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Decisions in Economics and Finance

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27-06-2020

Incoherence measures and relations between coherence conditions for pairwise comparisons

Authors: Matteo Brunelli, Bice Cavallo

Published in: Decisions in Economics and Finance | Issue 2/2020

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Abstract

Coherence of preferences, and the measurement of its violation, has been a long-standing issue in decision analysis. This paper continues the inquiry into coherence conditions for pairwise comparisons following a distance-based approach, in which the deviations from coherence conditions are measured on a continuous scale. Firstly, we consider eight coherence conditions already introduced in the literature and provide a complete study on their inclusion relations. Then, we consider four of these conditions and introduce optimization problems to quantify the extent of their violation.

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Angilella, S., Mazzù, S.: The financing of innovative SMEs: a multicriteria credit rating model. Eur. J. Oper. Res. 244(2), 540–554 (2015)CrossRef

Arunraj, N., Maiti, J.: Risk-based maintenance policy selection using AHP and goal programming. Saf. Sci. 48(2), 238–247 (2010)CrossRef

Barzilai, J.: Consistency measures for pairwise comparison matrices. J. Multi-Criteria Decision Anal. 7(3), 123–132 (1998)CrossRef

Basile, L., D’Apuzzo, L.: Ranking and weak consistency in the A.H.P. context. Riv. Mat. Sci. Econ. Soc. 20(1), 99–109 (1997)

Brunelli, M.: On the conjoint estimation of inconsistency and intransitivity of pairwise comparisons. Oper. Res. Lett. 44(5), 672–675 (2016)CrossRef

Brunelli, M.: A survey of inconsistency indices for pairwise comparisons. Int. J. Gen. Syst. 47(8), 751–771 (2018)CrossRef

Brunelli, M., Cavallo, B.: Distance-based measures of incoherence for pairwise comparisons. Knowl. Based Syst. 187, 104808 (2020)CrossRef

Cavallo, B.: A further discussion of “A Semiring-basedstudy of judgment matrices: properties and models” [Information Sciences 181 (2011) 2166–2176]. Inf. Sci. 287, 61–67 (2014)CrossRef

Cavallo, B.: Coherent weights for pairwise comparison matrices and a mixed-integer linear programming problem. J. Global Optim. 75(1), 143–161 (2019a)CrossRef

Cavallo, B.: \({{\cal{G}}}\)-distance and \({{\cal{G}}}\)-decomposition for improving \({{\cal{G}}}\)-consistency of a pairwise comparison matrix. Fuzzy Optim. Decision Mak. 18(1), 57–83 (2019b)CrossRef

Cavallo, B., D’Apuzzo, L.: A general unified framework for pairwise comparison matrices in multicriterial methods. Int. J. Intell. Syst. 24(4), 377–398 (2009)CrossRef

Cavallo, B., D’Apuzzo, L.: Reciprocal transitive matrices over abelian linearly ordered groups: characterizations and application to multi-criteria decision problems. Fuzzy Sets Syst. 266, 33–46 (2015)CrossRef

Cavallo, B., D’Apuzzo, L.: Ensuring reliability of the weighting vector: weak consistent pairwise comparison matrices. Fuzzy Sets Syst. 296, 21–34 (2016)CrossRef

Cavallo, B., D’Apuzzo, L.: Preservation of preferences intensity of an inconsistent pairwise comparison matrix. Int. J. Approx. Reason. 116, 33–42 (2020)CrossRef

Cavallo, B., D’Apuzzo, L., Basile, L.: Weak consistency for ensuring priority vectors reliability. J. Multi-Criteria Decision Anal. 23(3–4), 126–138 (2016)CrossRef

Chao, H.C.J., Yang, K.L., Chu, P.: Note on diagonal procedure in analytic hierarchy process. Math. Comput. Model. 40(9–10), 1089–1092 (2004)CrossRef

Cinelli, M., Coles, S.R., Kirwan, K.: Analysis of the potentials of multi criteria decision analysis methods to conduct sustainability assessment. Ecol. Indic. 46, 138–148 (2014)CrossRef

D’Apuzzo, L., Marcarelli, G., Squillante, M.: Generalized consistency and intensity vectors for comparison matrices. Int. J. Intell. Syst. 22(12), 1287–1300 (2007)CrossRef

