# Modelling influence in group decision making

- 842 Downloads
- 21 Citations

## Abstract

Group decision making has been widely studied since group decision making processes are very common in many fields. Formal representation of the experts’ opinions, aggregation of assessments or selection of the best alternatives has been some of main areas addressed by scientists and researchers. In this paper, we focus on another promising area, the study of group decision making processes from the concept of influence and social networks. In order to do so, we present a novel model that gathers the experts’ initial opinions and provides a framework to represent the influence of a given expert over the other(s). With this proposal it is feasible to estimate both the evolution of the group decision making process and the final solution before carrying out the group discussion process and consequently foreseeing possible actions.

## Keywords

Group decision making Aggregation operators Social network Influence## Notes

### Acknowledgments

This research work has been supported with Feder funding by the research project of Education Ministery TIN2013-40658-P. No sources of funding were used to assist in the preparation of this study.

### **Compliance with ethical standards**

No sources of funding were used to assist in the preparation of this study.

### Funding

This study was funded by the research project of Education Ministery TIN2013-40658-P.

### Conflict of interest

The authors declare that they have no conflict of interest.

### Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

## References

- Alonso S, Cabrerizo FJ, Chiclana F, Herrera F, Herrera-Viedma E (2009) Group decision making with incomplete fuzzy linguistic preference relations. Int J Intell Syst 24(2):201–222CrossRefzbMATHGoogle Scholar
- 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(23):4477–4495MathSciNetCrossRefGoogle Scholar
- Bezdek JC, Spillman B, Spillman R (1978) A fuzzy relation space for group decision theory. Fuzzy Sets Syst 1(4):255–268MathSciNetCrossRefzbMATHGoogle Scholar
- Cabrerizo F, Chiclana F, Al-Hmouz R, Morfeq A, Balamash A, Herrera-Viedma E (2015) Fuzzy decision making and consensus: challenges. J Intell Fuzzy Syst 29(3):1109–1118MathSciNetCrossRefGoogle Scholar
- Cabrerizo F, Moreno J, Pérez I, Herrera-Viedma E (2010) Analyzing consensus approaches in fuzzy group decision making: advantages and drawbacks. Soft Comput 14(5):451–463CrossRefGoogle Scholar
- Calza F, Gaeta M, Loia V, Orciuoli F, Piciocchi P, Rarità L, Spohrer J, Tommasetti A (2015) Fuzzy consensus model for governance in smart service systems. Procedia Manuf 3:3567–3574CrossRefGoogle Scholar
- Chiclana F, Herrera-Viedma E, Alonso S, Herrera F (2007) Consistency of reciprocal preference relations. In: 2007 IEEE International Conference on Fuzzy Systems, FUZZYGoogle Scholar
- Chiclana F, Herrera-Viedma E, Alonso S, Herrera F (2008) A note on the estimation of missing pairwise preference values: a uninorm consistency based method. Int J Uncertain Fuzziness Knowledge-Based Syst 16(SUPPL.2):19–32Google Scholar
- Chiclana F, Herrera-Viedma E, Alonso S, Herrera F (2009) Cardinal consistency of reciprocal preference relations: a characterization of multiplicative transitivity. IEEE Trans Fuzzy Syst 17(1):14–23CrossRefGoogle Scholar
- Chiclana F, Herrera-Viedma E, Herrera F, Alonso S (2007) Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations. Eur J Oper Res 182(1):383–399CrossRefzbMATHGoogle Scholar
- Ciasullo MV, Gaeta M, Monetta G, Rarità L (2015) E-cultural value co-creation. A proposed model for the heritage management. In: Proceedings of 18th Toulon-Verona International Conference, “Excellence in Services”, vol. U, pp 139–158Google Scholar
- Dubois DJ, Prade H (1980) Fuzzy sets and systems: theory and application. Academic Press, New YorkzbMATHGoogle Scholar
- French JR (1956) A formal theory of social power. Psychol Rev 63(3):181–194MathSciNetCrossRefGoogle Scholar
- Friedkin NE, Johnsen EC (1990) Social influence and opinions. J Math Sociol 15:193–206Google Scholar
- Friedkin NE, Johnsen EC (1999) Social influence networks and opinion change. Adv Gr Process 16:1–29Google Scholar
- Gong Z, Xu X, Zhang H, Ozturk UA, Herrera-Viedma E, Xu C (2015) The consensus models with interval preference opinions and their economic interpretation. Omega 55:81–90CrossRefGoogle Scholar
- Harary F (1959) A criterion for unanimity in French’s theory of social power. Studies in social power. University of Michigan, Ann Arbor, Oxford, pp 168–182Google Scholar
- Kacprzyk J (1986) Group decision making with a fuzzy linguistic majority. Fuzzy Sets Syst 18(2):105–118MathSciNetCrossRefzbMATHGoogle Scholar
- Kacprzyk J, Fedrizzi M, Nurmi H (1997) Consensus under fuzziness. Kluwer Academic Publishers, New YorkGoogle Scholar
- Kacprzyk J, Roubens M (1988) Non-conventional preference relations in decision making. Springer, BerlinCrossRefzbMATHGoogle Scholar
