1. 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,

2. 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

3. DEFINITION OF 1. RULE Cijena konkurencije Troškovi proizvodnje Naša cijena 1 Pr. Premise 1 IF any price of competition Premise 2 AND any production costs Conclusion THEN must exist fuzzy set HIGH price R1 Our price must be high (unconditional) (Proposed by financial director) competition priceproduction costs our price unit singletons over universe of discourse

4. Troškovi proizvodnje Naša cijena 1 Cijena konkurencije Pr. Premise 1 IF any price of competition Premise 2 AND any production costs Conclusion THEN 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 costsour price

5. Ovaj fuzzy skup je nastao transformacijom skalara (22) u pi krivu 1 11 Cijena konkurencije Troškovi proizvodnje Naša cijena Pr. Premise 1 IF any price of competition Premise 2 AND discrete value of production costs (11) Conclusion THEN 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 R3Our 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

6. fuzzy skup nije vrlo visoka stepen članstva za ulazni parametar ulazni parametar Troškovi proizvodnje Naša cijena Pr. Premise 1 IF price of competition is not very HIGH Premise 2 AND for any product costs Conclusion THEN our price need to be around value of competition price R4 Stepen članstva za Ulazni paramet ar DEFINITION OF 4. RULE our price production costs input parameter (26) Fuzzy set not very HIGH Value of member- ship (0.8) for input parameter (26) R4if 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.)

7. AGREGATION OF RFS AT 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 have empty RFS. RFS after performing of rule R1. CONCLUSION PART Notice: For unconditional fuzzy rules RFS is produced by minimization of fuzzy sets in conclusion parts of rules. Fuzzyset in conclusion of Rule 1 Activation of Rule 1

8. 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 o RFS after performing of Rule 2 Fuzzyset in conclusion of Rule2 CONCLUSION PARTs Activation of Rule 2

9. AGREGATION OF RFS SECOND 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 conclusion of Rule 3 RFS after Rule 3 was carried out. CONCLUSION PARTs Activation of Rule 3

10. AGREGATION OF RFS THIRD 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.

11. 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) Center of Area - COA (Centroid- CT) B’ Result Fuzzy Set μB’μB’ M= number of discrete points for activated plateau; Ym= value of y in discrete point m; m= 1 to M

12. 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 LOW fuzzy set HIGH

13. 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)

14. CONCLUSIONS This 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.