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Acceptably consistent incomplete interval-valued intuitionistic multiplicative preference relations

Published: 01 November 2018 Publication History

Abstract

We study the consistency property, and especially the acceptably consistent property, for incomplete interval-valued intuitionistic multiplicative preference relations. We propose a technique which first estimates the initial values for all missing entries in an incomplete interval-valued intuitionistic multiplicative preference relation and then improves them by a local optimization method. Two examples are presented in order to illustrate applications of the proposed method in group decision-making problems.

References

[1]
Aczél J, Saaty TL (1983) Procedures for synthesizing ratio judgments. J Math-Mat Psychol 27:93-102.
[2]
Alonso S, Chiclana F, Herrera F, Herrera-viedma E, Alcala-Fernadez J, PorcelC(2008)Aconsistency based procedure to estimatemissing pairwise preference values. Int J Intell Syst 23:155-175.
[3]
Alonso S, Herrera-Viedma E, Chiclana F, Herrera F (2010) A web based consensus support system for group decision making problems and incomplete preferences. Inf Sci 180:4477-4495.
[4]
Atanassov, K. (2012). On intuitionistic fuzzy sets theory. Springer, Berlin.
[5]
Atanassov K, Gargov G (1989) Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst 31:343-349.
[6]
Brans JP, Vincke P (1985) A preference ranking organization method. Manag Sci 31:647-656.
[7]
Chen SM, Lin TE, Lee LW(2014) Group decision making using incomplete fuzzy preference relations based on the additive consistency and the order consistency. Inf Sci 259:1-15.
[8]
Chiclana F, Herrera F, Herrera Viedma E (2001) Integrating multiplicative preference relations in amultipurpose decision-making model based on fuzzy preference relations. Fuzzy Sets Syst 122:277-291.
[9]
Deschrijver G, Kerre EE (2003) On the composition of intuitionistic fuzzy relations. Fuzzy Sets Syst 136:333-361.
[10]
Elsner L, Johnson CR, Dias Da Silva JA (1988) The Perron root of a weighted geometric mean of nonnegative matrices. Linear and Multilinear Algebra 24:1-13.
[11]
Fan ZP, Ma J, Jiang YP, Sun YH, Ma L (2006) A goal programming approach to group decision making based on multiplicative preference relation and fuzzy preference relations. Eur J Oper Res 174:311-321.
[12]
Fedrizzi M, Giove S (2007) Incomplete pair wise comparison and consistency optimization. Eur J Oper Res 183:303-313.
[13]
Figueira J, Greco S, Ehrgott M (eds) (2005) Multiple criteria decision analysis: state of the art surveys. International series in operations research and management science. Springer, New York, p 78.
[14]
Gong ZW, Li LS, Forrest J, Zhao Y (2011) The optimal priority models of the intuitionis tic fuzzy preference relation and their application in selecting industries with higher meteorological sensitivity. Expert Syst Appl 38:4394-4402.
[15]
Harker PT (1987a) Alternative modes of questioning in the analytic hierarchy process. Math Modell 9:353-360.
[16]
Harker PT (1987b) Incomplete pairwise comparisons in the analytic hierarchy process. Math Modell 9:837-848.
[17]
Hwang CL, Yoon K (1981) Multiple attribute decision making: methods and applications. Springer, New York.
[18]
Jiang Y, Xu ZS, Xu JP (2014) Interval-valued intuitionistic multiplicative sets. Int J Uncertain, Fuzziness Knowl-Based Syst 22(3):385-406.
[19]
Jiang Y, Xu ZS, Yu XH (2013) Compatibility measures and consensus models for group decision making with intuitionistic multiplicative preference relations. Appl Soft Comput 13:2075-2086.
[20]
Jiang Y, Xu ZS, Yu XH (2015) Group decision making based on incomplete intuitinistic multiplicative preference relations. Inf Sci 295:33-52.
[21]
Kou G, Peng Y, Chen Z, Shi Y (2009) Multiple criteria mathematical programming for multi-class classification and application in network intrusion detection. Inf Sci 179:371-381.
[22]
Liao HC, Xu ZS, Xia MM (2014) Multiplicative consistency of interval-valued intuitionistic fuzzy preference relation. J Intell Fuzzy Syst 27:2969-2985.
[23]
Lio H, Xu Z (2014) Priorities of intuitionistic fuzzy preference relation based on multiplicative consistency. IEEE Trans Fuzzy Syst 22:1669-1689.
[24]
Liu F (2009) Acceptable consistency analysis of interval reciprocal comparison matrices. Fuzzy Sets Syst 160:2686-2700.
[25]
Liu F, Zhang WG, Wang ZX (2012) A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making. Eur J Oper Res 218:747- 754.
[26]
Meng F, Chen X (2015) An approach to incomplete multiplicative preference relations and its application in group decision making. Inf Sci 309:119-137.
[27]