- Kitainik L (1993) Fuzzy decision procedures with binary relations: towards a unified theory. Springer, New YorkGoogle Scholar
- Klement EP, Mesiar R, Pap E (1996) On the relationship of associative compensatory operators to triangular norms and conorms. Int J Uncertain Fuzziness Knowlege-Based Syst 4(2):129–144MathSciNetCrossRefzbMATHGoogle Scholar
- Luce RD, Suppes, P (1965) Preferences, utility and subject probability. Handbook of mathematical psychology, vol III. Wiley, New York, pp 249–410Google Scholar
- Massanet S, Riera JV, Torrens J, Herrera-Viedma E (2014) A new linguistic computational model based on discrete fuzzy numbers for computing with words. Inf Sci 258:277–290MathSciNetCrossRefzbMATHGoogle Scholar
- Mata F, Martínez 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):279–290CrossRefGoogle Scholar
- Mata F, Pérez L, Zhou SM, Chiclana F (2014) Type-1 OWA methodology to consensus reaching processes in multi-granular linguistic contexts. Knowledge-Based Syst 58:11–22CrossRefGoogle Scholar
- Mitchell HB, Estrakh DD (1997) A modified OWA operator and its use in lossless dpcm image compression. Int J Uncertain Fuzziness Knowledge-Based Syst 5:429–436CrossRefzbMATHGoogle Scholar
- Morente-Molinera J, Pérez I, Ureña M, Herrera-Viedma E (2015) Building and managing fuzzy ontologies with heterogeneous linguistic information. Knowl Based Syst 88:154–164Google Scholar
- Morente-Molinera J, Al-hmouz R, Morfeq A, Balamash A, Herrera-Viedma E (2016) A decision support system for decision making in changeable and multi-granular fuzzy linguistic contexts. J Mult Valued Logic Soft Comput
**(In press)**Google Scholar - Nurmi H (1981) Approaches to collective decision making with fuzzy preference relations. Fuzzy Sets Syst 6(3):249–259MathSciNetCrossRefzbMATHGoogle Scholar
- Pérez IJ, Cabrerizo FJ, Alonso S, Herrera-Viedma E (2014) A new consensus model for group decision making problems with non-homogeneous experts. Syst Man Cybern Syst IEEE Trans on 44(4):494–498CrossRefGoogle Scholar
- Pérez IJ, Cabrerizo FJ, Herrera-Viedma E (2010) A mobile decision support system for dynamic group decision-making problems. IEEE Trans Syst Man Cybern Part A Syst Hum 40(6):1244–1256CrossRefGoogle Scholar
- Pérez L, Mata F, Chiclana F (2014) Social network decision making with linguistic trustworthiness based induced OWA operators. Int J Intell Syst 29(12):1117–1137CrossRefGoogle Scholar
- Pérez-Asurmendi P, Chiclana F (2014) Linguistic majorities with difference in support. Appl Soft Comput 18:196–208CrossRefzbMATHGoogle Scholar
- Roubens M (1997) Fuzzy sets and decision analysis. Fuzzy Sets Syst 90(2):199–206MathSciNetCrossRefzbMATHGoogle Scholar
- Saaty T (1980) The analytic hierarchy process. McGraw-Hill, New yorkzbMATHGoogle Scholar
- Scott JP, Carrington PJ (2011) The SAGE handbook of social network analysis. SAGE, LondonCrossRefGoogle Scholar
- Seo F, Sakawa M (1985) Fuzzy multiattribute utility analysis for collective choice. IEEE Trans Syst Man Cybern 15(1):45–53Google Scholar
- Tanino T (1984) Fuzzy preference orderings in group decision making. Fuzzy Sets Syst 12(2):117–131Google Scholar
- Tanino T (1988) Fuzzy preference relations in group decision making. Non-conventional preference relations in decision making. Springer-Verlag, Berlin, pp 54–71Google Scholar
- Tanino T (1990) On group decision making under fuzzy preferences. Multiperson decision making using fuzzy sets and possibility theory. Kluwer Academic Publisher, Dordrecht, pp 172–185Google Scholar
- Ureña R, Chiclana F, Morente-Molinera J, Herrera-Viedma E (2015) Managing incomplete preference relations in decision making: a review and future trends. Inf Sci 302:14–32MathSciNetCrossRefGoogle Scholar
- Wasserman S, Faust K (1994) Social network analysis: methods and applications. Cambridge University Press, New YorkGoogle Scholar
- Wu J, Chiclana F, Herrera-Viedma E (2015) Trust based consensus model for social network in an incomplete linguistic information context. Appl Soft Comput 35:827–839CrossRefGoogle Scholar
- Yager RR (1983) Quantifiers in the formulation of multiple objective decision functions. Inf Sci 31(2):107–139MathSciNetCrossRefzbMATHGoogle Scholar
- Yager RR (1988) On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans Syst Man Cybern 18(1):183–190MathSciNetCrossRefzbMATHGoogle Scholar
- Yager RR (1996) Quantifier guided aggregation using OWA operators. Int J Intell Syst 11(1):49–73CrossRefGoogle Scholar
- Yager RR (2003) Induced aggregation operators. Fuzzy Sets Syst 137:59–69MathSciNetCrossRefzbMATHGoogle Scholar
- Yager RR, Filev D (1998) Operations for granular computing: mixing words and numbers. IEEE Int Conf Fuzzy Syst 1:123–128Google Scholar
- Yager RR, Filev D (1999) Induced ordered weighted averaging operators. IEEE Trans Syst Man Cybern 29:141–150CrossRefGoogle Scholar
- Zadeh LA (1983) A computational approach to fuzzy quantifiers in natural languages. Comput Math Appl 9(1):149–184MathSciNetCrossRefzbMATHGoogle Scholar