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Modeling consensus using logic-based similarity measures

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Abstract

One of the key issues when it comes to measuring similarity is the discrepancy that exists between the idealized measures and actual human perception. The aim of this paper is to explore the possibility of using logic-based similarity measures for modeling consensus. We propose a soft consensus model for calculating the consensus and proximity degrees on two different levels. The proposed model relies on logic-based similarity measures and the appropriate aggregation functions. It is a fresh approach as it includes logic when perceiving similarity. Several similarity measures based on min, product and Lukasiewicz fuzzy bi-implications are introduced for modeling consensus. We also define a measure of similarity based on interpolative Boolean algebra (IBA) equivalence, and provide its comprehensive theoretical background. In our approach, we analyze how these different logic-based measures treat similarity, and whether they are appropriate to explain the notion of consensus. Finally, we show that IBA equivalence is the only measure that is both appropriate for modeling consensus and interpretable at the same time. The proposed model is illustrated on a problem of project selection in the context of sustainable development and the numerical results are discussed.

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References

  • Alonso S, Chiclana F, Herrera F, Herrera-Viedma E, Alcal-Fdez J, Porcel C (2008) A consistency-based procedure to estimate missing pairwise preference values. Int J Intell Syst 23(2):155–175

    Article  MATH  Google Scholar 

  • Baczynski M, Jayaram B (2008) Fuzzy implications. Studies in fuzziness and soft computing 231. Springer, Dordrecht

    Google Scholar 

  • Beliakov G, Calvo T, James S (2014) Consensus measures constructed from aggregation functions and fuzzy implications. Knowl Based Syst 55:1–8

    Article  Google Scholar 

  • Bezdek J, Spillman B, Spillman R (1978) A fuzzy relation space for group decision theory. Fuzzy Sets Syst 1(4):255–268

    Article  MathSciNet  MATH  Google Scholar 

  • Bosch R (2005) Characterizations of voting rules and consensus measures. Ph.D. Dissertation, Tilburg University

  • Cabrerizo FJ, Moreno JM, Perez IJ, Herrera-Viedma E (2010) Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks. Soft Comput 14:451–463

    Article  Google Scholar 

  • Callejas C, Marcos J, Bedregal BRC (2012) On some subclasses of the Fodor–Roubens fuzzy bi-implication. In: Ong L, De Queiroz R (eds) Logic, language, information and computation, lecture notes in computer science, vol 7456. Springer, Dordrecht, pp 206–215

    Chapter  Google Scholar 

  • Chiclana F, Herrera F, Herrera-Viedma E (2001) Multiperson decision making based on multiplicative preference relations. Eur J Oper Res 129:372–385

    Article  MathSciNet  MATH  Google Scholar 

  • Chiclana F, Tapia Garcia JM, Del Moral JM, Herrera-Viedma E (2013) A statistical comparative study of different similarity measures of consensus in group decision making. Inf Sci 221:110–123

    Article  Google Scholar 

  • Deza MM, Deza E (2009) Encyclopedia of distances. Springer, Dordrecht

    Book  MATH  Google Scholar 

  • Di Nola A, Pedrycz W, Sessa S (1988) Fuzzy relation equations with equality and difference composition operators. Fuzzy Sets Syst 25:205–215

    Article  MATH  Google Scholar 

  • Dong YC, Zhang GQ, Hong WC, Xu YF (2010) Consensus models for AHP group decision making under row geometric mean prioritization method. Decis Support Syst 49:281–289

    Article  Google Scholar 

  • Dragovic I, Turajlic N, Radojevic D, Petrovic B (2014) Combining boolean consistent fuzzy logic and ahp illustrated on the web service selection problem. Int J Comput Intell Syst 7(supp. 1):84–93. doi:10.1080/18756891.2014.853935

    Article  Google Scholar 

  • Fedrizzi M, Pasi G (2008) Fuzzy logic approaches to consensus modelling in group decision making. In: Ruan D, Hardeman F, Van Der Meer K (eds) Intelligent Decision and Policy Making Support Systems: Studies in Computational Intelligence, vol 117. Springer, Berlin, pp 19–37

    Chapter  Google Scholar 

  • Formato F, Gerla G, Scarpati F (1999) Fuzzy subgroups and similarities. Soft Comput 3:1–6

