Neutrosophic structured element

Correspondence Seyyed Ahmad Edalatpanah, Applied Mathematics, Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran. Email: saedaltpanah@gmail.com Abstract This paper presents a new concept in neutrosophic sets (NS) called neutrosophic structured element (NSE). Based on this concept, we define the operational laws, score function, and some aggregation operators of NS. Finally, as an application of this concept, we propose a decision-making method for a multi-attribute decision making (MADM) problem under NSE information. The results indicate that this concept is a useful tool for dealing with neutrosophic decision problems.

[1]  Lin Li,et al.  Multi-criteria decision-making method based on single-valued neutrosophic linguistic Maclaurin symmetric mean operators , 2016, Neural Computing and Applications.

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

[3]  Arindam Dey,et al.  Neutrosophic Shortest Path Problem , 2018 .

[4]  Wei-Kang Wang,et al.  A fuzzy multi-objective two-stage DEA model for evaluating the performance of US bank holding companies , 2014, Expert Syst. Appl..

[5]  Peide Liu,et al.  The generalized hybrid weighted average operator based on interval neutrosophic hesitant set and its application to multiple attribute decision making , 2015, Neural Computing and Applications.

[6]  Jun Ye,et al.  Improved cosine similarity measures of simplified neutrosophic sets for medical diagnoses , 2015, Artif. Intell. Medicine.

[8]  A. Soliman,et al.  Author Biography , 2018, Understanding Language Use in the Classroom.

[9]  S. A. Edalatpanah,et al.  Neutrosophic perspective on DEA , 2018 .

[10]  Yun-zhi Liu,et al.  Fuzzy Multi-objective Programming Problem with Fuzzy Structured Element Solution , 2012 .

[11]  Harish Garg,et al.  Linguistic single-valued neutrosophic prioritized aggregation operators and their applications to multiple-attribute group decision-making , 2018, Journal of Ambient Intelligence and Humanized Computing.

[12]  F. Smarandache,et al.  Correlation Coefficient of Interval Neutrosophic Set , 2013 .

[13]  Shengyue Deng,et al.  Solving the Fuzzy BiLevel Linear Programming with Multiple Followers through Structured Element Method , 2014 .

[14]  Eser Sert,et al.  Brain tumor segmentation using neutrosophic expert maximum fuzzy-sure entropy and other approaches , 2019, Biomed. Signal Process. Control..

[15]  S. A. Edalatpanah,et al.  A note on “A new method for solving fully fuzzy linear programming problems” , 2013 .

[16]  Florentin Smarandache,et al.  Data Envelopment Analysis for Simplified Neutrosophic Sets , 2019 .

[17]  Zhang-peng Tian,et al.  Simplified Neutrosophic Linguistic Multi-criteria Group Decision-Making Approach to Green Product Development , 2017 .

[18]  Xudong Sun,et al.  Solving Fuzzy Linear Systems Based on the Structured Element Method , 2008, ACFIE.

[19]  Jun Ye,et al.  An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers , 2015, J. Intell. Fuzzy Syst..

[20]  Yong Shi,et al.  Homeomorphism Problems of Fuzzy Real Number Space and The Space of Bounded Functions with Same Monotonicity on [-1, 1] , 2015, Int. J. Comput. Commun. Control.

[21]  Florentin Smarandache,et al.  Interval Valued Bipolar Neutrosophic Sets and Their Application in Pattern Recognition , 2016 .

[22]  Jun Wan,et al.  Evaluation Model of Credibility of E-Commerce Website Using Fuzzy Multi-Attribute Group Decision Making: Based on Fuzzy Structured Element , 2010, ACFIE.

[23]  Jun Ye,et al.  Similarity measures between interval neutrosophic sets and their applications in multicriteria decision-making , 2014, J. Intell. Fuzzy Syst..

[24]  Jun Ye,et al.  Single valued neutrosophic cross-entropy for multicriteria decision making problems , 2014 .

[25]  Ming Zhang,et al.  A neutrosophic approach to image segmentation based on watershed method , 2010, Signal Process..

[26]  Dong-xiao Dong,et al.  The Study of the Fuzzy Net Present Value Based on Structured Element , 2009, ICFIE.

[27]  Zhiwen Mo,et al.  Infinitely Small Quantity and Infinitely Large Quantity of Fuzzy Valued Functions for Linear Generation of Structural Elements , 2016 .

[28]  Vinay Kumar,et al.  A novel computer vision based neutrosophic approach for leaf disease identification and classification , 2019, Measurement.

[29]  Ramesh C. Jain,et al.  Imprecision in Computer Vision , 1982, Computer.

[30]  I. Turksen.  Interval valued fuzzy sets based on normal forms , 1986 .

[31]  Yan Yan,et al.  The Method of Fuzzy Network Shortest Path Based on the Structured Element Theory , 2009, ICFIE.

[32]  Sizong Guo.  FUZZY ANALYSIS AND CALCULATION BASED ON THE STRUCTURED ELEMENT , 2004 .

[33]  Florentin Smarandache,et al.  A unifying field in logics : neutrosophic logic : neutrosophy, neutrosophic set, neutrosophic probability , 2020 .

[34]  G. Si-cong.  Method of structuring element in fuzzy analysis(II) , 2002 .

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

[36]  Yang Yang,et al.  Fuzzy Number Intuitionistic Fuzzy Set and its Representation of Structured Element , 2008, 2008 International Symposium on Intelligent Information Technology Application Workshops.

