
Pr. Premise 1IF price of competition is not very HIGH
Premise 2AND for any product costs
ConclusionTHEN our price need to be around value of competition price
R4
Stepen članstva za
Ulazni parametar
DEFINITION OF 4. RULE
our price production costs
input parameter (26)
Fuzzy setnot very HIGH
Value of member-ship (0.8) for input parameter (26)
R4 if competition price is not very HIGH then our price must be around value of competition price(conditional)(Proposed by marketing personal and making sure that value of product price be close to value of competition product price.)
AGREGATION OF RFSAT THE START
Activating the first rule we have got (in conclusion of that unconditional rule) fuzzy set HIGH and that set was transferred into RFS.
First we haveempty RFS.
RFS after performingof rule R1.
CONCLUSION PARTNotice: For unconditional fuzzy rules RFS is produced by
minimization of fuzzy sets in conclusion parts of rules .
Fuzzyset in conclusionof Rule 1Activation
of Rule 1
FIRST STEP
Now, RFS from START is not empty and because of that we take minimum value of START-RFS membership , and corresponding value of fuzzy set LOW produced by activation of Rule2.
AGREGATION OF RFS
RFS from START
RFS after performing
of Rule 2
Fuzzyset in conclusionof Rule2
CONCLUSION PARTs
Activation of Rule 2
AGREGATION OF RFSSECOND STEP
RFS from FIRST step
New RFS was produced taking minimum value of membership of FIRST STEP, and fuzzy set around values 2*production costs.
Activation of Rule 3
Fuzzyset in conclusionof Rule 3
RFS after Rule 3 was carried out.
CONCLUSION PARTs
Activation of Rule 3
AGREGATION OF RFSTHIRD STEP
Now we have carrying out of conditional Rule 4. For input parameter (competition price 26) in process of fuzzyfication we define membership value of fuzzy set not very HIGH. This value was used (in implication method) for cutting of fuzzy set in conclusion part of Rule 4. Fuzzy set in conclusion part of Rule 4 was produced by scalar ( value of competition price) transformation into fuzzy set around values competition price.
RFS from SECOND step
Fuzzy set from activation of
Rule 4
Activation of Rule 4
Final RFS
Final RFS was produced by maximization of RFS produced in step 2 and fuzzy set derived in firing of Rule 4. Notice : when we have conditional Rule then aggregation is based on maximaization of membership values.
RFS after Rule 4 was carried out.
DEFUZZIFICATION OF FINAL RFS
WE use defuzyfication methods (COA and MOM) to get crisp (concrete) values for recommended price.
CM (Composite Maximum) MOM (Maximum of Medium)
M
m
m
M
yy
1
*
Center of Area - COA (Centroid- CT)
B’ Result Fuzzy Set
μB’
M= number of discrete points for activated plateau;Ym= value of y in discrete point m; m= 1 to M
MODEL FOR ESTIMATING THE NUMBER OF PRODUCTS SOLD
IF price of products is LOW, THEN number of products sold is HIGH
output values from
previous model
results for planning sales and
production
fuzzy set LOWfuzzy set HIGH
RESULTS
Center of Area - COA (Centroid)- CT Defuzzified value changes softly through the resulting fuzzy set with changing of the value of parameters that affect the input fuzzy sets. It is simply calculated and can be applied to fuzzy output and constant output value.
CM (Composite Maximum) MOM (Maximum of Medium)- CO Expected value depends on one rule that dominates in the set of rules. Output value "jumps" from one "plateau" to another, as the height of resulting fuzzy set changes (see 17 and 18)
CONCLUSIONSThis work highlighted:
the main characteristics of the used monotonic fuzzy reasoning
applied to two defuzzyfication methods(COA i CM),
connection of more models in solving problems from economic area,
simple modification of fuzzy models changing the labels of fuzzy sets, number of rules and ...
Simple clearness based on graphic representation,
Reasoning process tolerant regarding imprecise and uncomplete data.
All these are reasons why fuzzy models should be seen as a supplement to the classic mathematical models in development of economic models.