Uogólnienie metody TOPSIS w warunkach niepewnosci rozmytej

• Autorzy: Tikhonenko-Kedziak A.

Warianty tytułu

EN

The generalisation of TOPSIS metod under fuzzy uncertainty

• Języki publikacji: PL

Abstrakty

PL

Technika obliczania odległości od rozwiązania idealnego (TOPSIS) jest jedną z najbardziej znanych klasycznych metod wielokryterialnego podejmowania decyzji (MCDM). W klasycznej metodzie TOPSIS wartości i wagi kryteriów są zwykłymi liczbami. Czasami jednak rozwiązanie zagadnienia dokładnego wyznaczenia wartości kryteriów jest trudne, dlatego w konsekwencji ich wartości są przedstawione w postaci liczb rozmytych. Istnieje kilka publikacji dotyczących zastosowania metody TOPSIS w ramach niepewności rozmytej, lecz autorzy zazwyczaj wprowadzają rozmaite ograniczenia oraz uproszczenia sformułowanego problemu, które mogą prowadzić do otrzymania niepoprawnych wyników. W niniejszym opracowaniu przedstawiono nowe podejście oparte na matematyce przedziałowej.

EN

The TOPSIS method is a technique for establishing order preference by similarity to the ideal solution and was primarily developed for dealing with real-valued data. This technique is currently one of most popular methods for Multiple Criteria Decision Making (MCDM). In many cases, it is hard to present precisely exact ratings of alternatives with respect to local criteria and as a result these ratings are seen as fuzzy values. A number of papers have been devoted to fuzzy extensions of the TOPSIS method in the literature, but in most of them, a defuzzification of elements of the fuzzy decision matrix is used, that leads inevitably to a loss of important information and may even produce the wrong results. In this paper a new direct approach to the fuzzy extension of the TOPSIS based on interval arithmetic had proposed.

Słowa kluczowe

PL

MCDM; TOPSIS; matematyka przedziałowa; liczby rozmyte

EN

MCDM; TOPSIS; interval arithmetic; fuzzy numbers

• Wydawca: Oficyna Wydawnicza Europejskiej Uczelni
• Czasopismo: Studia i Materiały / Europejska Uczelnia Informatyczno-Ekonomiczna w Warszawie
• Rocznik: 2014
• Tom: Nr 1(7)
• Strony: 13--38
• Opis fizyczny: Bibliogr. 63 poz., tab., wykr.

Twórcy

autor

Tikhonenko-Kedziak A.

• Politechnika Częstochowska ul. Dabrowskiego 69/73, 42-201 Częstochowa
• Europejska Uczelnia Informatyczno-Ekonomiczna w Warszawie, ul. Białostocka 22, 03-741 Warszawa

