Bonferroni Distances and Their Application in Group Decision Making

Abstract The aim of the paper is to develop new aggregation operators using Bonferroni means, ordered weighted averaging (OWA) operators and some distance measures. We introduce the Bonferroni-Hamming weighted distance (BON-HWD), Bonferroni OWA distance (BON-OWAD), Bonferroni OWA adequacy coefficient (BON-OWAAC) and Bonferroni distances with OWA operators and weighted averages (BON-IWOWAD). The main advantages of using these operators are that they allow the consideration of different aggregations contexts to be considered and multiple comparison between each argument and distance measures in the same formulation. An application is developed using these new algorithms in combination with Pichat algorithm to solve a group decision-making problem. Creative personality is taken as an example for forming creative groups. The results show fuzzy dissimilarity relations in order to establish the maximum similarity subrelations and find groups according to each individual’s creative personality similarities.

[1]  J. Merigó,et al.  New aggregation operators for decision-making under uncertainty: an applications in selection of entrepreneurial opportunities , 2017 .

[2]  Peide Liu,et al.  The trapezoid fuzzy linguistic Bonferroni mean operators and their application to multiple attribute decision making , 2012 .

[3]  Zeshui Xu,et al.  Geometric Bonferroni means with their application in multi-criteria decision making , 2013, Knowl. Based Syst..

[4]  M. Mumford,et al.  Leading creative people: Orchestrating expertise and relationships , 2002 .

[5]  J. Merigó,et al.  The generalized adequacy coefficient and its application in strategic decision making , 2008 .

[6]  José M. Merigó,et al.  Heavy Moving Averages and Their Application in Econometric Forecasting , 2018, Cybern. Syst..

[7]  Ronald R. Yager,et al.  On generalized Bonferroni mean operators for multi-criteria aggregation , 2009, Int. J. Approx. Reason..

[8]  José M. Merigó,et al.  Bonferroni induced heavy operators in ERM decision-making: A case on large companies in Colombia , 2018, Appl. Soft Comput..

[9]  Dejian Yu,et al.  Generalized Hesitant Fuzzy Bonferroni Mean and Its Application in Multi-criteria Group Decision Making ⋆ , 2012 .

[10]  A. M. Gil-Lafuente.  Fuzzy Logic in Financial Analysis , 2005 .

[11]  José M. Merigó,et al.  Government transparency measurement through prioritized distance operators , 2018, J. Intell. Fuzzy Syst..

[12]  José M. Merigó,et al.  Induced Heavy Moving Averages , 2018, Int. J. Intell. Syst..

[13]  Dimitar Filev,et al.  On the concept of immediate probabilities , 1995, Int. J. Intell. Syst..

[14]  Etienne Pichat.  Contribution à l'algorithmique non numérique dans les ensembles ordonnés , 1970 .

[15]  G. Wei,et al.  Uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making , 2013 .

[16]  Anna Maria Gil Lafuente,et al.  A Method for Decision Making Based on Generalized Aggregation Operators , 2013, Int. J. Intell. Syst..

[17]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decision-making , 1988 .

[18]  Dejian Yu.  Triangular Atanassov's intuitionistic fuzzy Bonferroni mean and application to supplier selection , 2015, J. Intell. Fuzzy Syst..

[19]  Richard W. Hamming,et al.  Error detecting and error correcting codes , 1950 .

[20]  Ezequiel Avilés Ochoa,et al.  Exchange rate USD/MXN forecast through econometric models, time series and HOWMA operators , 2016 .

[21]  Ronald R. Yager,et al.  On ordered weighted averaging aggregation operators in multicriteria decisionmaking , 1988, IEEE Trans. Syst. Man Cybern..

[22]  Huayou Chen,et al.  Intuitionistic Fuzzy Power Geometric Bonferroni Means and Their Application to Multiple Attribute Group Decision Making , 2015, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[23]  Peide Liu,et al.  Intuitionistic Linguistic Weighted Bonferroni Mean Operator and Its Application to Multiple Attribute Decision Making , 2014, TheScientificWorldJournal.

[24]  M. Mumford,et al.  Creativity syndrome: Integration, application, and innovation. , 1988 .

[25]  Zeshui Xu.  Hybrid Weighted Distance Measures and Their Application to Pattern Recognition , 2008, IDEAL.

[26]  José M. Merigó,et al.  Exploring the Ordered Weighted Averaging Operator Knowledge Domain: A Bibliometric Analysis , 2017, Int. J. Intell. Syst..

[27]  Carlo Bonferroni.  Sulle medie multiple di potenze , 1950 .

[28]  J. Gil-Aluja.  Elements for a Theory of Decision in Uncertainty , 2010 .

[29]  Zeshui Xu,et al.  Intuitionistic Fuzzy Bonferroni Means , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[30]  Huayou Chen,et al.  Hesitant Fuzzy Power Bonferroni Means and Their Application to Multiple Attribute Decision Making , 2015, IEEE Transactions on Fuzzy Systems.

