Approaches Based on Interval Type-2 Fuzzy Aggregation Operators for Multiple Attribute Group Decision Making

This paper aims to develop interval type-2 fuzzy aggregation operators including interval type-2-dependent ordered weighted averaging (IT2DOWA) operator and interval type-2 power averaging (IT2PA) operator. Properties of new aggregation operators are discussed, and interval type-2 weighted-dependent ordered weighted averaging (IT2WDOWA) operator and interval type-2 power averaging (IT2WPA) operator are presented by combining objective weights with subjective weights. Moreover, we utilize new operators to develop approaches for multiple attribute group decision making (MAGDM) with interval type-2 fuzzy numbers. Finally, we give an illustrative example to verify the developed approaches and simultaneously, some existing methods are referred to make comparison in order to demonstrate practicality and effectiveness of new ones. The primary contribution of this paper is twofold. One is to develop some new aggregation operators whose aggregation weights in MAGDM mainly depend on the relationship of aggregated interval type-2 fuzzy numbers by using different deviation measures. Another is to propose approaches with new interval type-2 aggregation operators to MAGDM problems, which begin with natural linguistic evaluation and EKM algorithms.

[1]  Türkay Dereli,et al.  Technology evaluation through the use of interval type-2 fuzzy sets and systems , 2013, Comput. Ind. Eng..

[2]  Marc Roubens,et al.  Fuzzy sets and decision analysis , 1997, Fuzzy Sets Syst..

[3]  Jerry M. Mendel,et al.  Enhanced Interval Approach for Encoding Words Into Interval Type-2 Fuzzy Sets and Its Convergence Analysis , 2012, IEEE Transactions on Fuzzy Systems.

[4]  Ling Huang,et al.  An Approach to Group Decision Making Problems Based on 2-Tuple Linguistic Aggregation Operators , 2008, 2008 ISECS International Colloquium on Computing, Communication, Control, and Management.

[5]  Z. S. Xu,et al.  Eowa And Eowg Operators For Aggregating Linguistic Labels Based On Linguistic Preference Relations , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[6]  Jerry M. Mendel,et al.  Encoding Words Into Interval Type-2 Fuzzy Sets Using an Interval Approach , 2008, IEEE Transactions on Fuzzy Systems.

[7]  Francisco Herrera,et al.  A model of consensus in group decision making under linguistic assessments , 1996, Fuzzy Sets Syst..

[8]  Huayou Chen,et al.  Generalized Interval-Valued Atanassov's Intuitionistic Fuzzy Power Operators and Their Application to Group Decision Making , 2013 .

[9]  Huayou Chen,et al.  Intuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making , 2014, Inf. Sci..

[10]  Francisco Herrera,et al.  A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets , 2013, Inf. Sci..

[11]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[12]  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..

[13]  Yejun Xu,et al.  Standard and mean deviation methods for linguistic group decision making and their applications , 2010, Expert Syst. Appl..

[14]  Shyi-Ming Chen,et al.  A new method for tool steel materials selection under fuzzy environment , 1997, Fuzzy Sets Syst..

[15]  Peide Liu,et al.  Some generalized dependent aggregation operators with intuitionistic linguistic numbers and their application to group decision making , 2013, J. Comput. Syst. Sci..

[16]  R. Yager.  Quantifier guided aggregation using OWA operators , 1996, Int. J. Intell. Syst..

[17]  Zhiming Zhang,et al.  A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets , 2013 .

[18]  V. Torra.  The weighted OWA operator , 1997, International Journal of Intelligent Systems.

[19]  Ronald R. Yager,et al.  Applications and Extensions of OWA Aggregations , 1992, Int. J. Man Mach. Stud..

[20]  Ferhan Çebi,et al.  Multi-Criteria and Multi-Stage Facility Location Selection under Interval Type-2 Fuzzy Environment: A Case Study for a Cement Factory , 2015, Int. J. Comput. Intell. Syst..

[21]  Zaiwu Gong,et al.  A Novel Distance Measure of Multi-Granularity Linguistic Variables and Its Application to MADM , 2014 .

[22]  Jerry M. Mendel,et al.  Perceptual Computing: Aiding People in Making Subjective Judgments , 2010 .

[23]  Jerry M. Mendel,et al.  Computing With Words for Hierarchical Decision Making Applied to Evaluating a Weapon System , 2010, IEEE Transactions on Fuzzy Systems.

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

[25]  Shyi-Ming Chen,et al.  Fuzzy risk analysis based on interval-valued fuzzy numbers , 2009, Expert Syst. Appl..