    Article  Google Scholar 

  • Garcia-Lapresta JL, Perez-Roman D (2011) Measuring Consensus in Weak Orders. In: Herrera-Viedma E, Garcia-Lapresta JL, Kacprzyk J, Fedrizzi M, Nurmi H, Zadrozny S (eds) Consensual Processes: Studies in Fuzziness and Soft Computing 267. Springer, Berlin, pp 213–234

    Chapter  Google Scholar 

  • Herrera F, Herrera-Viedma E, Verdegay JL (1996) A model of consensus in group decision making under linguistic assessments. Fuzzy Sets Syst 78:73–87

    Article  MathSciNet  Google Scholar 

  • Herrera-Viedma E, Herrera F, Chiclana F (2002) A consensus model for multiperson decision making with different preference structures. IEEE Trans Syst Man Cybern - Part A: Systems and Humans 32(3):394–402

    Article  Google Scholar 

  • Herrera-Viedma E, Martinez L, Mata F, Chiclana F (2005) A consensus support system model for group decision-making problems with multigranular linguistic preference relations. IEEE Trans Fuzzy Syst 13(5):644–658

    Article  Google Scholar 

  • Herrera-Viedma E, Alonso S, Chiclana F, Herrera F (2007) A consensus model for group decision making with incomplete fuzzy preference relations. IEEE Trans Fuzzy Syst 15:863–877

    Article  Google Scholar 

  • Herrera-Viedma E, Garcia-Lapresta JL, Kacprzyk J, Fedrizzi M, Nurmi H, Zadrozny S (2011) Consensual Processes. Springer, Berlin

    Book  Google Scholar 

  • Herrera-Viedma E, Cabrerizo FJ, Kacprzyk J, Pedrycz W (2014) A review of soft consensus models in a fuzzy environment. Inf Fus 17:4–13

    Article  Google Scholar 

  • Janowicz K, Raubal M, Kuhn W (2011) The semantics of similarity in geographic information retrieval. J Sp Inf Sci 2:29–57

    Google Scholar 

  • Kacprzyk J, Fedrizzi M (1988) A soft measure of consensus in the setting of partial (fuzzy) prefe-rences. Eur J Oper Res 34:316–323

    Article  MathSciNet  Google Scholar 

  • Kacprzyk J, Zadrozny S, Fedrizzi M, Nurmi H (2007) On group decision making, consensus reaching, voting and voting paradoxes under fuzzy preferences and a fuzzy majority: A survey and some perspectives. In: Bustince H, Herrera H, Montero J (eds) Fuzzy Sets and Their Extensions: Representation. Aggregation and Models, Springer, Berlin, pp 263–295

    Google Scholar 

  • Khorshid S (2010) Soft consensus model based on coincidence between positive and negative ideal degrees of agreement under a group decision-making fuzzy environment. Expert Syst Appl 37:3977–3985

    Article  Google Scholar 

  • Klawonn F, Castro JL (1995) Similarity in Fuzzy Reasoning. Mathw Soft Comput 2:197–228

    MathSciNet  MATH  Google Scholar 

  • Klement EP, Mesiar R, Pap E (2002) Triangular norms. Kluwer Academic Publishers, Dordrecht

    Google Scholar 

  • Le Capitaine H (2012) A relevance-based learning model of fuzzy similarity measures. IEEE Trans Fuzzy Syst 20(1):57–68

    Article  MathSciNet  Google Scholar 

  • Li P, Jin Q (2012) Fuzzy relational equations with min-biimplication composition. Fuzzy Optim Decis Mak 11(2):227–240

    Article  MathSciNet  MATH  Google Scholar 

  • Lu J, Zhang G, Ruan D (2008) Intelligent multi-criteria fuzzy group decision-making for situation assessments. Soft Comput 12:289–299

    Article  MATH  Google Scholar 

  • Lukka P, Leppalampi T (2006) Similarity classifier with generalized mean applied to medical data. Comput Biol Med 36(9):1026–1040

    Article  Google Scholar 

  • Luukka P (2011) Feature selection using fuzzy entropy measures with similarity classifier. Expert Syst Appl 38(4):4600–4607

    Article  Google Scholar 

  • Mata F, Martinez L, Herrera-Viedma E (2009) An adaptive consensus support model for group decision making problems in a multi-granular fuzzy linguistic context. IEEE Trans Fuzzy Syst 17(2):279–290

