MADM Based on Generalized Interval Neutrosophic Schweizer-Sklar Prioritized Aggregation Operators

The interval neutrosophic set (INS) can make it easier to articulate incomplete, indeterminate, and inconsistent information, and the Schweizer-Sklar (Sh-Sk) t-norm (tm) and t-conorm (tcm) can make the information aggregation process more flexible due to a variable parameter. To take full advantage of INS and Sh-Sk operations, in this article, we expanded the Sh-Sk and to IN numbers (INNs) in which the variable parameter takes values from [ ∞ − , 0 ) , develop the Sh-Sk operational laws for INNs and discussed its desirable properties. After that, based on these newly developed operational laws, two types of generalized prioritized aggregation operators are established, the generalized IN Sh-Sk prioritized weighted averaging (INSh-SkPWA) operator and the generalized IN Sh-Sk prioritized weighted geometric (INSh-SkPWG) operator. Additionally, we swot a number of valuable characteristics of these intended aggregation operators (AGOs) and created two novel decision-making models to match with multiple-attribute decision-making (MADM) problems under IN information established on INSh-SkPWA and INSh-SkPRWG operators. Finally, an expressive example regarding evaluating the technological innovation capability for the high-tech enterprises is specified to confirm the efficacy of the intended models.

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

[2]  Peide Liu,et al.  Application of Interval Neutrosophic Power Hamy Mean Operators in MAGDM , 2019, Informatica.

[3]  Li Pan,et al.  An Interval Neutrosophic Projection-Based VIKOR Method for Selecting Doctors , 2017, Cognitive Computation.

[4]  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.

[5]  Jun Ye,et al.  Multiple attribute decision-making method based on the possibility degree ranking method and ordered weighted aggregation operators of interval neutrosophic numbers , 2015, J. Intell. Fuzzy Syst..

[6]  Lishi Zhang.  Intuitionistic fuzzy averaging Schweizer-Sklar operators based on interval-valued intuitionistic fuzzy numbers and its applications , 2018, 2018 Chinese Control And Decision Conference (CCDC).

[7]  Xindong Peng,et al.  ALGORITHMS FOR INTERVAL NEUTROSOPHIC MULTIPLE ATTRIBUTE DECISION-MAKING BASED ON MABAC, SIMILARITY MEASURE, AND EDAS , 2018 .

[8]  Fei Wang,et al.  Multi-Criteria Decision-Making Method Based on Single-Valued Neutrosophic Schweizer-Sklar Muirhead Mean Aggregation Operators , 2019, Symmetry.

[9]  Harish Garg,et al.  Some modified results of the subtraction and division operations on interval neutrosophic sets , 2019, J. Exp. Theor. Artif. Intell..

[10]  Peide Liu,et al.  Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi-Attribute Decision-Making , 2018, Symmetry.

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

[12]  Keyun Qin,et al.  New Similarity and Entropy Measures of Interval Neutrosophic Sets with Applications in Multi-Attribute Decision-Making , 2019, Symmetry.

[13]  Ridvan Sahin,et al.  Normal neutrosophic multiple attribute decision making based on generalized prioritized aggregation operators , 2017, Neural Computing and Applications.

[14]  Jun Ye,et al.  Single-Valued Neutrosophic Hybrid Arithmetic and Geometric Aggregation Operators and Their Decision-Making Method , 2017, Inf..

[15]  S. Broumi,et al.  A new perspective on traffic control management using triangular interval type-2 fuzzy sets and interval neutrosophic sets , 2019, Operations Research Perspectives.

[16]  Peide Liu,et al.  Multi-Attribute Decision-Making Based on Prioritized Aggregation Operator under Hesitant Intuitionistic Fuzzy Linguistic Environment , 2017, Symmetry.

[17]  Peide Liu,et al.  Interval Neutrosophic Muirhead mean Operators and Their Application in Multiple Attribute Group Decision Making , 2017 .

[18]  Etienne Kerre,et al.  A generalization of operators on intuitionistic fuzzy sets using triangular norms and conorms , 2002 .

[19]  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..

[20]  Wende Zhang,et al.  Exponential Aggregation Operator of Interval Neutrosophic Numbers and Its Application in Typhoon Disaster Evaluation , 2018, Symmetry.

[21]  Peide Liu,et al.  An Extended TOPSIS Method for the Multiple Attribute Decision Making Problems Based on Interval Neutrosophic Set , 2014 .

