Unlimited Enthusiasm... International University of Sarajevo Paromlinska 66, SARAJEVO Optimization of Transport Problems with Fuzzy Coefficients By: Amir Omerovic, Jasmin Jusufovic and Mehmet Can The place where boundaries do not exist... Filled with...

Optimization of Transport Problems with Fuzzy Coefficients In this paper, we concentrate on fuzzy linear programming problems with fuzzy right-hand sides. We consider here only the case of fuzzy numbers with linear membership functions. The symmetric method of Bellman and Zadeh [2] is used for a defuzzification of these problems. The crisp problems obtained after the defuzzification are non-linear and even non-convex in general. Finally, we give illustrative example and their numerical solutions. Pula, September 06 Amir Omerović, Jasmin Jusufović, Mehmet Can

In this paper, we concentrate on fuzzy linear programming problems with fuzzy right-hand sides. We consider here only the case of fuzzy numbers with linear membership functions. The symmetric method of Bellman and Zadeh [2] is used for a defuzzification of these problems. The crisp problems obtained after the defuzzification are non-linear and even non-convex in general. Finally, we give illustrative example and their numerical solutions.

Brief historical overview Fuzzy logic theory was initiated in 1965. Three phases in its development: Academic phase ( 1965 – 1977) Transormation phase ( 1978 – 1988) Fuzzy boom phase ( 1989 – nowadays). Pula, September 06 Amir Omerović, Jasmin Jusufović, Mehmet Can

Fuzzy logic theory was initiated in 1965.

Three phases in its development:

Academic phase ( 1965 – 1977)

Transormation phase ( 1978 – 1988)

Fuzzy boom phase ( 1989 – nowadays).

Founder of the Fuzzy theory Born on 4 th February 1921 in Baku, Azerbaijan. High school graduation had in Teheran, and B.S. Degree in Electrical Engineering at the University of Teheran. During II World War, he moved with his family to U.S. where he persuaded S.M. Deg. and Ph.D. Deg. in electrical engineering. He made great breakthrough in 1965 when he published his work on Fuzzy sets. He lives in California, U.S.A. Pula, September 06 Amir Omerović, Jasmin Jusufović, Mehmet Can

Born on 4 th February 1921 in Baku, Azerbaijan.

High school graduation had in Teheran, and B.S. Degree in Electrical Engineering at the University of Teheran.

During II World War, he moved with his family to U.S. where he persuaded S.M. Deg. and Ph.D. Deg. in electrical engineering.

He made great breakthrough in 1965 when he published his work on Fuzzy sets.

He lives in California, U.S.A.

Pula, September 06 Amir Omerović, Jasmin Jusufović, Mehmet Can

Pula, September 06 Amir Omerović, Jasmin Jusufović, Mehmet Can

Pula, September 06 Amir Omerović, Jasmin Jusufović, Mehmet Can

Pula, September 06 Amir Omerović, Jasmin Jusufović, Mehmet Can

Example: Fuzzy transport problem A company has two production centers . Markets sell the products of this company. The factory produces daily at least 200 items. This production may go to 300, depending on the raw materials and the motivation of workers. Similarly the factory produces at least 150 items a day and this production may go to 200. Market sells 250 items a day, and it may increase it to 300 items. Market sells 100 items a day, and it may increase it to 200 items. Pula, September 06 Amir Omerović, Jasmin Jusufović, Mehmet Can

A company has two production centers . Markets sell the products of this company. The factory produces daily at least 200 items. This production may go to 300, depending on the raw materials and the motivation of workers. Similarly the factory produces at least 150 items a day and this production may go to 200. Market sells 250 items a day, and it may increase it to 300 items. Market sells 100 items a day, and it may increase it to 200 items.

Pula, September 06 Amir Omerović, Jasmin Jusufović, Mehmet Can Market Place M 1 M 2 Production Center F 1 10 8 F 2 6 7

Pula, September 06 Amir Omerović, Jasmin Jusufović, Mehmet Can

Pula, September 06 Amir Omerović, Jasmin Jusufović, Mehmet Can

Pula, September 06 Amir Omerović, Jasmin Jusufović, Mehmet Can

Pula, September 06 Amir Omerović, Jasmin Jusufović, Mehmet Can

Pula, September 06 Amir Omerović, Jasmin Jusufović, Mehmet Can

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