    Article  Google Scholar 

  • Milosevic P, Poledica A, Dragovic I, Radojevic D, Petrovic B (2013) Logic-based similarity measures for consensus. In: Mladenovic N, Savic G, Kuzmanovic M, Makajic-Nikolic D, Stanojevic M (eds) Proceedings of XI Balkan conference on operational research (BALCOR 2013). Newpress, Smederevo, pp 473–481

  • Milosevic P, Petrovic B, Radojevic D, Kovacevic D (2014) A software tool for uncertainty modeling using interpolative Boolean algebra. Knowl Based Syst 62:1–10

    Article  Google Scholar 

  • Montero J (2008) The impact of fuzziness in social choice paradoxes. Soft Comput 12:177–182

  • Moser B (2006) On representing and generating kernels by fuzzy equivalence relations. J Mach Learn Res 7:2603–2620

    MathSciNet  MATH  Google Scholar 

  • Niittymakia J, Turunen E (2003) Traffic signal control on similarity logic reasoning. Fuzzy Sets Syst 133:109–131

  • Palomares I, Liu J, Xu Y, Martinez L (2012) Modelling experts’ attitudes in group decision making. Soft Comput 16:1755–1766

    Article  MATH  Google Scholar 

  • Poledica A, Milosevic P, Dragovic I, Radojevic D, Petrovic B (2013) A consensus model in group decision making based on interpolative boolean algebra. In: Pasi G, Montero J, Ciucci D (eds) Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-13). doi:10.2991/eusflat.2013.98

  • Radojevic D (2000) New [0, 1]-valued logic: a natural generalization of Boolean logic. Yugosl J Oper Res 10(2):185–216

    MathSciNet  MATH  Google Scholar 

  • Radojevic D (2008) Logical aggregation based on interpolative Boolean algebra. Mathw Soft Comput 15:125–141

    MathSciNet  MATH  Google Scholar 

  • Radojevic D (2010) Generalized (real-valued) order and equivalence relations. In: Forca B, Kovac M, Cabarkapa O, Petrovic D (eds) Proceedings of the 37th symposium on operational research (SYM-OP-IS 2010). Medija centar Odbrana, Belgrade, pp 451–454

  • Rissland EL (2006) Ai and similarity. IEEE Intell Syst 21(3):39–49. doi:10.1109/mis.2006.38

    Article  Google Scholar 

  • Spillman B, Bezdek J, Spillman R (1979) Coalition analysis with fuzzy sets. Kybern 8:203–211

    Article  MATH  Google Scholar 

  • Tapia Garcia JM, Del Moral MJ, Martinez MA, Herrera-Viedma E (2012) A consensus model for group decision making problems with linguistic in-terval fuzzy preference relations. Expert Syst Appl 39:10022–10030

    Article  Google Scholar 

  • Tversky A (1977) Features of similarity. Psychol Rev 84(4):327–352

    Article  Google Scholar 

  • Wang WJ (1997) New similarity measures on fuzzy sets and on elements. Fuzzy Sets Syst 85(3):305–309

    Article  MATH  Google Scholar 

  • Wu Z, Xu J (2012) Consensus reaching models of linguistic preference relations based on distance functions. Soft Comput 16:577–589

    Article  MATH  Google Scholar 

  • Xu ZS (2005) An approach to group decision making based on incomplete linguistic preference relations. Int J Inf Technol Decis Mak 4(1):153–160

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Faculty of Organizational Sciences, University of Belgrade, Jove Ilića 154, 11000, Belgrade, Serbia

    Ana Poledica, Pavle Milošević, Ivana Dragović & Bratislav Petrović

  2. Mihajlo Pupin Institute, Volgina 15, 11000, Belgrade, Serbia

    Dragan Radojević

Authors
  1. Ana Poledica
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  2. Pavle Milošević
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  3. Ivana Dragović
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  4. Bratislav Petrović
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  5. Dragan Radojević
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Corresponding author

Correspondence to Ana Poledica.

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Communicated by V. Loia.

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Poledica, A., Milošević, P., Dragović, I. et al. Modeling consensus using logic-based similarity measures. Soft Comput 19, 3209–3219 (2015). https://doi.org/10.1007/s00500-014-1476-5

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