Some Remarks of Different Aggregation Modes Applications Within the Framework of Intuitionistic Fuzzy Weights

• Autorzy: Tikhonenko-Kędziak A. , Kurkowski M.

Identyfikatory

DOI

10.16926/m.2016.21.13

• Języki publikacji: EN

Abstrakty

EN

In the classical intuitionistic fuzzy sets theory it is known, that the use of all aggregation modes is not always possible, because of the lack of definition of raising intuitionistic fuzzy values to the intuitionistic fuzzy power. The main aim of this work is to introduct an operation of raising of intuitionistic fuzzy values to an intuitionistic fuzzy power,which does not require conversion to intuitionistic fuzzy values. Additionally, we will present a heuristic method of raising an intuitionistic fuzzy values to the intuitionistic fuzzy power and consideration about its properties.

Słowa kluczowe

EN

fuzzy set; real numbers; MCDM

PL

zbiór rozmyty; liczba rzeczywista; MCDM

• Wydawca: Wydawnictwo Uniwersytetu Humanistyczno-Przyrodniczego im. Jana Długosza w Częstochowie
• Czasopismo: Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
• Rocznik: 2016
• Tom: Vol. 21
• Strony: 145--159
• Opis fizyczny: Bibliogr. 41 poz., tab.

Twórcy

autor

Tikhonenko-Kędziak A.

• Cardinal Stefan Wyszyński University, Institute of Computer Science, ul. Dewajtis 5, Warsaw, Poland

autor

Kurkowski M.

• Cardinal Stefan Wyszyński University, Institute of Computer Science, ul. Dewajtis 5, Warsaw, Poland

