New Operations of Picture Fuzzy Relations and Fuzzy Comprehensive Evaluation

In this paper, some new operations and basic properties of picture fuzzy relations are intensively studied. First, a new inclusion relation (called type-2 inclusion relation) of picture fuzzy relations is introduced, as well as the corresponding type-2 union, type-2 intersection and type-2 complement operations. Second, the notions of anti-reflexive kernel, symmetric kernel, reflexive closure and symmetric closure of a picture fuzzy relation are introduced and their properties are explored. Moreover, a new method to solve picture fuzzy comprehensive evaluation problems is proposed by defining the new composition operation of picture fuzzy relations, and the picture fuzzy comprehensive evaluation model is built. Finally, an application example (about investment risk) of picture fuzzy comprehensive evaluation is given, and the effective experiment results are obtained.

[1]  Theresa Beaubouef,et al.  Rough Sets , 2019, Lecture Notes in Computer Science.

[2]  Miao Qi-guang.  On the Intuitionistic Fuzzy Relations with Compositional Operations , 2005 .

[3]  Fuad E. Alsaadi,et al.  Projection models for multiple attribute decision making with picture fuzzy information , 2016, International Journal of Machine Learning and Cybernetics.

[4]  Humberto Bustince,et al.  Construction of intuitionistic fuzzy relations with predetermined properties , 2000, Fuzzy Sets Syst..

[5]  Andrzej Skowron,et al.  Interactive granular computing , 2016 .

[6]  D. Ciucci.  Orthopairs and granular computing , 2016 .

[7]  Xiaohong Zhang,et al.  Fuzzy anti-grouped filters and fuzzy normal filters in pseudo-BCI algebras , 2017, J. Intell. Fuzzy Syst..

[8]  Li Sheng-gang,et al.  Restudy of Intuitionistic Fuzzy Relations , 2009 .

[9]  D. Molodtsov.  Soft set theory—First results , 1999 .

[10]  Lorenzo Livi,et al.  Granular computing, computational intelligence, and the analysis of non-geometric input spaces , 2016 .

[11]  Le Hoang Son,et al.  Some novel hybrid forecast methods based on picture fuzzy clustering for weather nowcasting from satellite image sequences , 2016, Applied Intelligence.

[12]  Lei Ying-jie.  Information Security Evaluation Based on Multilevel Intuitionistic Fuzzy Comprehensive Method , 2009 .

[13]  Le Hoang Son,et al.  Picture inference system: a new fuzzy inference system on picture fuzzy set , 2016, Applied Intelligence.

[14]  Ming-Wen Shao,et al.  Feature subset selection based on fuzzy neighborhood rough sets , 2016, Knowl. Based Syst..

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

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

[17]  Pham Van Hai,et al.  Some Fuzzy Logic Operators for Picture Fuzzy Sets , 2015, 2015 Seventh International Conference on Knowledge and Systems Engineering (KSE).

[18]  Shinichi Tamura,et al.  Pattern Classification Based on Fuzzy Relations , 1971, IEEE Trans. Syst. Man Cybern..

[19]  Jun Liu,et al.  Catoptrical rough set model on two universes using granule-based definition and its variable precision extensions , 2017, Inf. Sci..

[20]  Georg Peters,et al.  DCC: a framework for dynamic granular clustering , 2016 .

[21]  Huaxiong Li,et al.  Distance-based information granularity in neighborhood-based granular space , 2018 .

[22]  Peng Li,et al.  A general frame for intuitionistic fuzzy rough sets , 2012, Inf. Sci..

[23]  Guijun Wang,et al.  Approximation performance of the nonlinear hybrid fuzzy system based on variable universe , 2017, GRC 2017.

[24]  Muhammad Akram,et al.  A NEW MULTIPLE CRITERIA DECISION-MAKING METHOD BASED ON BIPOLAR FUZZY SOFT GRAPHS , 2018 .

[25]  Didier Dubois,et al.  Bridging gaps between several forms of granular computing , 2016, Granular Computing.

[26]  Bui Cong Cuong,et al.  Picture fuzzy sets , 2015 .

[27]  Muhammad Akram,et al.  (1611-3300) A NEW MULTIPLE CRITERIA DECISION-MAKING METHOD BASED ON BIPOLAR FUZZY SOFT GRAPHS , 2017 .

[28]  Mauricio A. Sanchez,et al.  Fuzzy higher type information granules from an uncertainty measurement , 2017, GRC 2017.

[29]  Martine De Cock,et al.  On (un)suitable fuzzy relations to model approximate equality , 2003, Fuzzy Sets Syst..

[30]  Arsham Borumand Saeid,et al.  Hesitant Fuzzy Filters in BE-algebras , 2016, Int. J. Comput. Intell. Syst..

[31]  Fang Qi,et al.  Research on the Comprehensive Evaluation of Sports Management System with Interval-valued Intuitionistic Fuzzy Information , 2012 .

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

[33]  Humberto Bustince,et al.  Intuitionistic fuzzy relations (Part I). , 1995 .

[34]  Guangming Lang,et al.  Shadowed sets of dynamic fuzzy sets , 2017, GRC 2017.

[35]  Alsaedi Ahmed,et al.  Hesitant Fuzzy Linguistic Arithmetic Aggregation Operators in Multiple Attribute Decision Making , 2016 .

[36]  J. Blin.  Fuzzy Relations in Group Decision Theory , 1974 .

[37]  Ji Ju-liang.  Fuzzy comprehensive evaluation model based on improved analytic hierarchy process , 2004 .

[38]  Yiyu Yao.  A triarchic theory of granular computing , 2016 .

[39]  Miin-Shen Yang,et al.  Cluster analysis based on fuzzy relations , 2001, Fuzzy Sets Syst..

[40]  Bijan Davvaz,et al.  S-APPROXIMATION SPACES: A FUZZY APPROACH , 2017 .

[41]  Chunyong Wang,et al.  SOME GEOMETRIC AGGREGATION OPERATORS BASED ON PICTURE FUZZY SETS AND THEIR APPLICATION IN MULTIPLE ATTRIBUTE DECISION MAKING , 2017 .

[42]  Zeshui Xu,et al.  Hesitant Fuzzy Sets Theory , 2014, Studies in Fuzziness and Soft Computing.

[43]  Keyun Qin,et al.  On soft equality , 2010, J. Comput. Appl. Math..

[44]  Jianming Zhan,et al.  A novel soft rough set: Soft rough hemirings and corresponding multicriteria group decision making , 2017, Appl. Soft Comput..