Generalized Cubic Aggregation Operators with Application in Decision Making Problem

Yıl 2018, Sayı: 21, 1 - 30, 27.02.2018

Muhammad Shakeel Saleem Abdullah Aliya Fahmi

Öz

There are many aggregation operators and their applications have been developed up to date, but in this paper we introduced the idea of generalized aggregation operator. The main idea of this paper is to study the generalized aggregation operators with cubic numbers. In this paper, we introduced three types of cubic aggregation operators called generalized cubic weighted averaging (GCWA) operator, generalized cubic ordered weighted averaging (GCOWA) operator and generalized cubic hybrid averaging (GCHA) operator. We extend the theory of cubic numbers to generalized ordered weighted averaging operators that are characterized by interval membership and exact membership. In last section we provide an application of these aggregation operators to multiple attribute group decision making problem.

Anahtar Kelimeler

Cubic sets, GCWA Operator, GCOWA Operator, GCHA operator

Kaynakça

• [1] Zadeh L A, Fuzzy sets, Inform Control, (8) (1965) 338 - 353
• [2] Atanassov K, Intuitionistic fuzzy sets, Fuzzy Sets Syst, (20) (1986) 87 - 96
• [3] Boran F E, Genc S, Kurt M, Akay D A, multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method, Expert Systems with Applications, (36) (2009) 11363 - 11368
• [4] Wei G W, GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting, Knowledge- Based Systems, (23) (2010) 243 - 47
• [5] Xu Z S, Da Q L, An overview of operators for aggregating information, Int J Intell Syst, (18) (2003) 953- 969
• [6] Xu Z S, Intuitionistic fuzzy aggregation operators, IEEE Trans Fuzzy Syst, (15) (2007) 1179 - 1187
• [7] Xu Z S, Yager R R, Dynamic intuitionistic fuzzy multiple attribute decision making, International Journal of Approximate Reasoning, (48) (2008) 246 - 262 [8] Jun Y B, Kim C S, Yang K O, Cubic sets, Ann. Fuzzy Math. Inf, (4) (2012) 83 - 98
• [9] Sambuc R , Functions - Flous, Application à l'aide au Diagnostic en Pathologie Thyroidienne, Thèse de Doctorat en Medecine, Marseille, 1975
• [10] Turksen I B, Interval-valued fuzzy sets and compensatory AND, Fuzzy Sets Syst, (51) (1992) 295 - 307
• [11] Turksen I B, Interval-valued strict preference with Zadeh triples, Fuzzy Sets Syst, (78) (1996) 183 - 195.
• [12] Jun Y B, Kim C S, Kang M S, Cubic subalgebras and ideals of BCK/BCI-algebras, Far Ease J Math Sci, (44) (2010) 239 - 250
• [13] Jun Y B, Kim C S, Kang J G, Cubic q-ideals of BCI-algebras, Ann Fuzzy Math Inf, (1) (2011a) 25 - 34.
• [14] Jun Y B, Lee K J, Kang M S, Cubic structures applied to ideals of BCI-algebras, Comput Math Appl, (62) (2011b) 3334 -3342
• [15] Yager R R, Kacprzyk J, Beliakov G, Recent Developments in the Ordered Weighted Averaging Operators, Theory and Practice, Springer-Verlag, Berlin, 2010
• [16] Zhao H, Xu Z S, Ni M F, Liu S S, Generalized aggregation operators for intuitionistic fuzzy sets, International Journal of Intelligent Systems, (25) (2010) 1 - 30