Bibliografia

• [1] Anniseh M., Piri F., Shahraki M. R., Agamohamadi F., Fuzzy extension of TOPSIS model for group decision making under multiple criteria, “Artificial Intelligence Review” 38 (2012) 325-338.
• [2] Awasthi A., Chauhan S. S., A hybrid approach integrating affinity diagram, AHP and fuzzy TOPSIS for sustainable city logistics planning, “Applied Mathematical Modelling” 36 (2012) 573-584.
• [3] Bao Q., Ruan D., Shena Y., Hermans E., Janssens D., Improved hierarchical fuzzy TOPSIS for road safety performance evaluation, “Knowledge-Based Systems” 32 (2012) 84-90.
• [4] Behzadian M., Otaghsara S. K., Yazdani M., Ignatius J., A state-of the-art survey of TOPSIS applications, “Expert Systems with Applications” 39 (2012) 13051-13069.
• [5] Bäyäközkan G., Çifçi G., A combined fuzzy AHP and fuzzy TOPSIS based strategic analysis of electronic service quality in healthcare industry, “Expert Systems with Applications” 39 (2012) 2341-2354.
• [6] Bäyäközkan G., Çifçi G., A novel hybrid MCDM approach based on fuzzy DEMATEL, fuzzy ANP and fuzzy TOPSIS to evaluate green suppliers, “Expert Systems with Applications” 39 (2012) 3000-3011.
• [7] Chamodrakas I., Martakos D., A utility-based fuzzy TOPSIS method for energy efficient network selection in heterogeneous wireless networks, “Applied Soft Computing” 12 (2012) 1929-1938.
• [8] Chanas S., Delgado M., Verdegay J. L., Vila M. A., Ranking fuzzy interval numbers in the setting of random sets, “Information Sciences” 69 (1993) 201-217.
• [9] Chen C.-T., A fuzzy approach to select the location of distribution center, “Fuzzy sets and systems” 118 (2001) 65-73.
• [10] Chen M. F., Tzeng G. H., Combining grey relation and TOPSIS concepts for selecting an expatriate host country, “Mathematical and Computer Modelling” 40 (2004) 1473-1490.
• [11] Chen Y.-J., Structured methodology for supplier selection and evaluation in a supply chain, “Information Sciences” 181 (2011) 1651-1670.
• [12] Choi D. Y, Oh K. W., Asa and its application to multi-criteria decision making, “Fuzzy Sets and Systems” 114 (2000) 89-102.
• [13] 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.
• [14] Chu T. C., Selecting plant location via a fuzzy TOPSIS approach, “The International Journal of Advanced Manufacturing Technology” 20 (2002) 859-864.
• [15] Chu T. C., Lin Y. C., A fuzzy TOPSIS method for robot selection, “The International Journal of Advanced Manufacturing Technology” 21 (2003) 284-290.
• [16] Chu T. C., Lin Y. C., An interval arithmetic based fuzzy TOPSIS model, “Expert Systems with Applications” 36 (2009) 10870-10876.
• [17] Dimova L., Sevastjanov P., Sevastjanov D., MCDM in a fuzzy setting: investment projects assessment application, “International Journal of Production Economy” 100 (2006) 10-29.
• [18] Dymowa L., Soft Computing in Economics and Finance, Springer, 2010.
• [19] Dymova L., Sevastjanov P., Fuzzy multiobjective evaluation of investments with applications, [in:] Fuzzy Engineering Economics with Applications, Cengiz Kahraman (Ed.), Springer-Verlag, Berlin, Heidelberg 2008, pp. 243-287.
• [20] Dubois D., Koenig J. L., Social choice axioms for fuzzy set aggregation, “Fuzzy Sets and Systems” 43 (1991) 257-274.
• [21] Dyckhoff H., Basic concepts for theory of evaluation: hierarchical aggregation via autodistributive connectives in fuzzy set theory, “European J. Operation Research” 20 (1985) 221-233.
• [22] Facchinetti G., Ricci R. G., Muzzioli S., Note on ranking fuzzy triangular numbers, “International Journal of Intelligent Systems” 13 (1998) 613-622.
• [23] Fan Z.-P., Feng B., A multiple attributes decision making method using individual and collaborative attribute data in a fuzzy environment, “Information Sciences” 179 (2009) 3603-3618.
• [24] Hauke W., Using Yager’s t-norms for aggregation of fuzzy intervals, “Fuzzy Sets and Systems” 101 (1999) 59-65.
• [25] Hwang C. L., Yoon K., Multiple Attribute Decision Making Methods and Applications, Springer, Berlin, Heidelberg 1981.
• [26] Iç Y. T., Development of a credit limit allocation model for banks using an integrated fuzzy TOPSIS and linear programming, “Expert Systems with Applications” 39 (2012) 5309-5316.
• [27] Kahraman C., Büyüközkan G., Ates N. Y., A two phase multi-attribute decision-making approach for new product introduction, “Information Sciences” 177 (2007) 1567-1582.
• [28] Kaufmann A., Gupta M., Introduction to fuzzy arithmetic-theory and applications, Van Nostrand Reinhold, New York 1985, p. 349.
• [29] Kuo M.-S., Tzeng G.-H., Huang W.-C., Group decision-making based on concepts of ideal and anti-ideal points in a fuzzy environment, “Mathematical and Computer Modelling” 45 (2007) 324-339.
• [30] Migdalas A., Pardalos P. M., Editorial: hierarchical and believel programming, “J. Global Optimization” 8 (1996) 209-215.
• [31] Mitra G., Mathematical Models for Decision Support, Springer, Berlin 1988.
