Maclaurin symmetric mean aggregation operators based on t-norm operations for the dual hesitant fuzzy soft set

AbstractThe objective of this paper is to present a Maclaurin symmetric mean (MSM) operator to aggregate dual hesitant fuzzy (DHF) soft numbers. The salient feature of MSM operators is that it can reflect the interrelationship between the multi-input arguments. Under DHF soft set environment, we develop some aggregation operators named as DHF soft MSM averaging (DHFSMSMA) operator, the weighted DHF soft MSM averaging (WDHFSMSMA) operator, DHF soft MSM geometric (DHFSMSMG) operator, and the weighted DHF soft MSM geometric (WDHFSMSMG) operator. Further, some properties and the special cases of these operators are discussed. Then, by utilizing these operators, we develop an approach for solving the multicriteria decision-making problem and illustrate it with a numerical example. Finally, a comparison analysis has been done to analyze the advantages of the proposed operators.

[1]  Harish Garg,et al.  Generalized intuitionistic fuzzy soft power aggregation operator based on t‐norm and their application in multicriteria decision‐making , 2018, Int. J. Intell. Syst..

[2]  Pabitra Kumar Maji,et al.  FUZZY SOFT SETS , 2001 .

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

[4]  Enrique Herrera-Viedma,et al.  Fuzzy rankings for preferences modeling in group decision making , 2018, Int. J. Intell. Syst..

[5]  Zeshui Xu,et al.  Distance and similarity measures for hesitant fuzzy sets , 2011, Inf. Sci..

[6]  Harish Garg,et al.  Complex Interval-valued Intuitionistic Fuzzy Sets and their Aggregation Operators , 2019, Fundam. Informaticae.

[7]  Gagandeep Kaur,et al.  Algorithm for Probabilistic Dual Hesitant Fuzzy Multi-Criteria Decision-Making Based on Aggregation Operators With New Distance Measures , 2018, Mathematics.

[8]  Zeshui Xu,et al.  Group Decision Making with Dual Hesitant Fuzzy Preference Relations , 2016, Cognitive Computation.

[9]  Dejian Yu,et al.  Multi-Criteria Decision Making Based on Choquet Integral under Hesitant Fuzzy Environment , 2011 .

[10]  Harish Garg,et al.  TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment , 2016, Computational and Applied Mathematics.

[11]  Harish Garg,et al.  Intuitionistic Fuzzy Hamacher Aggregation Operators with Entropy Weight and Their Applications to Multi-criteria Decision-Making Problems , 2019, Iranian Journal of Science and Technology, Transactions of Electrical Engineering.

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

[13]  Harish Garg,et al.  Bonferroni mean aggregation operators under intuitionistic fuzzy soft set environment and their applications to decision-making , 2018, J. Oper. Res. Soc..

[14]  Harish Garg,et al.  An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making , 2018, Soft Computing.

[15]  Wattana Viriyasitavat,et al.  Multi-criteria selection for services selection in service workflow , 2016 .

[16]  Harish Garg,et al.  A novel exponential distance and its based TOPSIS method for interval-valued intuitionistic fuzzy sets using connection number of SPA theory , 2018, Artificial Intelligence Review.

[17]  Wenkai Zhang,et al.  Some dual hesitant fuzzy Hamacher aggregation operators and their applications to multiple attribute decision making , 2014, J. Intell. Fuzzy Syst..

[18]  Harish Garg,et al.  A robust correlation coefficient measure of dual hesitant fuzzy soft sets and their application in decision making , 2018, Eng. Appl. Artif. Intell..

[19]  Harish Garg,et al.  HESITANT PYTHAGOREAN FUZZY SETS AND THEIR AGGREGATION OPERATORS IN MULTIPLE ATTRIBUTE DECISION-MAKING , 2018 .

[20]  Harish Garg,et al.  A robust aggregation operators for multi-criteria decision-making with intuitionistic fuzzy soft set environment , 2017 .

[21]  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.

[22]  Jindong Qin,et al.  Approaches to uncertain linguistic multiple attribute decision making based on dual Maclaurin symmetric mean , 2015, J. Intell. Fuzzy Syst..

[23]  M. Tadi,et al.  Optimal infinite-dimensional estimator and compensator for a Timoshenko beam , 1994 .

[24]  Isabel da Silva Lopes,et al.  Classification methodology for spare parts management combining maintenance and logistics perspectives , 2018 .

[25]  Fanyong Meng,et al.  Correlation Coefficients of Hesitant Fuzzy Sets and Their Application Based on Fuzzy Measures , 2015, Cognitive Computation.

[26]  Lan Shu,et al.  Dual Hesitant Fuzzy Soft Set and Its Properties , 2016 .

[27]  Vicenç Torra,et al.  On hesitant fuzzy sets and decision , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[28]  Arun Kumar Sangaiah,et al.  A study for project risk management using an advanced MCDM-based DEMATEL-ANP approach , 2018, J. Ambient Intell. Humaniz. Comput..

[29]  Peide Liu,et al.  Maclaurin symmetric mean operators of linguistic intuitionistic fuzzy numbers and their application to multiple-attribute decision-making , 2017, J. Exp. Theor. Artif. Intell..

[30]  Gagandeep Kaur,et al.  Generalized Cubic Intuitionistic Fuzzy Aggregation Operators Using t-Norm Operations and Their Applications to Group Decision-Making Process , 2018, Arabian Journal for Science and Engineering.

