A multi-attribute ranking approach based on net inferiority and superiority indexes, two weight vectors, and generalized Heronian means

Hidouri, M.; Rebaï, A.

Growing Science » Decision Science Letters » A multi-attribute ranking approach based on net inferiority and superiority indexes, two weight vectors, and generalized Heronian means

Journals

DSL Volumes

Volume 1 (10)
- Issue 1 (5)
- Issue 2 (5)

Volume 2 (30)
- Issue 1 (5)
- Issue 2 (6)
- Issue 3 (9)
- Issue 4 (10)

Volume 3 (53)
- Issue 1 (15)
- Issue 2 (10)
- Issue 3 (19)
- Issue 4 (9)

Volume 4 (48)
- Issue 1 (10)
- Issue 2 (12)
- Issue 3 (14)
- Issue 4 (12)

Volume 5 (39)
- Issue 1 (12)
- Issue 2 (10)
- Issue 3 (8)
- Issue 4 (9)

Volume 6 (30)
- Issue 1 (8)
- Issue 2 (6)
- Issue 3 (9)
- Issue 4 (7)

Volume 7 (41)
- Issue 1 (8)
- Issue 2 (8)
- Issue 3 (8)
- Issue 4 (17)

Volume 8 (38)
- Issue 1 (8)
- Issue 2 (6)
- Issue 3 (14)
- Issue 4 (10)

Volume 9 (39)
- Issue 1 (8)
- Issue 2 (9)
- Issue 3 (14)
- Issue 4 (8)

Volume 10 (43)
- Issue 1 (7)
- Issue 2 (8)
- Issue 3 (20)
- Issue 4 (8)

Volume 11 (49)
- Issue 1 (9)
- Issue 2 (9)
- Issue 3 (14)
- Issue 4 (17)

Volume 12 (64)
- Issue 1 (12)
- Issue 2 (24)
- Issue 3 (13)
- Issue 4 (15)

Volume 13 (78)
- Issue 1 (21)
- Issue 2 (18)
- Issue 3 (19)
- Issue 4 (20)

Countries

Decision Science Letters

ISSN 1929-5812 (Online) - ISSN 1929-5804 (Print) Quarterly Publication Volume 8 Issue 4 pp. 471-482 , 2019

A multi-attribute ranking approach based on net inferiority and superiority indexes, two weight vectors, and generalized Heronian means Pages 471-482 Download PDF

Authors: Moufida Hidouri, Abdelwaheb Rebaï

DOI: 10.5267/j.dsl.2019.4.005

Keywords: Multi-attribute ranking, Averaging operator, Generalized Heronian mean, Inferiority, Superiority

Abstract: In this paper, we propose a three-phase multi-attribute ranking approach having as outcomes of the modeling phase what we refer to as net superiority and inferiority indexes. These are defined as bounded differences between the classical superiority and inferiority indexes. The suggested approach herein named MANISRA (Multi-Attribute Net Inferiority and Superiority based Ranking Approach) employs in the aggregation phase a bi-parameterized family of compound averaging operators (CAOPs) referred to as generalized Heronian OWAWA (GHROWAWA) operators having the usual OWAWA operators as special instances. Note that the new defined operators are built by using a composition of an arbitrary bi-parameterized binary Heronian mean with the weighted average (WA) and the ordered weighted averaging (OWA) operators. Also, note that the current developed MANISRA method generalizes the superiority and inferiority ranking (SIR-SAW) method which is known to coincide with the quite popular PROMETHEE II method when the net flow rule is used. With net superiority and inferiority indexes and GHROWAWA operators, we are better equipped to rank rationally prespecified alternatives. The basic formulations, notations, phases and interlocking tasks related to the proposed approach are presented herein and its feasibility and effectiveness are shown in a real problem.

How to cite this paper

 Hidouri, M & Rebaï, A. (2019). A multi-attribute ranking approach based on net inferiority and superiority indexes, two weight vectors, and generalized Heronian means.Decision Science Letters , 8(4), 471-482.

