The main goal of the paper is presentation some possibilities of application ordered fuzzy numbers in multi-criteria decision making. In the paper we present several examples of interpretation ordering fuzzy numbers, propositions application ordered fuzzy numbers in multi-criteria decision making for representation type of criterion as well verbal description. The fuzzy saw and fuzzy TOPSIS methods based on ordered fuzzy numbers were presented. The paper have a methodological character and can inspire to future research concerning application ordered numbers in multi-criteria decision making.
multi-criteria decision ma king, ordered fuzzy numbers, linguistic variables, fuzzy SAW, fuzzy TOPSIS
Bilgiç T., Türken I. B., (2000), Measurement of Membership Functions: Theoretical and Empirical Work, w: Dubois D., Prade H., (red.), Fundamental of Fuzzy Sets, The Handbook of Fuzzy Sets, 7, Kluwer, Dordrecht.
Chen S. J., Hwang C. L., (1992), Fuzzy Multiple Attribute Decision Making: Methods and Applications, Springer Verlag, Berlin.
Dubois D., Prade H., (1979), Fuzzy Real Algebra: Some Results, Fuzzy Sets and Systems, 2 (4), 327–348.
Dubois D., Prade H., (1980), Fuzzy Sets and Systems: Theory and Application, Academic Press, New York.
Dubois D., Prade H., (1988), Possibility Theory, New York, London.
Górecka D., Roszkowska E., Wachowicz T., (2016), The MARS Approach in the Verbal and Holistic Evaluation of the Negotiation Template, Group Decision and Negotiation, 25 (138), 1–40.
Herrera F., Herrera-Viedma E., (2000), Linguistic Decision Analysis: Steps for Solving Decision Problems under Linguistic Information, Fuzzy Sets and Systems, 115, 67–82.
Kacprzak D., (2010), Skierowane liczby rozmyte w modelowaniu ekonomicznych, Optimum, Studia Ekonomiczne, 3, 263–281.
Kacprzak D., Roszkowska E., (2014), The Application of Ordered Fuzzy Numbers in the SAW Procedure, The Sixth Podlasie Conference on Mathematics, czerwiec 1–4, 2014, Białystok.
Kacprzak D., Roszkowska E., (2016), The Fuzzy Saw and Fuzzy TOPSIS Procedures Based on Ordered Fuzzy Numbers, Information Sciences, 369, 564–584.
Kosiński W., (2006), On Fuzzy Number Calculus, International Journal of Applied Mathematics and Computer Science, 16 (1), 51–57.
Kosiński W., Prokopowicz P., (2004), Algebra liczb rozmytych, Matematyka Stosowana, 5 (46), 37–63.
Kosiński W., Prokopowicz P., Ślęzak D., (2002), Drawback of Fuzzy Arthmetics – New Intuitions and Propositions, w: Burczyński T., Cholewa W., Moczulski W., (red.), Methods of Artificial Intelligence, Gliwice.
Kosiński W., Prokopowicz P., Ślęzak D., (2003), Ordered Fuzzy Numbers, Bulletin of the Polish Academy of Sciences Mathematic, 52 (3), 327–338.
Kosiński W., Wilczyńska-Sztyma D., (2010), Defuzzification and Implication within Ordered Fuzzy Numbers, w: WCCI 2010 IEEE World Congress on Computational Intelligence, Barcelona, Spain, 1073–1079.
Norwich A. M., Türken I. B, (1998), A Model for the Measurement of Membership and the Consequences of is Empirical Implementation, Fuzzy Sets and Systems, 12, 1–25.
Piasecki K., (2017), O pewnych modyfikacjach teorii skierowanych liczb rozmytych, Optimum. Studia Ekonomiczne, 3 (87), 3–18.
Prokopowicz P., Pedrycz W., (2015), The Directed Compatibility Between Ordered Fuzzy Numbers – A Base Tool for a Direction Sensitive Fuzzy Information Processing, Artificial Intelligence and Soft Computing, 9119, 249–259.
Roszkowska E., (2014), Ocena ofert negocjacyjnych w słabo ustrukturyzowanych problemach negocjacyjnych z wykorzystaniem rozmytej procedury SAW, Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu, 327, 237–247.
Roszkowska E., Wachowicz T., (2015a), Application of Fuzzy TOPSIS to Scoring the Negotiation Offers in Ill-Structured Negotiation Problems, European Journal of Operational Research, 242 (3), 920–932.
Roszkowska E., Wachowicz T., (2015b), Inaccuracy in Defining Preferences by the Electronic Negotiation System Users, w: Kamiński B., Kersten G., Szapiro T., (red.), Outlooks and Insights on Group Decision and Negotiation, GDN 2015, Lecture Notes in Business Information Processing, 218, Springer, Cham.
Roszkowska E., Wachowicz T., (2016), Negocjacje : analiza i wspomaganie decyzji, Warszawa, Wolters Kluwer.
Salo A., Hämäläinen R. P., (2010), Multicriteria Decision Analysis in Group Decision Processes, w: Kilgour D. M., Eden C., (red.), Handbook of Group Decision and Negotiation, Springer, New York, 269–283.
Trzaskalik T., (2014), Wielokryterialne wspomaganie decyzji. Metody i zastosowania, PWE.
Wachowicz T., (2010), Metody i narzędzia wspomagania fazy prenegocjacyjnej, Decyzje 14, 55–84.
Wilczyńska-Sztyma D., (2010), Direction of Research into Methods of Defuzzification for Ordered Fuzzy Numbers, XII International PhD Workshop OWD 2010.
Wilczyńska-Sztyma D., (2009), Idea skierowanych liczb rozmytych. Przykłady interpretacji. I International PhD Workshop OWD 2009.
Yager R. R., Filev D. P., (1994), Essentials of Fuzzy Modeling and Control, John Wiley & Sons, Inc., New York.
Zadeh L. A., (1965), Fuzzy sets, Information and Control, 8, 338–353.
Zadeh L. A., (1975), The Concept of a Linguistic Variable and its Application to Approximate Reasoning, Part I, Information Linguistic Variable, Expert Systems with Applications, 36 (2), 3483–3488.
Zimmermann H. J., (2001), Fuzzy Set Theory and Applications, 4th Rev. ed. Boston: Kluwer Academic Publishers.