[37]  Mai Mohamed,et al.  RETRACTED: The role of single valued neutrosophic sets and rough sets in smart city: Imperfect and incomplete information systems , 2018, Measurement.

[38]  Surapati Pramanik,et al.  New Trends in Neutrosophic Theory and Applications , 2016, ArXiv.

[39]  Yike Guo,et al.  A rule based fuzzy model for the prediction of petrophysical rock parameters , 2001 .

[40]  S. A. Edalatpanah,et al.  A new approach for solving fully fuzzy linear fractional programming problems using the multi-objective linear programming , 2017, RAIRO Oper. Res..

[41]  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..

[42]  Jun Ye,et al.  A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets , 2014, J. Intell. Fuzzy Syst..

[43]  F. Smarandache,et al.  An Introduction to Bipolar Single Valued Neutrosophic Graph Theory , 2016 .

[44]  Tzu-Kuang Hsu,et al.  The preference analysis for tourist choice of destination: A case study of Taiwan , 2009 .

[45]  Jing Wang,et al.  An interval neutrosophic linguistic multi-criteria group decision-making method and its application in selecting medical treatment options , 2017, Neural Computing and Applications.

[46]  L. Zadeh.  Fuzzy sets and their application to pattern classification and clustering analysis , 1996 .

[47]  Yanhui Guo,et al.  New neutrosophic approach to image segmentation , 2009, Pattern Recognit..

[48]  Florentin Smarandache,et al.  A Group Decision Making Framework Based on Neutrosophic TOPSIS Approach for Smart Medical Device Selection , 2019, Journal of Medical Systems.

[49]  Peide Liu,et al.  Multiple attribute decision-making method based on single-valued neutrosophic normalized weighted Bonferroni mean , 2014, Neural Computing and Applications.

[50]  S. A. Edalatpanah,et al.  A mathematical model for solving fully fuzzy linear programming problem with trapezoidal fuzzy numbers , 2016, Applied Intelligence.

[51]  Surapati Pramanik,et al.  TOPSIS method for multi-attribute group decision-making under single-valued neutrosophic environment , 2014, Neural Computing and Applications.

[52]  Wang Jian-qiang,et al.  Fuzzy multi-criteria decision making method based on fuzzy structured element with incomplete weight information , 2016 .

[53]  Sha-Sha Li,et al.  Study on the construction and application of discrete space fault tree modified by fuzzy structured element , 2018, Cluster Computing.

[54]  Mehmet Sahin,et al.  Similarity measures of bipolar neutrosophic sets and their application to multiple criteria decision making , 2018, Neural Computing and Applications.

[56]  Manju Khari,et al.  Neutrosophic soft set decision making for stock trending analysis , 2018, Evol. Syst..

[57]  Ting Lei,et al.  Fuzzy Bi-matrix games based on fuzzy structured element , 2017, 2017 13th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD).

[58]  Cunbao Deng,et al.  Comprehensive decision-making with fuzzy combined weighting and its application on the order of gob management , 2018, J. Intell. Fuzzy Syst..

[59]  Aboul Ella Hassanien,et al.  Neutrosophic rule-based prediction system for toxicity effects assessment of biotransformed hepatic drugs , 2019, Expert Syst. Appl..

[60]  Hong-yu Zhang,et al.  Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems , 2016, Int. J. Syst. Sci..

[61]  Jun Ye,et al.  Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment , 2013, Int. J. Gen. Syst..

[62]  S. A. Edalatpanah,et al.  An Improved Model for Iterative Algorithms in Fuzzy Linear Systems , 2013 .

[63]  S. A. Edalatpanah,et al.  A nonlinear model for fully fuzzy linear programming with fully unrestricted variables and parameters , 2016 .

[64]  Hong-yu Zhang,et al.  A projection-based TODIM method under multi-valued neutrosophic environments and its application in personnel selection , 2016, Neural Computing and Applications.

[65]  Sudan Jha,et al.  Neutrosophic image segmentation with Dice Coefficients , 2019, Measurement.

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

[67]  Harish Garg,et al.  Non-linear programming method for multi-criteria decision making problems under interval neutrosophic set environment , 2017, Applied Intelligence.

[68]  Florentin Smarandache,et al.  Neutrosophic triplet group , 2016, Neural Computing and Applications.

[69]  Ridvan Sahin,et al.  Subsethood measure for single valued neutrosophic sets , 2014, J. Intell. Fuzzy Syst..

[70]  S. A. Edalatpanah,et al.  A Multi Objective Programming Approach to Solve Integer Valued Neutrosophic Shortest Path Problems , 2018 .

[71]  Yong Shi,et al.  Homeomorphism Between Fuzzy Number Space and the Space of Bounded Functions with Same Monotonicity on [-1, 1] , 2015, ICDS.

[72]  Umberto Rivieccio,et al.  Neutrosophic logics: Prospects and problems , 2008, Fuzzy Sets Syst..

[73]  Liu Cui,et al.  New Approach to Exponential Stability Analysis and Stabilization for Delayed T-S Fuzzy Markovian Jump Systems , 2016 .

[74]  Jun Ye.  Single valued neutrosophic cross-entropy for multicriteria decision making problems , 2014 .

[75]  Norazak Senu,et al.  Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications , 2018, Symmetry.

[76]  Si-zong Guo,et al.  Comparison and Ordering of Fuzzy Numbers Based on Method of Structured Element , 2009 .

[77]  Francisco Gallego Lupiáñez,et al.  Interval neutrosophic sets and topology , 2008, Kybernetes.

[78]  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..