Novel decision-making algorithms based on intuitionistic fuzzy rough environment

Intuitionistic fuzzy sets and rough sets are two different mathematical models to deal the problem of how to understand and manipulate imperfect knowledge. An intuitionistic fuzzy rough framework is made by combining these two models, which is a more flexible and expressive for modeling and processing incomplete information in information systems. In this research study, we introduce intuitionistic fuzzy rough graphs, and describe certain types of intuitionistic fuzzy rough graphs with several examples. We present applications of intuitionistic fuzzy rough graphs in decision-making problems. We develop efficient algorithms to solve decision-making problems and compute time complexity of each algorithm.

[1]  Qinghua Hu,et al.  Feature Selection Based on Neighborhood Discrimination Index , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[2]  Rajab Ali Borzooei,et al.  New concepts of vague graphs , 2017, Int. J. Mach. Learn. Cybern..

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

[4]  Shouyang Wang,et al.  Bipolar fuzzy rough set model on two different universes and its application , 2012, Knowl. Based Syst..

[5]  Ming-Wen Shao,et al.  A unified information measure for general binary relations , 2017, Knowl. Based Syst..

[6]  Krassimir T. Atanassov,et al.  Intuitionistic Fuzzy Sets - Theory and Applications , 1999, Studies in Fuzziness and Soft Computing.

[7]  Wen-Xiu Zhang,et al.  Composition of General Fuzzy Approximation Spaces , 2002, AFSS.

[8]  Wei-Zhi Wu.  Intuitionistic Fuzzy Rough Sets Determined by Intuitionistic Fuzzy Implicators , 2010, 2010 IEEE International Conference on Granular Computing.

[9]  Sudarsan Nanda,et al.  Fuzziness in rough sets , 2000, Fuzzy Sets Syst..

[10]  D. Dubois,et al.  ROUGH FUZZY SETS AND FUZZY ROUGH SETS , 1990 .

[11]  Muhammad Akram,et al.  Neutrosophic Soft Rough Graphs with Application , 2018, Axioms.

[12]  Bing Huang,et al.  Intuitionistic fuzzy multigranulation rough sets , 2014, Inf. Sci..

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

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

[15]  John N. Mordeson,et al.  Fuzzy Graphs and Fuzzy Hypergraphs , 2000, Studies in Fuzziness and Soft Computing.

[16]  Jue Wang,et al.  Rough set over dual-universes in intuitionistic fuzzy approximation space and its application , 2015, J. Intell. Fuzzy Syst..

[17]  Kiran R. Bhutani,et al.  On automorphisms of fuzzy graphs , 1989, Pattern Recognit. Lett..

[18]  Bijan Davvaz,et al.  Roughness in Cayley graphs , 2010, Inf. Sci..

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

[20]  Madhumangal Pal,et al.  Interval-valued fuzzy planar graphs , 2016, Int. J. Mach. Learn. Cybern..

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

[22]  John N. Mordeson,et al.  Operations on Fuzzy Graphs , 1994, Inf. Sci..

[23]  Muhammad Akram,et al.  A Novel Decision-Making Method Based on Rough Fuzzy Information , 2018, Int. J. Fuzzy Syst..

[24]  Sunil Mathew,et al.  Types of arcs in a fuzzy graph , 2009, Inf. Sci..

[25]  Xizhao Wang,et al.  Comparison of reduction in formal decision contexts , 2017, Int. J. Approx. Reason..

[26]  Tina Anggitta Novia,et al.  Complement of a Fuzzy Graph , 2009 .

[27]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[28]  Zongben Xu,et al.  Transformation of rough set models , 2007, Knowl. Based Syst..

[29]  Sunil Mathew,et al.  Strongest Strong Cycles and $\theta$-Fuzzy Graphs , 2013, IEEE Transactions on Fuzzy Systems.

[30]  Ronald R. Yager,et al.  Intuitionistic fuzzy graph interpretations of multi-person multi-criteria decision making , 2003, EUSFLAT Conf..

[31]  Muhammad Akram,et al.  Bipolar Fuzzy Digraphs in Decision Support Systems , 2016, J. Multiple Valued Log. Soft Comput..

[32]  Mansoor Sarwar,et al.  Novel Applications of Intuitionistic Fuzzy Digraphs in Decision Support Systems , 2014, TheScientificWorldJournal.

[33]  Muhammad Akram,et al.  Rough fuzzy digraphs with application , 2019 .

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

[35]  Chris Cornelis,et al.  Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge , 2003 .

[36]  Guilong Liu,et al.  Rough set theory based on two universal sets and its applications , 2010, Knowl. Based Syst..

[37]  Jianhua Dai,et al.  Uncertainty measurement for incomplete interval-valued information systems based on α-weak similarity , 2017, Knowl. Based Syst..

[38]  Yike Guo,et al.  Improving data exploration in graphs with fuzzy logic and large-scale visualisation , 2017, Appl. Soft Comput..

[39]  Xiaohong Zhang,et al.  Soft set theoretical approach to pseudo-BCI algebras , 2018, J. Intell. Fuzzy Syst..

[40]  Prabir Bhattacharya,et al.  Some remarks on fuzzy graphs , 1987, Pattern Recognit. Lett..

[41]  Jianming Zhan,et al.  Fuzzy parameterized fuzzy soft sets and decision making , 2016, Int. J. Mach. Learn. Cybern..

[42]  Muhammad Akram,et al.  Certain types of fuzzy sets in a fuzzy graph , 2016, Int. J. Mach. Learn. Cybern..

[43]  Wei-Zhi Wu,et al.  Maximal-Discernibility-Pair-Based Approach to Attribute Reduction in Fuzzy Rough Sets , 2018, IEEE Transactions on Fuzzy Systems.

[44]  Zhengxin Chen,et al.  Rough set extension of Tcl for data mining , 1998, Knowl. Based Syst..

[45]  Muhammad Akram,et al.  A new approach based on intuitionistic fuzzy rough graphs for decision-making , 2018, J. Intell. Fuzzy Syst..

[46]  Jinhai Li,et al.  Incomplete decision contexts: Approximate concept construction, rule acquisition and knowledge reduction , 2013, Int. J. Approx. Reason..

[47]  Muhammad Akram,et al.  Novel intuitionistic fuzzy soft multiple-attribute decision-making methods , 2016, Neural Computing and Applications.

[48]  Qinghua Hu,et al.  Feature selection based on maximal neighborhood discernibility , 2018, Int. J. Mach. Learn. Cybern..

[49]  Sheng-Gang Li,et al.  Transformation of bipolar fuzzy rough set models , 2012, Knowl. Based Syst..

[50]  Krassimir T. Atanassov,et al.  Operations on intuitionistic fuzzy graphs , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[51]  Lei Zhou,et al.  On generalized intuitionistic fuzzy rough approximation operators , 2008, Inf. Sci..

[52]  Muhammad Akram,et al.  Certain types of intuitionistic fuzzy directed hypergraphs , 2016, Int. J. Mach. Learn. Cybern..

[53]  Muhammad Akram,et al.  Fuzzy soft graphs with applications , 2016, J. Intell. Fuzzy Syst..