Bibliografia

• [1] Agrawal V. P., Kohli V., Gupta, S., Computer aided robot selection: The multiple attribute decision making approach, International Journal of Production Research 29 (1991) 1629–1644.
• [2] Alsina C., On a family of connectives for fuzzy sets, Fuzzy Sets and Systems 16 (1985) 231-235.
• [3] Atanassov K.T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986) 87-96.
• [4] Atanassov K., New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems 61 (1994) 137-142.
• [5] Atanassov K., Pasi G., Yager R., Intuitionistic fuzzy interpretations of multi-person multicriteria decision making, Proc. of 2002 First International IEEE Symposium Intelligent Systems 1 (2002) 115-119.
• [6] Atanassov K., Pasi G., Yager R., Atanassova V., Intuitionistic fuzzy graph interpretations of multi-person multi-criteria decision making, Proc. of the Third Conference of the European Society for Fuzzy Logic and Technology EUSFLAT’2003, Zittau, 10-12 September (2003) 177-182.
• [7] Beliakov G., Bustince H., Goswami D.P., U.K. Mukherjee,N.R Pal, On averaging operators for Atanassov’s intuitionistic fuzzy sets, Information Sciences 182 (2011) 1116-1124.
• [8] Boran F. E., Cenc S., Kurt M., Akay D., A multi-criteria untuitionistic fuzzy group decision making for supplier selection with TOPSIS method, Expert Systems with Applications 36 (2009) 11363–11368.
• [9] Chen S.M., Tan J.M., Handling multicriteria fuzzy decision-maiking problemsbased on vague set theory, Fuzzy Sets and Systems 67 (1994) 163-172
• [10] Cheng S., Chan C. W., Huang G. H., An integrated multi-criteria decision analysis and inexact mixed integer linear programming approach for solid waste management, Engineering Applications of Artificial Intelligence 16 (2003) 543–554.
• [11] Choi D.Y, Oh K.W., Asa and its application to multi-criteria decision making, Fuzzy Sets and Systems 114 (2000) 89-102.
• [12] Chu T. C., Facility location selection using fuzzy TOPSIS under group decisions, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10 (2002a) 687–701.
• [13] Chu T. C., Selecting plant location via a fuzzy TOPSIS approach, The International Journal of Advanced Manufacturing Technology 20 (2002b) 859–864.
• [14] Deluca A., Termini S., A definition of a nonprobabilistic entropy the of fuzzy sets theory, Information and Control 20 (1972) 301-312.
• [15] Dempster A.P., Upper and lower probabilities induced by a muilti-valued mapping, Ann. Math. Stat. 38 (1967) 325-339.
• [16] Dey S.K., Biswas R., Roy A.R., Some operations on intuitionistic fuzzy sets, Fuzzy Sets and Systems 114 (2000) 477-484.
• [17] Dymowa L., Soft Computing in Economics and Finance, Springer (2010).
• [18] Dymova L., Sevastjanov P., An interpretation of intuitionistic fuzzy sets in terms of evidence theory. Decision making aspect, Knowledge-Based Systems 23 (2010) 772-782.
• [19] Dymova L., Sevastjanov P., The operations on intuitionistic fuzzy values in the framework of Dempster-Shafer theory, Knowledge- Based Systems 35 (2012), 132- 143.
• [20] Dymova L., Sevastjanov P., Two-criteria method for comparing real-valued and interval-valued intuitionistic fuzzy values, Knowledge- Based Systems 45 (2013), 166- 173.
• [21] Dymova L., Sevastjanov P., A direct interval extension of TOPSIS method, Expert Systems with Applications 40 (2013), 4841-4847.
• [22] Fodor J.C., Roubens M., Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer Academic Publishers, Dordrecht, 1994.
• [23] Hinde C.J., Patching R.S., McCoy S.A., Inconsistent Intuitionistic Fuzzy Sets and Mass Assignment, EXIT, 2007.
• [24] Hinde C.J., Patching R.S., McCoy S.A., Semantic transfer and contradictory evidence in intuitionistic fuzzy sets, in: Proc. of 2008 IEEE International Conference on Fuzzy Systems, (2008) pp. 2095-2102. DOI: 10.1109/FUZZY.2008.4630659
• [25] Hong D.H.,Choi C.-H., Multicriteria fuzzy decision-making problems based on vague set theory, Fuzzy Sets and Systems 114 (2000), 103-113.
• [26] Li D-F., Multiattribute decision making models and methods using intuitionistic fuzzy sets, Journal of Computer and System Sciences 70 (2005) 73-85.
• [27] Li F., Lu A., Cai L., Methods of multi-criteria fuzzy decision making based on vague sets, Journal of Huazhong University of Science and Technology 29 (2001) 1-3 (in Chinese).
• [28] Li F., Rao Y., Weighted methods of multi-criteria fuzzy decision making based on sets, Computer Science 28 (2001) 60-65 (in Chinese).
• [29] Lin L., Yuan X-H., Xia, Z-Q Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets, Journal of Computer and System Sciences 73 (2007) 84-88.
• [30] Liu H.-W., Wang G.-J., Multi-criteria decision-making methods based on intuitionistic fuzzy sets, European Journal of Operational Research 179 (2007) 220-233.
• [31] Moore R.E., Interval analysis, N.J. Prentice-Hall, Englewood Cliffs (1966).
• [32] Pasi G., Yager Y., Atanassov K., Intuitionistic fuzzy graph interpretations of multiperson multi-criteria decision making: Generalized net approach, in: Proceedings of 2004 second International IEEE Conference Intelligent Systems (2004) pp. 434-439.
• [33] Pasi G., Atanassov K., Melo Pinto P., Yager R., Atanassova V., Multi-person multicriteria decision making: Intuitionistic fuzzy approach and generalized net model, in: Proc. of the 10th ISPE International Conference on Concurrent Engineering „Advanced Design, Production and Management Systems", 26-30 July 2003, Madeira (2003) pp. 1073-1078.
• [34] Shafer G., A mathematical theory of evidence, Princeton, Princeton University Press, 1976.
• [35] Szmidt E., Kacprzyk J., Applications of intuitionistic fuzzy sets in decision making, in: Proc. Eighth Cong. EUSFLAT98, Pampelona (1998) 150-158.
• [36] Szmidt E., Kacprzyk J., Group decision making under intuitionistic fuzzy preference relations, in: Proceedings of Seventh International Conference (IMPU98), Paris (1998) 172-178.
• [37] Szmidt E., Kacprzyk J., Intuitionistic fuzzy sets in decision making, Notes IFS 2 (1996) 15-32.
• [38] Szmidt E., Kacprzyk J., Remarks on some applications on intuitionistic fuzzy sets in decision making, Notes IFS 2 (1996) 22-31.
• [39] Xu Z., Intuitionistic preference relations and their applications in group decision making, Information Sciences 177 (2007) 2363-2379.
• [40] Xu Z., Xia M., Induced generalized intuitionistic fuzzy operators, Knowledge- Based Systems 24 (2011) 197-209.
• [41] Yang W., Chen Z., The quasi-arithmetic intuitionistic fuzzy OWA operators, Knowledge-Based Syst. (2011).