Fedrizzi, M.: Distance-based characterization of inconsistency in pairwise comparisons. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds.) Advances in Computational Intelligence, pp. 30–36. Springer, Berlin (2012)CrossRef

Finan, J.S., Hurley, W.J.: A note on a method to ensure rank-order consistency in the analytic hierarchy process. Int. Trans. Oper. Res. 3(1), 99–103 (1996)CrossRef

Fishburn, P.C.: Binary choice probabilities: on the varieties of stochastic transitivity. J. Math. Psychol. 10(4), 327–352 (1973)CrossRef

Irwin, F.W.: An analysis of the concepts of discrimination and preference. Am. J. Psychol. 71(1), 152–163 (1958)CrossRef

Keeney, R.L., Raiffa, H.: Decisions with Multiple Objectives: Preferences and Value Tradeoffs. Wiley, New York (1976)

Kéri, G.: On qualitatively consistent, transitive and contradictory judgment matrices emerging from multiattribute decision procedures. Central Eur. J. Oper. Res. 19(2), 215–224 (2011)CrossRef

Koczkodaj, W.W., Szwarc, R.: On axiomatization of inconsistency indicators for pairwise comparisons. Fundam. Inform. 132(4), 485–500 (2014)CrossRef

Kułakowski, K., Talaga, D.: Inconsistency indices for incomplete pairwise comparisons matrices. Int. J. Gen. Syst. 49(2), 174–200 (2020)CrossRef

Lavalle, I.H., Fishburn, P.C.: Decision analysis under states-additive SSB preferences. Oper. Res. 35(5), 722–735 (1987)CrossRef

Lootsma, F.A.: Multi-Criteria Decision Analysis via Ratio and Difference Judgement, vol. 29. Springer, Berlin (2007)

Luce, R., Suppes, P.: Utility, preference and subjective probability. In: Luce, R.D., Bush, R.R., Galanter, E. (eds.) Handbook of Mathematical Psychology, vol. 3, pp. 249–410. Wiley, New York (1965)

Mazurek, J., Ramík, J.: Some new properties of inconsistent pairwise comparisons matrices. Int. J. Approx. Reason. 113, 119–132 (2019)CrossRef

Nida-Rümelin, J.: Rationality: coherence and structure. In: Nida-Rümelin, J., Spohn, W. (eds.) Rationality, Rules, and Structure, pp. 1–16. Springer, Dordrecht (2000)CrossRef

Öztürk, M., Tsoukiàs, A., Vincke, P.: Preference modelling. In: Multiple Criteria Decision Analysis: State of The Art Surveys, pp. 27–59. Springer, New York (2005)

Regenwetter, M., Dana, J., Davis-Stober, C.P.: Transitivity of preferences. Psychol. Rev. 118(1), 42–56 (2011)CrossRef

Saaty, T.L.: A scaling method for priorities in hierarchical structures. J. Math. Psychol. 15(3), 234–281 (1977)CrossRef

Saaty, T.L., Vargas, L.G.: The possibility of group choice: pairwise comparisons and merging functions. Social Choice Welf. 38(3), 481–496 (2012)CrossRef

Shimura, M.: Fuzzy sets concept in rank-ordering objects. J. Math. Anal. Appl. 43(3), 717–733 (1973)CrossRef

Tanino, T.: Fuzzy preference orderings in group decision making. Fuzzy Sets Syst. 12(2), 117–131 (1984)CrossRef

Ureña, R., Chiclana, F., Morente-Molinera, J.A., Herrera-Viedma, E.: Managing incomplete preference relations in decision making: a review and future trends. Inf. Sci. 302, 14–32 (2015)CrossRef

Xia, M., Chen, J.: Consistency and consensus improving methods for pairwise comparison matrices based on abelian linearly ordered group. Fuzzy Sets Syst. 266, 1–32 (2015)CrossRef

Zopounidis, C., Doumpos, M.: Multi-criteria decision aid in financial decision making: methodologies and literature review. J. Multi-Criteria Decision Anal. 11(4–5), 167–186 (2002)CrossRef

Title: Incoherence measures and relations between coherence conditions for pairwise comparisons
Authors: Matteo Brunelli
Bice Cavallo
Publication date: 27-06-2020
Publisher: Springer International Publishing
Published in: Decisions in Economics and Finance / Issue 2/2020
Print ISSN: 1593-8883
Electronic ISSN: 1129-6569
DOI: https://doi.org/10.1007/s10203-020-00291-x

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