Aggregation of infinite chains of intuitionistic fuzzy sets and their application to choices with temporal intuitionistic fuzzy information

Abstract We propose the first method for aggregating infinite sequences of intuitionistic fuzzy sets in the literature. This new tool allows us to aggregate an infinite list of intuitionistic fuzzy sets over time –a particular case of temporal intuitionistic fuzzy sets– into a traditional intuitionistic fuzzy set. As an application, we define scores and accuracy degrees of temporal intuitionistic fuzzy elements. Then we use these tools to solve the decision making problem where data come in the form of intuitionistic fuzzy sets along an indefinitely long number of periods.

[1]  Naim Çagman,et al.  Soft sets and soft groups , 2007, Inf. Sci..

[2]  P. Samuelson.  A Note on Measurement of Utility , 1937 .

[3]  Krassimir T. Atanassov,et al.  TEMPORAL INTUITIONISTIC FUZZY SETS , 1991 .

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

[5]  R. Thaler,et al.  Anomalies: Intertemporal Choice , 1989 .

[6]  Fanyong Meng,et al.  Decision making with interval-valued intuitionistic fuzzy preference relations based on additive consistency analysis , 2018, Inf. Sci..

[7]  José Carlos Rodriguez Alcantud,et al.  Necessary and possible hesitant fuzzy sets: A novel model for group decision making , 2019, Inf. Fusion.

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

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

[10]  Young Bae Jun,et al.  Soft sets and soft rough sets , 2011, Inf. Sci..

[11]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[12]  Krassimir T. Atanassov,et al.  On Intuitionistic Fuzzy Sets Theory , 2012, Studies in Fuzziness and Soft Computing.

[13]  Deng-Feng Li,et al.  Multiattribute decision making models and methods using intuitionistic fuzzy sets , 2005, J. Comput. Syst. Sci..

[14]  Hülya Behret,et al.  Group decision making with intuitionistic fuzzy preference relations , 2014, Knowl. Based Syst..

[15]  Guiwu Wei,et al.  Some induced correlated aggregating operators with intuitionistic fuzzy information and their application to multiple attribute group decision making , 2012, Expert Syst. Appl..

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

[17]  Li Zheng,et al.  A novel approach to multi-attribute decision making based on intuitionistic fuzzy sets , 2012, Expert Syst. Appl..

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

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

[20]  Azadeh Zahedi Khameneh,et al.  A fuzzy majority-based construction method for composed aggregation functions by using combination operator , 2019, Inf. Sci..

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

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

[23]  José Carlos Rodriguez Alcantud,et al.  Intertemporal Choice of Fuzzy Soft Sets , 2018, Symmetry.

[24]  Pabitra Kumar Maji,et al.  FUZZY SOFT SETS , 2001 .

[25]  V. Torra,et al.  A framework for linguistic logic programming , 2010 .

[26]  Marc Roubens,et al.  Fuzzy Preference Modelling and Multicriteria Decision Support , 1994, Theory and Decision Library.

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

[28]  Vicenç Torra,et al.  Decomposition theorems and extension principles for hesitant fuzzy sets , 2018, Inf. Fusion.

[29]  Adem Kiliçman,et al.  Application of a preference relationship in decision-making based on intuitionistic fuzzy soft sets , 2017, J. Intell. Fuzzy Syst..

[30]  Manish Agarwal,et al.  Generalized intuitionistic fuzzy soft sets with applications in decision-making , 2013, Appl. Soft Comput..

[31]  Ted O’Donoghue,et al.  Doing It Now or Later , 1999 .

[32]  Edmundas Kazimieras Zavadskas,et al.  Fuzzy multiple criteria decision-making techniques and applications - Two decades review from 1994 to 2014 , 2015, Expert Syst. Appl..