[22]  Cuiping Wei,et al.  Generalized prioritized aggregation operators , 2012, Int. J. Intell. Syst..

[23]  Guiwu Wei,et al.  Some single-valued neutrosophic dombi prioritized weighted aggregation operators in multiple attribute decision making , 2018, J. Intell. Fuzzy Syst..

[24]  Jian-qiang Wang,et al.  Cross-Entropy and Prioritized Aggregation Operator with Simplified Neutrosophic Sets and Their Application in Multi-Criteria Decision-Making Problems , 2016, International Journal of Fuzzy Systems.

[25]  Yao Ouyang,et al.  Interval neutrosophic numbers Choquet integral operator for multi-criteria decision making , 2015, J. Intell. Fuzzy Syst..

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

[27]  He Huacan,et al.  A fuzzy logic system based on Schweizer-Sklar t-norm , 2006 .

[28]  Zhang-peng Tian,et al.  Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets , 2015, Int. J. Syst. Sci..

[29]  Hong-yu Zhang,et al.  Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems , 2014, TheScientificWorldJournal.

[30]  Yu-Han Huang,et al.  VIKOR Method for Interval Neutrosophic Multiple Attribute Group Decision-Making , 2017, Inf..

[31]  Hong-yu Zhang,et al.  An outranking approach for multi-criteria decision-making problems with interval-valued neutrosophic sets , 2015, Neural Computing and Applications.

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

[33]  Peng Wang,et al.  Some interval-valued intuitionistic fuzzy Schweizer–Sklar power aggregation operators and their application to supplier selection , 2018, Int. J. Syst. Sci..

[34]  Yi Wang,et al.  Fuzzy stochastic multi-criteria decision-making methods with interval neutrosophic probability based on regret theory , 2018, J. Intell. Fuzzy Syst..

[35]  Surajit Borkotokey,et al.  Interval neutrosophic hesitant fuzzy Einstein Choquet integral operator for multicriteria decision making , 2019, Artificial Intelligence Review.

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

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

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

[40]  Hong-yu Zhang,et al.  Frank prioritized Bonferroni mean operator with single-valued neutrosophic sets and its application in selecting third-party logistics providers , 2016, Neural Computing and Applications.

[41]  Wolfram Burgard,et al.  Socially compliant mobile robot navigation via inverse reinforcement learning , 2016, Int. J. Robotics Res..

[42]  Ronald R. Yager,et al.  Prioritized aggregation operators , 2008, Int. J. Approx. Reason..

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

[44]  Sun Hur,et al.  An optimization technique for national income determination model with stability analysis of differential equation in discrete and continuous process under the uncertain environment , 2019, RAIRO Oper. Res..

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

[46]  Fanyong Meng,et al.  Interval neutrosophic preference relations and their application in virtual enterprise partner selection , 2019, Journal of Ambient Intelligence and Humanized Computing.

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

[48]  Peide Liu,et al.  Multiple-attribute decision making based on single-valued neutrosophic Schweizer-Sklar prioritized aggregation operator , 2019, Cognitive Systems Research.

[49]  Yi Zhang,et al.  Methods for Evaluating the Technological Innovation Capability for the High-Tech Enterprises With Generalized Interval Neutrosophic Number Bonferroni Mean Operators , 2019, IEEE Access.

[50]  Jun Ye,et al.  Some distances, similarity and entropy measures for interval-valued neutrosophic sets and their relationship , 2017, International Journal of Machine Learning and Cybernetics.

[51]  Peide Liu,et al.  Some Maclaurin symmetric mean aggregation operators based on Schweizer-Sklar operations for intuitionistic fuzzy numbers and their application to decision making , 2019, J. Intell. Fuzzy Syst..

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

[53]  Shu-Ping Wan,et al.  Two New Approaches for Multi-Attribute Group Decision-Making With Interval-Valued Neutrosophic Frank Aggregation Operators and Incomplete Weights , 2019, IEEE Access.

[54]  Mohamed Slim Masmoudi,et al.  Fuzzy Logic Based Control for Autonomous Mobile Robot Navigation , 2016, Comput. Intell. Neurosci..

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

[56]  Yang Xu,et al.  A fuzzy logic system based on Schweizer-Sklar t-norm , 2006, Science in China Series F: Information Sciences.

[57]  Glad Deschrijver,et al.  Generalized arithmetic operators and their relationship to t-norms in interval-valued fuzzy set theory , 2009, Fuzzy Sets Syst..