[31]  Dejian Yu,et al.  Some Generalized Dual Hesistant Fuzzy Geometric Aggregation Operators and Applications , 2014, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

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

[33]  Harish Garg,et al.  Interval-Valued Pythagorean Fuzzy Maclaurin Symmetric Mean Operators in Multiple Attribute Decision Making , 2018, IEEE Access.

[34]  Guiwu Wei,et al.  Dual hesitant fuzzy aggregation operators in multiple attribute decision making , 2014, J. Intell. Fuzzy Syst..

[35]  Harish Garg,et al.  Hesitant Pythagorean fuzzy Maclaurin symmetric mean operators and its applications to multiattribute decision‐making process , 2018, Int. J. Intell. Syst..

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

[37]  Harish Garg,et al.  Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision‐making , 2018, Expert Syst. J. Knowl. Eng..

[38]  Zeshui Xu,et al.  Hesitant fuzzy information aggregation in decision making , 2011, Int. J. Approx. Reason..

[39]  Zeshui Xu,et al.  Dual hesitant fuzzy information aggregation with Einstein t-conorm and t-norm , 2017, Journal of Systems Science and Systems Engineering.

[40]  Harish Garg,et al.  Correction to: Some Aggregation Operators for Linguistic Intuitionistic Fuzzy Set and its Application to Group Decision-Making Process Using the Set Pair Analysis , 2018, Arabian Journal for Science and Engineering.

[41]  Sadigh Raissi,et al.  An integrated simulation-based optimization technique for multi-objective dynamic facility layout problem , 2017, J. Ind. Inf. Integr..

[42]  Jindong Qin,et al.  An approach to intuitionistic fuzzy multiple attribute decision making based on Maclaurin symmetric mean operators , 2014, J. Intell. Fuzzy Syst..

[43]  Zeshui Xu,et al.  On distance and correlation measures of hesitant fuzzy information , 2011, Int. J. Intell. Syst..

[44]  Dejian Yu,et al.  Archimedean Aggregation Operators Based on Dual Hesitant Fuzzy Set and Their Application to GDM , 2015, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[45]  Enrique Herrera-Viedma,et al.  Group decision-making based on heterogeneous preference relations with self-confidence , 2017, Fuzzy Optim. Decis. Mak..

[46]  Zeshui Xu,et al.  Dual Hesitant Fuzzy Sets , 2012, J. Appl. Math..

[47]  Zhiming Zhang,et al.  A novel technique for multiple attribute group decision making in interval-valued hesitant fuzzy environments with incomplete weight information , 2018, Journal of Ambient Intelligence and Humanized Computing.

[48]  Madhumangal Pal,et al.  Bipolar fuzzy Dombi aggregation operators and its application in multiple-attribute decision-making process , 2018, J. Ambient Intell. Humaniz. Comput..

[49]  Chen-Tung Chen,et al.  Linguistic VIKOR method for project evaluation of ambient intelligence product , 2018, Journal of Ambient Intelligence and Humanized Computing.

[50]  Harish Garg,et al.  Novel scaled prioritized intuitionistic fuzzy soft interaction averaging aggregation operators and their application to multi criteria decision making , 2018, Eng. Appl. Artif. Intell..

[51]  Zeshui Xu,et al.  Distance and Aggregation-Based Methodologies for Hesitant Fuzzy Decision Making , 2017, Cognitive Computation.

[52]  Harish Garg,et al.  Generalized and group-based generalized intuitionistic fuzzy soft sets with applications in decision-making , 2017, Applied Intelligence.

[53]  Na Chen,et al.  Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis , 2013 .

[54]  Nicola Capuano,et al.  A Fuzzy Group Decision Making Model for Ordinal Peer Assessment , 2017, IEEE Transactions on Learning Technologies.

[55]  Witold Pedrycz,et al.  Hesitant Fuzzy Maclaurin Symmetric Mean Operators and Its Application to Multiple-Attribute Decision Making , 2015, Int. J. Fuzzy Syst..

[56]  Enrique Herrera-Viedma,et al.  Fuzzy Group Decision Making With Incomplete Information Guided by Social Influence , 2018, IEEE Transactions on Fuzzy Systems.

[57]  George Q. Huang,et al.  Dual hesitant fuzzy aggregation operators , 2015 .

[58]  Harish Garg,et al.  Prioritized averaging/geometric aggregation operators under the intuitionistic fuzzy soft set environment , 2017 .

[59]  L. Xu,et al.  A fuzzy multiobjective programming algorithm in decision support systems , 1988 .

[60]  Harish Garg,et al.  Connection number of set pair analysis based TOPSIS method on intuitionistic fuzzy sets and their application to decision making , 2017, Applied Intelligence.

[61]  Harish Garg,et al.  DISTANCE AND SIMILARITY MEASURES FOR DUAL HESITANT FUZZY SOFT SETS AND THEIR APPLICATIONS IN MULTICRITERIA DECISION MAKING PROBLEM , 2017 .

[62]  J. Pečarić,et al.  A generalization of Maclaurin's inequalities and its applications , 2005 .

[63]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[64]  Harish Garg,et al.  Dual Hesitant Fuzzy Soft Aggregation Operators and Their Application in Decision-Making , 2018, Cognitive Computation.

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