Some New Operations of (α,β,γ) Interval Cut Set of Interval Valued Neutrosophic Sets

In this paper, we define the disjunctive sum, difference and Cartesian product of two interval valued neutrosophic sets and study their basic properties. The notions of the (α,β,γ) interval cut set of interval valued neutrosophic sets and the (α,β,γ) strong interval cut set of interval valued neutrosophic sets are put forward. Some related properties have been established with proof, examples and counter examples.

[1]  Yanqing Zhang,et al.  Interval Neutrosophic Sets and Logic: Theory and Applications in Computing , 2005, ArXiv.

[2]  Rajshekhar Sunderraman,et al.  Single Valued Neutrosophic Sets , 2010 .

[3]  Peide Liu,et al.  Multi-criteria Group Decision-Making Based on Interval Neutrosophic Uncertain Linguistic Variables and Choquet Integral , 2016, Cognitive Computation.

[4]  • ON (,,)- CUT FUZZY NEUTROSOPHIC SOFT SETS , 2014 .

[5]  Peide Liu,et al.  Some neutrosophic uncertain linguistic number Heronian mean operators and their application to multi-attribute group decision making , 2017, Neural Computing and Applications.

[6]  Peide Liu,et al.  Interval neutrosophic prioritized OWA operator and its application to multiple attribute decision making , 2016, J. Syst. Sci. Complex..

[7]  Peide Liu,et al.  Some Generalized Neutrosophic Number Hamacher Aggregation Operators and Their Application to Group Decision Making , 2014 .

[8]  Peide Liu,et al.  Some approaches to multi criteria decision making based on exponential operations of simplified neutrosophic numbers , 2017, Journal of Intelligent & Fuzzy Systems.

[9]  A. K. Adak,et al.  Interval cut-set of interval-valued intuitionistic fuzzy sets , 2011 .

[10]  Anjan Mukherjee,et al.  Restricted Interval Valued Neutrosophic Sets and Restricted Interval Valued Neutrosophic Topological Spaces , 2016 .

[11]  F. Smarandache,et al.  Interval Valued Neutrosophic Graphs , 2016 .

[12]  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.

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

[14]  Florentin Smarandache,et al.  Shortest Path Problem under Bipolar Neutrosphic Setting , 2016 .

[15]  Chenchen Liu,et al.  Interval Neutrosophic Fuzzy Stochastic Multi-Criteria Decision-making Methods Based on MYCIN Certainty Factor and Prospect Theory , 2017 .

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

[17]  Peide Liu,et al.  Multi-Valued Neutrosophic Number Bonferroni Mean Operators with their Applications in Multiple Attribute Group Decision Making , 2016, Int. J. Inf. Technol. Decis. Mak..

[18]  Peide Liu,et al.  Multiple attribute decision-making method based on some normal neutrosophic Bonferroni mean operators , 2015, Neural Computing and Applications.

[19]  F. Smarandache,et al.  Isolated Single Valued Neutrosophic Graphs , 2016 .

[20]  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..

[21]  Peide Liu,et al.  The Aggregation Operators Based on Archimedean t-Conorm and t-Norm for Single-Valued Neutrosophic Numbers and their Application to Decision Making , 2016, International Journal of Fuzzy Systems.

[22]  F. Smarandache.  A Unifying Field in Logics: Neutrosophic Logic. , 1999 .

[23]  Guangming Shi,et al.  Fuzzy Systems and Knowledge Discovery, Third International Conference, FSKD 2006, Xi'an, China, September 24-28, 2006, Proceedings , 2006, FSKD.

[24]  Florentin Smarandache,et al.  N-Valued Interval Neutrosophic Sets and Their Application in Medical Diagnosis , 2015 .

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

[26]  Khaleed Alhazaymeh,et al.  VAGUE SOFT MULTISET THEORY , 2014 .

[27]  Peide Liu,et al.  Some power generalized aggregation operators based on the interval neutrosophic sets and their application to decision making , 2016, J. Intell. Fuzzy Syst..

[28]  Khaleed Alhazaymeh,et al.  Ordering on vague soft set , 2015 .

[29]  Florentin Smarandache,et al.  Neutrosophic Modal Logic , 2017 .

[30]  Khaleed Alhazaymeh,et al.  Vague soft set relation mappings , 2015 .

[31]  Deyu Li,et al.  An interval-valued hesitant fuzzy multigranulation rough set over two universes model for steam turbine fault diagnosis , 2017 .

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

[33]  C. Antony Crispin Sweety,et al.  Rough sets in Neutrosophic Approximation Space , 2015 .