[31]  Zeshui Xu,et al.  Hesitant fuzzy geometric Bonferroni means , 2012, Inf. Sci..

[32]  Zeshui Xu,et al.  Generalized intuitionistic fuzzy Bonferroni means , 2012, Int. J. Intell. Syst..

[33]  José M. Merigó,et al.  Fuzzy decision making: A bibliometric-based review , 2017, J. Intell. Fuzzy Syst..

[34]  Debashree Guha,et al.  Article in Press G Model Applied Soft Computing Partitioned Bonferroni Mean Based on Linguistic 2-tuple for Dealing with Multi-attribute Group Decision Making , 2022 .

[35]  Peide Liu,et al.  Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean , 2014, Neural Computing and Applications.

[36]  Zeshui Xu,et al.  Hesitant fuzzy Bonferroni means for multi-criteria decision making , 2013, J. Oper. Res. Soc..

[37]  José M. Merigó,et al.  Logarithmic aggregation operators and distance measures , 2018, Int. J. Intell. Syst..

[38]  R. Yager,et al.  MODELLING DECISION MAKING USING IMMEDIATE PROBABILITIES , 1996 .

[39]  José M. Merigó,et al.  Partitioned Heronian means based on linguistic intuitionistic fuzzy numbers for dealing with multi-attribute group decision making , 2018, Appl. Soft Comput..

[40]  Wei Zhou,et al.  Intuitionistic Fuzzy Geometric Bonferroni Means and Their Application in Multicriteria Decision Making , 2012, Int. J. Intell. Syst..

[41]  José M. Merigó,et al.  Decision-making with distance measures and induced aggregation operators , 2011, Comput. Ind. Eng..

[42]  Ronald R. Yager,et al.  Generalized Bonferroni mean operators in multi-criteria aggregation , 2010, Fuzzy Sets Syst..

[43]  Sigifredo Laengle,et al.  Mean-Variance Portfolio Selection With the Ordered Weighted Average , 2017, IEEE Transactions on Fuzzy Systems.

[44]  Zeshui Xu,et al.  Uncertain Bonferroni Mean Operators , 2010, Int. J. Comput. Intell. Syst..

[45]  Janusz Kacprzyk,et al.  Recent Developments in the Ordered Weighted Averaging Operators: Theory and Practice , 2011, Studies in Fuzziness and Soft Computing.

[46]  Gui-Wu Wei,et al.  Some Bonferroni mean operators with 2-tuple linguistic information and their application to multiple attribute decision making , 2014, J. Intell. Fuzzy Syst..

[47]  José M. Merigó,et al.  Decision Making in Reinsurance with Induced OWA Operators and Minkowski Distances , 2016, Cybern. Syst..

[48]  José M. Merigó,et al.  A unified model between the weighted average and the induced OWA operator , 2011, Expert Syst. Appl..

[49]  Rajkumar Verma,et al.  Generalized Bonferroni Mean Operator for Fuzzy Number Intuitionistic Fuzzy Sets and its Application to Multiattribute Decision Making , 2015, Int. J. Intell. Syst..

[50]  Gleb Beliakov,et al.  On extending generalized Bonferroni means to Atanassov orthopairs in decision making contexts , 2013, Fuzzy Sets Syst..

[51]  A. Bonaert.  Introduction to the theory of Fuzzy subsets , 1977, Proceedings of the IEEE.

[52]  J. Merigó,et al.  Decision-making techniques with similarity measures and OWA operators , 2012 .

[53]  José M. Merigó,et al.  Fuzzy decision making with immediate probabilities , 2010, Comput. Ind. Eng..

[54]  José M. Merigó,et al.  Bonferroni means with distance measures and the adequacy coefficient in entrepreneurial group theory , 2016, Knowl. Based Syst..

[55]  Qingguo Li,et al.  Hesitant Triangular Fuzzy Information Aggregation Operators Based on Bonferroni Means and Their Application to Multiple Attribute Decision Making , 2014, TheScientificWorldJournal.

[56]  Huayou Chen,et al.  Intuitionistic Fuzzy Interaction Bonferroni Means and Its Application to Multiple Attribute Decision Making , 2015, IEEE Transactions on Cybernetics.

[57]  Na Hu,et al.  Multi-attribute group decision making method based on geometric Bonferroni mean operator of trapezoidal interval type-2 fuzzy numbers , 2015, Comput. Ind. Eng..

[58]  Zeshui Xu,et al.  Ordered weighted distance measure , 2008 .

[59]  José M. Merigó,et al.  New decision-making techniques and their application in the selection of financial products , 2010, Inf. Sci..

[60]  José M. Merigó,et al.  Distance measures, weighted averages, OWA operators and Bonferroni means , 2017, Appl. Soft Comput..

[61]  José M. Merigó,et al.  Redefining support vector machines with the ordered weighted average , 2018, Knowl. Based Syst..