Multi-Criteria Decision-Making Method Based on Type-2 Fuzzy Sets

Type-2 fuzzy sets (T2FSs) are the extension of type-1 fuzzy sets (T1FSs), which can convey more uncertainty information in solving multi-criteria decision-making (MCDM) problems. Motivated by the extension from interval numbers to triangular fuzzy numbers, three-trapezoidal-fuzzy-number-bounded type-2 fuzzy numbers (TT2FNs) are defined on the basis of interval type-2 trapezoidal fuzzy numbers (IT2TFNs), and they can convey more uncertainty information than T1FSs and IT2FSs. Moreover, the drawbacks of the existing computational models of generalized fuzzy numbers are analyzed, and a new computational model of fuzzy numbers is proposed, which is further extended to TT2FNs. Besides, a MCDM method is proposed to deal with the evaluation information given in the form of TT2FNs. Finally, an illustrative example and comparison analysis are provided to demonstrate the feasibility and validity of the proposed method.

[1]  Xiao-hong Chen,et al.  Intuitionistic random multi-criteria decision-making approach based on prospect theory with multiple reference intervals , 2014 .

[2]  Zeshui Xu,et al.  Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-norm , 2012, Knowl. Based Syst..

[3]  Przemyslaw Grzegorzewski,et al.  Trapezoidal approximations of fuzzy numbers , 2003, Fuzzy Sets Syst..

[4]  Jing Wang,et al.  Multi-valued Neutrosophic Sets and Power Aggregation Operators with Their Applications in Multi-criteria Group Decision-making Problems , 2015, Int. J. Comput. Intell. Syst..

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

[6]  Jing Wang,et al.  Simplified neutrosophic linguistic normalized weighted Bonferroni mean operator and its application to multi-criteria decision-making problems , 2015 .

[7]  Florentin Smarandache,et al.  Neutrosophic set - a generalization of the intuitionistic fuzzy set , 2004, 2006 IEEE International Conference on Granular Computing.

[8]  T. Chu,et al.  Ranking fuzzy numbers with an area between the centroid point and original point , 2002 .

[9]  Patricia Melin,et al.  Interval Type-2 Fuzzy Logic Applications in Image Processing and Pattern Recognition , 2010, 2010 IEEE International Conference on Granular Computing.

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

[11]  WangWeize,et al.  Multi-attribute group decision making models under interval type-2 fuzzy environment , 2012 .

[12]  Shyi-Ming Chen,et al.  Fuzzy risk analysis based on ranking generalized fuzzy numbers with different heights and different spreads , 2009, Expert Syst. Appl..

[13]  Ting-Yu Chen,et al.  A PROMETHEE-based outranking method for multiple criteria decision analysis with interval type-2 fuzzy sets , 2013, Soft Computing.

[14]  Tzuu-Hseng S. Li,et al.  Design of interval type-2 fuzzy sliding-mode controller , 2008, Inf. Sci..

[15]  Cengiz Kahraman,et al.  Fuzzy analytic hierarchy process with interval type-2 fuzzy sets , 2014, Knowl. Based Syst..

[16]  Shyi-Ming Chen,et al.  Fuzzy decision making systems based on interval type-2 fuzzy sets , 2013, Inf. Sci..

[17]  Rita Almeida Ribeiro,et al.  A framework for dynamic multiple-criteria decision making , 2011, Decis. Support Syst..

[18]  Shyi-Ming Chen,et al.  Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets , 2012, Expert Syst. Appl..

[19]  Chao Wang,et al.  Induced generalized hesitant fuzzy operators and their application to multiple attribute group decision making , 2014, Comput. Ind. Eng..

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

[21]  Shyi-Ming Chen,et al.  Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers , 2007, Applied Intelligence.

[22]  Shouzhen Zeng,et al.  Group multi-criteria decision making based upon interval-valued fuzzy numbers: An extension of the MULTIMOORA method , 2013, Expert Syst. Appl..

[23]  Krassimir T. Atanassov,et al.  Two theorems for intuitionistic fuzzy sets , 2000, Fuzzy Sets Syst..

[24]  Weize Wang,et al.  Multi-attribute decision making models under interval type-2 fuzzy environment , 2011, 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011).

[25]  Jian-qiang Wang,et al.  Some new operation rules and a new ranking method for interval-valued intuitionistic linguistic numbers , 2017, J. Intell. Fuzzy Syst..

[26]  Amit Kumar,et al.  A new approach for ranking nonnormal p-norm trapezoidal fuzzy numbers , 2011, Comput. Math. Appl..

[27]  Feilong Liu,et al.  An efficient centroid type-reduction strategy for general type-2 fuzzy logic system , 2008, Inf. Sci..

[28]  Yan Zhang,et al.  Multi-criteria decision making method based on possibility degree of interval type-2 fuzzy number , 2013, Knowl. Based Syst..

[29]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[30]  Ralph E. Steuer,et al.  Multiple Criteria Decision Making, Multiattribute Utility Theory: The Next Ten Years , 1992 .

[31]  Shuo-Yan Chou,et al.  A revised method for ranking fuzzy numbers using maximizing set and minimizing set , 2011, Comput. Ind. Eng..