Meng F, Tan C (2017) A new consistency concept for interval multiplicative preference relations. Appl Soft Comput 52:262-276.
[28]
Meng F, Tan C, Chen X (2017) Multiplicative consistency analysis for interval fuzzy preference relations: a comparative study. Omega 68:17-38.
[29]
Nishizawa K (1997) A method to find elements of cycles in an incomplete directed graph and its applications-binary AHP and petri nets. Comput Math Appl 33:33-46.
[30]
Orlovsky SA (1978) Decision-making with a fuzzy preference relation. Fuzzy Sets Syst 1:155-167.
[31]
Petra G, Lidija ZS (2012) Acceptably consistency of aggregated comparison matrices in analytic hierarchy process. Eur J Oper Res 223:417-420.
[32]
Rezaei J (2015) Best-worst multi-criteria decision-making method. Omega 53:49-57.
[33]
Roy B (1991) The outranking approach and the foundations of ELECTRE methods. Theor Decis 31:49-73.
[34]
Saaty TL (1977) A scaling method for priorities in hierarchical structures. J Math Psychol 15:234-281.
[35]
Saaty TL (1980) The analytic hierarchy process. McGraw-Hill, New York.
[36]
Saaty TL (2001) Fundamentals of decision making and priority theory with the analytic hierarchy process. RWS Publications, Pittsburgh.
[37]
Saaty TL, Vargas LG (1987) Uncertainty and rank order in the analytic hierarchy process. Eur J Oper Res 32:107-117.
[38]
Szmidt E, Kacprzyk J (2002) Using intuitinistic fuzzy sets in group decision making. Control Cybernet 31:1037-1053.
[39]
Triantaphyllou E (2000) Multi-criteria decision making methods: a comparative study, applied optimization series 44. Springer, NewYork.
[40]
Ureña R, Chiclana F, Morente-Molinera JA, Herrera-Viedma E (2015) Managing incomplete preference relations in decision making: a review and future trends. Inf Sci 302:14-32.
[41]
Wan S, Wang F, Dong J (2017) Additive consistent interval-valued Atanassov intuitionistic fuzzy preference relation and likelihood comparison algorithm based group decision making. Eur J Oper Res 263:571-582.
[42]
Wan S, Wang F, Dong J (2018) A threephase method for group decision making with interval-valued intuitionistic fuzzy preference relations. IEEE Trans Fuzzy Syst 26(2):998-1010.
[43]
Wan S, Xu GL, Dong J (2016) A novel method for group decision making with interval-valued Atanassov intuitionistic fuzzy preference relations. Inf Sci 372:53-71.
[44]
Wang YM, Yang JB, Xu DL (2005) A twostage logarithmic goal programming method for generating weights from interval comparison matrices. Fuzzy Sets Syst 152:475-498.
[45]
Xia MM, Xu ZS (2013) Group decision making based on intuitionistic multiplicative aggregation operators. Appl Math Model 37:5120- 5133.
[46]
Xia MM, Xu ZS, Liao HC (2013) Preference relations based on intuitionistic multiplicative information. IEEE Trans Fuzzy Syst 21:113-133.
[47]
Xu ZS (2004a) Goal programming models for obtaining the priority vector of incomplete fuzzy preference relation. Int J Approx Reason 36:261-270.
[48]
Xu ZS (2004b) On compatibility of interval fuzzy preference relations. Fuzzy Optim Decis Making 3:217-225.
[49]
Xu ZS (2007a) A survey of preference relations. Int J Gen Syst 36:179- 203.
[50]
Xu ZS (2007b) Intuitionistic preference relations and their application in group decision making. Inf Sci 177:2363-2379.
[51]
Xu ZS (2012) A consensus reaching process under incomplete multiplicative preference relations. Int J Gen Syst 41:333-351.
[52]
Xu ZS (2013) Priority weight intervals derived from intuitionistic multiplicative preference. IEEE Trans Fuzzy Syst 21:642-654.
[53]
Xu ZS, Cai XQ (2009) Incomplete interval-valued intuitionistic preference relations. Int J Gen Syst 38:871-886.
[54]
Xu ZS, Cai XQ (2012) Intuitionistic fuzzy information aggregation: theory and applications. Science Press, Berlin.
[55]
Xu GL, Wan S, Wang F, Dong J, Zeng YF (2016) Mathematical programming methods for consistency and consensus in group decision making with intuitionistic fuzzy preference relations. Knowl-Based Syst 98:30-43.
[56]
Yager RR, Xu ZS (2006) The continuous ordered weighted geometric operator and its application to decision making. Fuzzy Sets Syst 157:1393-1402.

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Published In

cover image Soft Computing - A Fusion of Foundations, Methodologies and Applications
Soft Computing - A Fusion of Foundations, Methodologies and Applications  Volume 22, Issue 22
November 2018
350 pages
ISSN:1432-7643
EISSN:1433-7479
Issue’s Table of Contents

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 November 2018

Author Tags

  1. Acceptably consistent preference relation
  2. Interval-valued intuitionistic fuzzy number
  3. Multi-criteria group decision-making problems
  4. Multiplicative preference relation

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