[26]  Siamak Safarzadegan Gilan,et al.  Computing with words for hierarchical competency based selection of personnel in construction companies , 2012, Appl. Soft Comput..

[27]  Ming Wang,et al.  Data-driven modeling and optimization of thermal comfort and energy consumption using type-2 fuzzy method , 2013, Soft Computing.

[28]  Zeshui Xu,et al.  Dependent uncertain ordered weighted aggregation operators , 2008, Inf. Fusion.

[29]  J. Merigó,et al.  Fuzzy Generalized Hybrid Aggregation Operators and its Application in Fuzzy Decision Making , 2010 .

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

[31]  Francisco Herrera,et al.  A fusion approach for managing multi-granularity linguistic term sets in decision making , 2000, Fuzzy Sets Syst..

[32]  Yejun Xu,et al.  Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment , 2011, Appl. Soft Comput..

[33]  Jerry Mendel,et al.  Type-2 Fuzzy Sets and Systems: An Overview [corrected reprint] , 2007, IEEE Computational Intelligence Magazine.

[34]  Ching-Gung Wen,et al.  River assimilative capacity analysis via fuzzy linear programming , 1996, Fuzzy Sets Syst..

[35]  Francisco Herrera,et al.  A Sequential Selection Process in Group Decision Making with a Linguistic Assessment Approach , 1995, Inf. Sci..

[36]  Zeshui Xu,et al.  A method based on linguistic aggregation operators for group decision making with linguistic preference relations , 2004, Inf. Sci..

[37]  Guiwu Wei,et al.  Some dependent aggregation operators with 2-tuple linguistic information and their application to multiple attribute group decision making , 2012, Expert Syst. Appl..

[38]  Eric Levrat,et al.  Subjective evaluation of car seat comfort with fuzzy set techniques , 1997 .

[39]  José L. Verdegay,et al.  On aggregation operations of linguistic labels , 1993, Int. J. Intell. Syst..

[40]  Xiao-hong Chen,et al.  Some interval-valued intuitionistic uncertain linguistic Choquet operators and their application to multi-attribute group decision making , 2014 .

[41]  Francisco Herrera,et al.  Combining Numerical and Linguistic Information in Group Decision Making , 1998, Inf. Sci..

[42]  Francisco Herrera,et al.  Fuzzy Sets and Their Extensions: Representation, Aggregation and Models , 2008 .

[43]  Shouzhen Zeng,et al.  Fuzzy Generalized Ordered Weighted Averaging Distance Operator and Its Application to Decision Making , 2012 .

[44]  Jerry M. Mendel,et al.  Aggregation Using the Linguistic Weighted Average and Interval Type-2 Fuzzy Sets , 2007, IEEE Transactions on Fuzzy Systems.

[45]  Francisco Herrera,et al.  Aggregation operators for linguistic weighted information , 1997, IEEE Trans. Syst. Man Cybern. Part A.

[46]  Zeshui Xu,et al.  Power-Geometric Operators and Their Use in Group Decision Making , 2010, IEEE Transactions on Fuzzy Systems.

[47]  José Ignacio Peláez,et al.  LAMA: A linguistic aggregation of majority additive operator , 2003, Int. J. Intell. Syst..

[48]  Jerry M. Mendel,et al.  Uncertainty measures for general type-2 fuzzy sets , 2009, 2009 IEEE International Conference on Systems, Man and Cybernetics.

[49]  Gloria Bordogna,et al.  A linguistic modeling of consensus in group decision making based on OWA operators , 1997, IEEE Trans. Syst. Man Cybern. Part A.

[50]  Jian-Bo Yang,et al.  Evidential reasoning‐based nonlinear programming model for MCDA under fuzzy weights and utilities , 2010, Int. J. Intell. Syst..

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

[52]  A. K. Ray,et al.  Construction of fuzzy edge image using Interval Type II fuzzy set , 2014, Int. J. Comput. Intell. Syst..

[53]  Zeshui Xu,et al.  Induced uncertain linguistic OWA operators applied to group decision making , 2006, Inf. Fusion.

[54]  Z. S. Xu,et al.  An overview of operators for aggregating information , 2003, Int. J. Intell. Syst..

[55]  Yejun Xu,et al.  Standard deviation method for determining the weights of group multiple attribute decision making under uncertain linguistic environment , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[56]  J. Merigó,et al.  Decision Making with Fuzzy Induced Heavy Ordered Weighted Averaging Operators , 2014 .