[32]  J. Mendel.  Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions , 2001 .

[33]  Hong-yu Zhang,et al.  New operators on triangular intuitionistic fuzzy numbers and their applications in system fault analysis , 2013, Inf. Sci..

[34]  Shyi-Ming Chen,et al.  Fuzzy multiple attributes group decision-making based on the ranking values and the arithmetic operations of interval type-2 fuzzy sets , 2010, Expert Syst. Appl..

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

[36]  Jianqiang Wang,et al.  Multi-criteria Group Decision-Making Method Based on Intuitionistic Interval Fuzzy Information , 2012, Group Decision and Negotiation.

[37]  Ying-Ming Wang,et al.  Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment , 2006, Expert Syst. Appl..

[38]  Radko Mesiar,et al.  Hesitant L ‐Fuzzy Sets , 2017, Int. J. Intell. Syst..

[39]  Jerry M. Mendel,et al.  Type-2 fuzzy sets made simple , 2002, IEEE Trans. Fuzzy Syst..

[40]  Hong-yu Zhang,et al.  Multi-criteria outranking approach with hesitant fuzzy sets , 2013, OR Spectrum.

[41]  I. Burhan Türksen,et al.  Type 2 representation and reasoning for CWW , 2002, Fuzzy Sets Syst..

[42]  Ahmad M. El-Nagar,et al.  Direct adaptive interval type-2 fuzzy logic controller for the multivariable anaesthesia system , 2011 .

[43]  K. Atanassov,et al.  Interval-Valued Intuitionistic Fuzzy Sets , 2019, Studies in Fuzziness and Soft Computing.

[44]  Jerry M. Mendel,et al.  A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets , 2009, Inf. Sci..

[45]  Mohammad Hossein Fazel Zarandi,et al.  Interval type-2 fuzzy expert system for prediction of carbon monoxide concentration in mega-cities , 2012, Appl. Soft Comput..

[46]  Jian-qiang Wang,et al.  A multi-valued neutrosophic qualitative flexible approach based on likelihood for multi-criteria decision-making problems , 2017, Int. J. Syst. Sci..

[47]  Peng Zhou,et al.  Multi-criteria decision-making method based on normal intuitionistic fuzzy-induced generalized aggregation operator , 2014, TOP.

[48]  S. Wan.  Power average operators of trapezoidal intuitionistic fuzzy numbers and application to multi-attribute group decision making , 2013 .

[49]  P. Hofstaetter.  [Similarity]. , 2020, Psyche.

[50]  Miin-Shen Yang,et al.  Similarity, inclusion and entropy measures between type-2 fuzzy sets based on the Sugeno integral , 2011, Math. Comput. Model..

[51]  Shyi-Ming Chen,et al.  Fuzzy multiple attributes group decision-making based on the interval type-2 TOPSIS method , 2010, Expert Syst. Appl..

[52]  Chin-Wang Tao,et al.  An Approximation of Interval Type-2 Fuzzy Controllers Using Fuzzy Ratio Switching Type-1 Fuzzy Controllers , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[53]  Hong-yu Zhang,et al.  An Interval Type-2 Fuzzy Number Based Approach for Multi-Criteria Group Decision-Making Problems , 2015, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[54]  Hsuan-Shih Lee,et al.  The revised method of ranking fuzzy numbers with an area between the centroid and original points , 2008, Comput. Math. Appl..

[55]  Zhou Ling,et al.  Grey-stochastic multi-criteria decision-making approach based on prospect theory , 2010 .

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

[57]  Yong Deng,et al.  A note on ranking generalized fuzzy numbers , 2012, Expert Syst. Appl..

[58]  Milos Manic,et al.  Interval Type-2 fuzzy voter design for fault tolerant systems , 2011, Inf. Sci..

[59]  Miin-Shen Yang,et al.  Similarity Measures Between Type-2 Fuzzy Sets , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[60]  Byung-In Choi,et al.  Interval type-2 fuzzy membership function generation methods for pattern recognition , 2009, Inf. Sci..

[61]  Jerry M. Mendel,et al.  Similarity measures for general type-2 fuzzy sets based on the α-plane representation , 2014, Inf. Sci..

[62]  Mao-Jiun J. Wang,et al.  Personnel selection using fuzzy MCDM algorithm , 1994 .

[63]  Hong-yu Zhang,et al.  outranking approach for multi-criteria decision-making problems ith simplified neutrosophic sets uan - , 2014 .

[64]  Shyi-Ming Chen,et al.  A new method for analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers , 2009, ICMLC 2009.

[65]  I. Turksen.  Type 2 representation and reasoning for CWW , 2002 .

[66]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[67]  Jerry M. Mendel,et al.  New results about the centroid of an interval type-2 fuzzy set, including the centroid of a fuzzy granule , 2007, Inf. Sci..

[68]  Pavel V. Sevastjanov,et al.  Aggregation of aggregating modes in MCDM: Synthesis of Type 2 and Level 2 fuzzy sets , 2007 .

[69]  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 .

[70]  Marc Roubens,et al.  Multiple criteria decision making , 1994 .