Intuitionistic fuzzy-valued Choquet integral and its application in multicriteria decision making

Our purpose in this paper is to show the integration properties of the intuitionistic fuzzy-valued Choquet integrals, by which improper applications of this type of Choquet integral in the multicriteria decision making can be avoided. We first propose some important operational properties of intuitionistic fuzzy values (IFVs) and give a short review of the methods of comparing IFVs in the framework of the multicriteria decision making. Then we give a detailed discussion on the aggregation properties of the intuitionistic fuzzy-valued Choquet integral (IFCI) and the intuitionistic fuzzy-valued conjugate Choquet integral (IFCCI). The difference in aggregation characteristics between the IFCI and the IFCCI in multicriteria decision making are also be investigated. Finally, we present an application of the IFCI and IFCCI-based multicriteria decision making method to assess the software development risks.

[1]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[2]  Janusz Kacprzyk,et al.  Using intuitionistic fuzzy sets in group decision making , 2002 .

[3]  M. Sugeno,et al.  An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy , 1989 .

[4]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[5]  Da Ruan,et al.  Choquet integral based aggregation approach to software development risk assessment , 2010, Inf. Sci..

[6]  Dug Hun Hong,et al.  Multicriteria fuzzy decision-making problems based on vague set theory , 2000, Fuzzy Sets Syst..

[7]  菅野 道夫,et al.  Theory of fuzzy integrals and its applications , 1975 .

[8]  Zhenyuan Wang,et al.  CONVERGENCE THEOREMS FOR SEQUENCES OF CHOQUET INTEGRALS , 1997 .

[9]  Guiwu Wei,et al.  Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making , 2010, Appl. Soft Comput..

[10]  G. Klir,et al.  Fuzzy Measure Theory , 1993 .

[11]  Ranjit Biswas,et al.  Some operations on intuitionistic fuzzy sets , 2000, Fuzzy Sets Syst..

[12]  Hsiang-Chuan Liu.  An addition-invariant partial order of ordered addition monoids of intuitionistic fuzzy values , 2010, 2010 International Symposium on Computer, Communication, Control and Automation (3CA).

[13]  Dayou Liu,et al.  Set-valued Choquet integrals revisited , 2004, Fuzzy Sets Syst..

[14]  Radko Mesiar,et al.  Aggregation functions: Construction methods, conjunctive, disjunctive and mixed classes , 2011, Inf. Sci..

[15]  Zhou-Jing Wang,et al.  An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights , 2009, Inf. Sci..

[16]  Hsiang-Chuan Liu.  Choquet integral on Liu's generalized intuitionistic fuzzy numbers , 2010, 2010 International Conference on Machine Learning and Cybernetics.

[17]  G. Choquet.  Theory of capacities , 1954 .

[18]  Xiaotong Li,et al.  Software development risk and project performance measurement: Evidence in Korea , 2007, J. Syst. Softw..

[19]  Zeshui Xu,et al.  Dynamic intuitionistic fuzzy multi-attribute decision making , 2008, Int. J. Approx. Reason..

[20]  Hsiang-chuan Liu.  Liu's Generalized Intuitionistic Fuzzy Sets , 2010 .

[21]  Xiaohong Chen,et al.  Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making , 2010, Expert Syst. Appl..

[22]  Kwong-Sak Leung,et al.  Fuzzy numbers and fuzzification of the Choquet integral , 2005, Fuzzy Sets Syst..

[23]  K. Atanassov.  More on intuitionistic fuzzy sets , 1989 .

[24]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[25]  Michio Sugeno,et al.  Fuzzy t -conorm integral with respect to fuzzy measures: generalization of Sugeno integral and choquet integral , 1991 .

[26]  M. Grabisch.  Fuzzy integral in multicriteria decision making , 1995 .

[27]  Zeshui Xu,et al.  Some geometric aggregation operators based on intuitionistic fuzzy sets , 2006, Int. J. Gen. Syst..

[28]  Shyi-Ming Chen,et al.  Handling multicriteria fuzzy decision-making problems based on vague set theory , 1994 .

[29]  R. Mesiar,et al.  ”Aggregation Functions”, Cambridge University Press , 2008, 2008 6th International Symposium on Intelligent Systems and Informatics.

[30]  Huawen Liu,et al.  Multi-criteria decision-making methods based on intuitionistic fuzzy sets , 2007, Eur. J. Oper. Res..

[31]  T. Mexia,et al.  Author ' s personal copy , 2009 .

[32]  R. Mesiar,et al.  Aggregation Functions: Aggregation on ordinal scales , 2009 .