Refrences

Brans, J.P., & Vincke, Ph. (1985). A Preference ranking organization method (The PROMETHEE Method for Multiple Criteria Decision-Making). Management Science, 31 (6), 647-656.
Brans, J.P., Vincke, Ph., & Mareschal, B. (1986). How to select and how to rank project: The PROMETHEE Method. European Journal of Operational Research, 24, 228-238.
Emrouznejad, A., & Marra, M. (2014). Ordered weighted averaging operators 1988–2014: A citation-based literature survey. International Journal of Intelligent Systems, 29 (11), 994–1014.
Fodor, J., Marichal, J.L., & Roubens, M. (1995). Characterization of the ordered weighted averaging operators. IEEE Transactions on Fuzzy Systems, 3, 236-240.
Hidouri, M., & Rebaï, A. (2018, July). The SISINA Method: A Distance-based multiattribute ranking approach with superiority and inferiority indexes. Paper session presentation at the International Conference of the African Federation of Operational Research Societies (AFROS), Tunis, Tunisia.
Janous, W. (2001). A note on generalized Heronian means. Mathematical Inequalities & Applications, 4(3), 369-375.
Labreuche, C. (2016). On capacities characterized by two weight vectors, in: Carvalho, M.J., Lesot, U., Kaymak, S., Vieira, B., Bouchon, M., Yager, R.R. (Eds.), Information Processing and Management of Uncertainty in Knowledge-Based Systems. Springer, Switzerland, pp. 23–34.
Llamazares, B. (2015). SUOWA operators: Constructing semi-uninorms and analyzing specific cases. Fuzzy Sets and Systems, 287, 119-136.
Merigo, J.M. (2012). OWA operator in the weighted average and application in decision making. Control and Cybernetics, 41, 605-643.
Rebaï, A. (1993). BBTOPSIS: A bag based technique for order preference by similarity ideal solution. Fuzzy Sets and Systems, 60, 143-162.
Rebaï, A. (1994). Canonical fuzzy bags and bag fuzzy measures as a basis for MADM with mixed non cardinal data. European Journal of Operational Research, 8, 34-48.
Rebaï, A., & Martel, J. M. (2000). Rangements BBTOPSIS fondés sur des intervalles de proximités relatives avec qualification des préférences (BBTOPSIS Rankings based on intervals of relative proximities with qualification of preferences). RAIRO Operational Research, 34, 449-465.
Reimann, O., Schumacher, C., & Vetschera, R. (2017). How well does the OWA operator represent realpreferences?. European Journal of Operational Research, 258 (3), 993-1003.
Roy, B. (1996). Multicriteria methodology for decision aiding. Kluwer Academic Publisher.
Roy, B. (2007). Double pondération pour calculer une moyenne : Pourquoi et comment ? (Double weighting for calculating an average: Why and how?). RAIRO Operations Research, 41, 125–139.
Torra, V. (1997). The weighted OWA operator. International Journal of Intelligent Systems, 12, 153–166.
Valahzaghard, M. K., Mozaffari, M. M, Valehzagharad, H. K. & Memarzade, M. (2011). Supplier selection by using fuzzy Delphi fuzzy AHP and SIR VIKOR. American Journal of Scientific Research, 35, 24-45.
Xu, X. (2001). The SIR method: A superiority and inferiority ranking method for multiple criteria decision making. European Journal of Operational Research, 131, 587-602.
Xu, Z.S., & Da, Q.L. (2002). The ordered weighted geometric averaging operators. International Journal of Intelligent Systems, 17 (7), 709-716.
Xu, Z.S., & Da, Q.L. (2003). An overview of operators for aggregating information. International Journal of Intelligent Systems, 18, 953–969.
Yager, R.R. (1988). On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Transactions on Systems Man and Cybernetics, 18, 193-90.
Yager, R.R. (2004). Generalized OWA aggregation operators. Fuzzy Optimization and Decision Making 3, 93-107.
Yager, R.R., & Kacprzyk, J. (1997). The Ordered Weighted Averaging Operators: Theory and Applications. Norwell, MA: Kluwer Academic Publishers.
Yager, R.R., Kacprzyk, J., & Beliakov, G. (2011). Recent Developments on the Ordered Weighted Averaging Operators: Theory and Practice. Springer-Verlag, Berlin.
Zadeh, L.A. (1975), Calculus of fuzzy restrictions, in: Zadeh, A.L., Fu, K.-S., Tanaka, K., Shimura, M. (Eds.), Fuzzy Sets and Their Applications to Cognitive and Decision Processes. Academic Press, New York.