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.