• [32] Mokhtarian M. N., Hadi-Vencheh A., A new fuzzy TOPSIS method based on left and right scores: an application for determining an industrial zone for dairy products factory, “Applied Soft Computing” 12 (2012) 2496-2505.
• [33] Moore R. E., Interval analysis, N.J. Prentice-Hall, Englewood Cliffs, 1966.
• [34] Paksoy T., Pehlivan N. Y., Kahraman C., Organizational strategy development in distribution channel management using fuzzy AHP and hierarchical fuzzy TOPSIS, “Expert Systems with Applications” 39 (2012) 2822-2841.
• [35] Peng Y., Wang G., Wang H., User preferences based software defect detection algorithms selection using MCDM, “Information Sciences” 191 (2012) 3-13.
• [36] Peneva V., Popchev I., Properties of the aggregation operators related with fuzzy relations, “Fuzzy Sets and Systems” 139 (2003) 615-633.
• [37] Roubens M., Fuzzy sets and decision analysis, “Fuzzy Sets and Systems” 90 (1997) 199-206.
• [38] Rouhani S., Ghazanfari M., Jafari M., Evaluation model of business intelligence for enterprise systems using fuzzy TOPSIS, “Expert Systems with Applications” 39 (2012) 3764-3771.
• [39] Sevastjanov P., Numerical methods for interval and fuzzy number comparison based on the probabilistic approach and Dempster Shafer theory, “Information Sciences” 177 (2007) 4645-4661.
• [40] Sevastjanov P., Dymova L., Stock screening with use of multiple criteria decision making and optimization, “Omega” 37 (2009) 659-671.
• [41] Sevastjanov P., Figat P., Aggregation of aggregating modes in MCDM. Synthesis of Type 2 and Level 2 fuzzy sets, “Omega” 35 (2007) 505-523.
• [42] Sewastianow P., Róg P., A probabilistic approach to fuzzy and interval ordering, Task Quarterly, “Special Issue Artificial and Computational Intelligence” 7 (2002) 147-156.
• [43] Sewastianow P., Róg P., Two-objective method for crisp and fuzzy interval comparison in Optimization, “Computers & Operations Research” 33 (2006) 115-131.
• [44] Sewastianow P., Róg P., Venberg A., The Constructive Numerical Method of Interval Comparison, [in:] Parallel Processing and Applied Mathematics, Wyrzykowski R., Dongarra J., Paprzycki M., Waśniewski J. (eds.), Springer, Heidelberg 2002, pp. 756-761.
• [45] Shin H. S., Lee E. S., Compensatory fuzzy multiple level decision making, “Fuzzy Sets and Systems” 114 (2000) 71-87.
• [46] Silvert W., Ecological impact classification with fuzzy sets, “Ecological Modelling” Vol. 96, Issues 1-3 (1997) 1-10.
• [47] Tsaur S. H., Chang T. Y., Yen C. H., The evaluation of airline service quality by fuzzy MCDM, “Tourism Management” 23 (2002) 107-115.
• [48] Vahdani B., Mousavi S. M., Tavakkoli-Moghaddam R., Group decision making based on novel fuzzy modified TOPSIS method, “Applied Mathematical Modelling” 35(9) (2011) 4257-4269.
• [49] Wang Y. M., Elhag T. M. S., Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment, “Expert Systems with Applications” 31 (2006) 309-319.
• [50] Wang X., Kerre E. E., Reasonable properties for the ordering of fuzzy quantities (I) (II), “Fuzzy Sets and Systems” 112 (2001) 387-405.
• [51] Wang Y. M., Luo Y., Hua Z.-S., A note on group decision-making based on concepts of ideal and anti-ideal points in a fuzzy environment, “Mathematical and Computer Modelling” 46 (2007) 1256-1264.
• [52] Wang Y. M., Yang J. B., Xu D. L., A preference aggregation method through the estimation of utility intervals, “Computers and Operations Research” 32 (2005) 2027- 2049.
• [53] Wang Y. M., Yang J. B., Xu D. L., A two-stage logarithmic goal programming method for generating weights from interval comparison matrices, “Fuzzy Sets and Systems” 152 (2005) 475-498.
• [54] Xu Z., Da Q., The uncertain OWA operator, “International Journal of Intelligent Systems” 17 (2002) 569-575.
• [55] Xu Z., Chen J., An interactive method for fuzzy multiple attribute group decision making, “Information Sciences” 177 (2007) 248-263.
• [56] Xu Z., Chen J., Some models for deriving the priority weights from interval fuzzy preference relations, “European Journal of Operational Research” 184 (2008) 266-280.
• [57] Yager R. R., On ordered weighted averaging aggregation operators in multicriteria decision making, “IEEE Trans. Systems Man and Cybern.” 18 (1988) 183-190.
• [58] Yager R., Multiple objective decision-making using fuzzy sets, “Int. J. Man-Mach. Stud.” 9 (1979) 375-382.
• [59] Yager R. R., Detyniecki M., Bouchon-Meunier B., A context-dependent method for ordering fuzzy numbers using probabilities, “Information Sciences” 138 (2001) 237- 255.
• [60] Zadeh L. A., Quantitative fuzzy semantics, “Information Sciences” 3 (1971) 177-200.
• [61] Zimmerman H. J., Zysno P., Latest connectives in human decision making, “Fuzzy Sets and Systems” 4 (1980) 37-51.
• [62] Zimmermann H. J., Zysno P., Decision and evaluations by hierarchical aggregation of information, “Fuzzy Sets and Systems” 104 (1983) 243-260.
• [63] Zouggari A., Benyoucef L., Simulation based fuzzy TOPSIS approach for group multicriteria supplier selection problem, “Engineering Applications of Artificial Intelligence” 25 (2012) 507-519.