[33]  Zeshui Xu,et al.  Intuitionistic Fuzzy Aggregation Operators , 2007, IEEE Transactions on Fuzzy Systems.

[34]  Michel Grabisch,et al.  p-Symmetric Fuzzy Measures , 2002, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[35]  Radko Mesiar,et al.  Aggregation functions: Means , 2011, Inf. Sci..

[36]  Ronald R. Yager.  On the dispersion measure of OWA operators , 2009, Inf. Sci..

[37]  John McManus.  Risk Management in Software Development Projects , 2003 .

[38]  Michel Grabisch,et al.  A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package , 2008, Eur. J. Oper. Res..

[39]  Márcio de Oliveira Barros,et al.  Evaluating software project portfolio risks , 2007, J. Syst. Softw..

[40]  Jean-Luc Marichal,et al.  An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria , 2000, IEEE Trans. Fuzzy Syst..

[41]  Michel Grabisch,et al.  A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid , 2010, Ann. Oper. Res..

[42]  Xizhao Wang,et al.  Induction of multiple fuzzy decision trees based on rough set technique , 2008, Inf. Sci..

[43]  Adrian I. Ban,et al.  Componentwise decomposition of some lattice-valued fuzzy integrals , 2007, Inf. Sci..

[44]  Xi-Zhao Wang,et al.  Improving Generalization of Fuzzy IF--THEN Rules by Maximizing Fuzzy Entropy , 2009, IEEE Transactions on Fuzzy Systems.

[45]  E. Pap.  Null-Additive Set Functions , 1995 .

[46]  Zeshui Xu,et al.  Choquet integrals of weighted intuitionistic fuzzy information , 2010, Inf. Sci..

[47]  M. Grabisch.  The application of fuzzy integrals in multicriteria decision making , 1996 .

[48]  Zun-Quan Xia,et al.  Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets , 2007, J. Comput. Syst. Sci..

[49]  Márcio de Oliveira Barros,et al.  Supporting risks in software project management , 2004, J. Syst. Softw..

[50]  Zeshui Xu,et al.  Intuitionistic preference relations and their application in group decision making , 2007, Inf. Sci..

[51]  Gülçin Büyüközkan,et al.  A fuzzy-logic-based decision-making approach for new product development , 2004 .

[52]  L. C. Jang,et al.  Some properties of Choquet integrals of set-valued functions , 1997, Fuzzy Sets Syst..

[53]  Huey-Ming Lee,et al.  A new algorithm for applying fuzzy set theory to evaluate the rate of aggregative risk in software development , 2003, Inf. Sci..

[54]  Lotfi A. Zadeh,et al.  Is there a need for fuzzy logic? , 2008, NAFIPS 2008 - 2008 Annual Meeting of the North American Fuzzy Information Processing Society.

[55]  Michel Grabisch,et al.  K-order Additive Discrete Fuzzy Measures and Their Representation , 1997, Fuzzy Sets Syst..

[56]  Qiang Zhang,et al.  2-order additive fuzzy measure identification method based on diamond pairwise comparison and maximum entropy principle , 2010, Fuzzy Optim. Decis. Mak..

[57]  Jean-Luc Marichal,et al.  An axiomatic approach to the definition of the entropy of a discrete Choquet capacity , 2005, Inf. Sci..

[58]  Radko Mesiar,et al.  Aggregation of infinite sequences , 2008, Inf. Sci..

[59]  Jean-Luc Marichal,et al.  Tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral , 2004, Eur. J. Oper. Res..

[60]  M. Sugeno,et al.  Some quantities represented by the Choquet integral , 1993 .

[61]  Ronald R. Yager,et al.  Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making , 2005, Int. J. Syst. Sci..

[62]  Radko Mesiar,et al.  Weighted aggregation operators based on minimization , 2008, Inf. Sci..

[63]  Stephen O. Ogunlana,et al.  Managing risk in software development projects: a case study , 2007, Ind. Manag. Data Syst..

[64]  Lotfi A. Zadeh,et al.  Toward a generalized theory of uncertainty (GTU) - an outline , 2005, GrC.

[65]  B. C. Brookes,et al.  Information Sciences , 2020, Cognitive Skills You Need for the 21st Century.

[66]  Qiang Zhang,et al.  Multicriteria decision making method based on intuitionistic fuzzy weighted entropy , 2011, Expert Syst. Appl..

[67]  Kwong-Sak Leung,et al.  Real-valued Choquet integrals with fuzzy-valued integrand , 2006, Fuzzy Sets Syst..