[57]  G. Bortolan,et al.  The problem of linguistic approximation in clinical decision making , 1988, Int. J. Approx. Reason..

[58]  Dejian Yu.  Multi-Criteria Decision Making Based on Generalized Prioritized Aggregation Operators under Intuitionistic Fuzzy Environment , 2013 .

[59]  Chao Wang,et al.  A new support vector machine based on type-2 fuzzy samples , 2013, Soft Comput..

[60]  Francisco Herrera,et al.  Linguistic decision analysis: steps for solving decision problems under linguistic information , 2000, Fuzzy Sets Syst..

[61]  Xiaohong Chen,et al.  Generalized Hesitant Fuzzy Generalized Shapley-Choquet Integral Operators and Their Application in Decision Making , 2014 .

[62]  V. Torra.  Negation functions based semantics for ordered linguistic labels , 1996 .

[63]  Zeshui Xu,et al.  Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment , 2004, Inf. Sci..

[64]  Francisco Herrera,et al.  Hesitant Fuzzy Linguistic Term Sets for Decision Making , 2012, IEEE Transactions on Fuzzy Systems.

[65]  Francisco Herrera,et al.  A 2-tuple fuzzy linguistic representation model for computing with words , 2000, IEEE Trans. Fuzzy Syst..

[66]  R. Yager,et al.  UNDERSTANDING THE MEDIAN AS A FUSION OPERATOR , 1997 .

[67]  Yong Qin,et al.  Multi-attribute group decision making models under interval type-2 fuzzy environment , 2012, Knowl. Based Syst..

[68]  Zeshui Xu,et al.  An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations , 2006, Decis. Support Syst..

[69]  Jerry M. Mendel,et al.  Interval Type-2 Fuzzy Logic Systems Made Simple , 2006, IEEE Transactions on Fuzzy Systems.

[70]  Shyi-Ming Chen,et al.  Fuzzy Multiple Criteria Hierarchical Group Decision-Making Based on Interval Type-2 Fuzzy Sets , 2010, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[71]  Zhibin Wu,et al.  The maximizing deviation method for group multiple attribute decision making under linguistic environment , 2007, Fuzzy Sets Syst..

[72]  Shyi-Ming Chen,et al.  A NEW METHOD FOR HANDLING MULTICRITERIA FUZZY DECISION-MAKING PROBLEMS USING FN-IOWA OPERATORS , 2003, Cybern. Syst..

[73]  Xin Zhang,et al.  Some intuitionistic uncertain linguistic Heronian mean operators and their application to group decision making , 2014, Appl. Math. Comput..

[74]  H. B. Mitchell.  Pattern recognition using type-II fuzzy sets , 2005, Inf. Sci..

[75]  Jerry M. Mendel,et al.  Operations on type-2 fuzzy sets , 2001, Fuzzy Sets Syst..

[76]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[77]  Jerry M. Mendel,et al.  Type-2 fuzzy sets and systems: an overview , 2007, IEEE Computational Intelligence Magazine.

[78]  Ronald R. Yager,et al.  Fusion of ordinal information using weighted median aggregation , 1998, Int. J. Approx. Reason..

[79]  Peide Liu,et al.  Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operators , 2014, Appl. Soft Comput..

[80]  Zhao Chen-xi.  Interactive approach for multiple attribute decision making with incomplete weight information under uncertain linguistic environment , 2009 .

[81]  Peide Liu,et al.  Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making , 2012, Inf. Sci..

[82]  Ronald R. Yager,et al.  An approach to ordinal decision making , 1995, Int. J. Approx. Reason..

[83]  Ronald R. Yager,et al.  The power average operator , 2001, IEEE Trans. Syst. Man Cybern. Part A.

[84]  Ting-Yu Chen,et al.  Collaborative decision-making method for patient-centered care based on interval type-2 fuzzy sets , 2012 .

[85]  Yanbing Gong,et al.  Fuzzy Multi-Attribute Group Decision Making Method Based on Interval Type-2 Fuzzy Sets and Applications to Global Supplier Selection , 2013 .

[86]  Huey-Ming Lee,et al.  Applying fuzzy set theory to evaluate the rate of aggregative risk in software development , 1996, Fuzzy Sets Syst..

[87]  Francisco Herrera,et al.  A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decision-making , 2001, IEEE Trans. Syst. Man Cybern. Part B.

[88]  R. John,et al.  On aggregating uncertain information by type-2 OWA operators for soft decision making , 2010 .