A novel fuzzy TOPSIS method using emerging interval-valued spherical fuzzy sets

Abstract All the extensions of ordinary fuzzy sets with three-dimensional membership functions such as intuitionistic fuzzy sets, second type intuitionistic fuzzy sets (or Pythagorean fuzzy sets) and neutrosophic sets aim at defining the judgments of decision makers/ experts with a more detailed description. As a new extension of intuitionistic fuzzy sets of second type, the emerging spherical fuzzy sets (SFS) have been proposed by Kutlu Gundogdu and Kahraman (2019b). In spherical fuzzy sets, the sum of membership, non-membership and hesitancy degrees must satisfy the condition 0 ≤ μ 2 + v 2 + π 2 ≤ 1 in which these parameters are assigned independently. SFS is an integration of Pythagorean fuzzy sets and neutrosophic sets. In this paper, novel interval-valued spherical fuzzy sets are introduced with their score and accuracy functions; arithmetic and aggregation operations such as interval-valued spherical fuzzy weighted arithmetic mean operator and interval-valued spherical fuzzy geometric mean operator. Later, interval-valued spherical fuzzy sets are employed in developing the extension of TOPSIS under fuzziness. Then, we use the proposed interval-valued spherical fuzzy TOPSIS method in solving a multiple criteria selection problem among 3D printers to verify the developed approach and to demonstrate its practicality and effectiveness. A comparative analysis with single-valued spherical TOPSIS is also performed.

[1]  R. Yager.  ON THE THEORY OF BAGS , 1986 .

[2]  B. Farhadinia,et al.  Multiple criteria decision-making methods with completely unknown weights in hesitant fuzzy linguistic term setting , 2016, Knowl. Based Syst..

[3]  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..

[4]  S. M. Mousavi,et al.  A new design of the elimination and choice translating reality method for multi-criteria group decision-making in an intuitionistic fuzzy environment , 2013 .

[5]  Huayou Chen,et al.  Intuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making , 2014, Inf. Sci..

[6]  B. B. Zaidan,et al.  Survey on fuzzy TOPSIS state-of-the-art between 2007 and 2017 , 2019, Comput. Oper. Res..

[7]  Zeshui Xu,et al.  Optimal discrete fitting aggregation approach with hesitant fuzzy information , 2015, Knowl. Based Syst..

[8]  Hong-yu Zhang,et al.  Atanassov's Interval-Valued Intuitionistic Linguistic Multicriteria Group Decision-Making Method Based on the Trapezium Cloud Model , 2015, IEEE Transactions on Fuzzy Systems.

[9]  Tabasam Rashid,et al.  TOPSIS for Hesitant Fuzzy Linguistic Term Sets , 2013, Int. J. Intell. Syst..

[10]  Fatih Emre Boran,et al.  The Evaluation of Renewable Energy Technologies for Electricity Generation in Turkey Using Intuitionistic Fuzzy TOPSIS , 2012 .

[11]  Yong Yang,et al.  Pythagorean Fuzzy Choquet Integral Based MABAC Method for Multiple Attribute Group Decision Making , 2016, Int. J. Intell. Syst..

[12]  Harish Garg,et al.  A Novel Improved Accuracy Function for Interval Valued Pythagorean Fuzzy Sets and Its Applications in the Decision‐Making Process , 2017, Int. J. Intell. Syst..

[13]  Yong Qin,et al.  Multi-attribute group decision making models under interval type-2 fuzzy environment , 2012, Knowl. Based Syst..

[14]  Cengiz Kahraman,et al.  A novel hesitant fuzzy EDAS method and its application to hospital selection , 2018, J. Intell. Fuzzy Syst..

[15]  Fanyong Meng,et al.  Induced generalized hesitant fuzzy Shapley hybrid operators and their application in multi-attribute decision making , 2015, Appl. Soft Comput..

[16]  Jing Li,et al.  Sustainable supplier selection based on SSCM practices: A rough cloud TOPSIS approach , 2019, Journal of Cleaner Production.

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

[18]  Haobo Zhang,et al.  Study of decision framework of wind farm project plan selection under intuitionistic fuzzy set and fuzzy measure environment , 2014 .

[19]  Zeshui Xu,et al.  The Properties of Continuous Pythagorean Fuzzy Information , 2016, Int. J. Intell. Syst..

[20]  Yong Yang,et al.  Some Results for Pythagorean Fuzzy Sets , 2015, Int. J. Intell. Syst..

[21]  Kuo-Ping Chiao,et al.  The multi-criteria group decision making methodology using type 2 fuzzy linguistic judgments , 2016, Appl. Soft Comput..

[22]  Li Zhu,et al.  Linguistic hesitant fuzzy power aggregation operators and their applications in multiple attribute decision-making , 2016, Inf. Sci..

[23]  Ronald R. Yager,et al.  Pythagorean Membership Grades, Complex Numbers, and Decision Making , 2013, Int. J. Intell. Syst..

[24]  Ting-Yu Chen,et al.  An ELECTRE-based outranking method for multiple criteria group decision making using interval type-2 fuzzy sets , 2014, Inf. Sci..

[25]  Pankaj Gupta,et al.  Intuitionistic fuzzy multi-attribute group decision-making with an application to plant location selection based on a new extended VIKOR method , 2016, Inf. Sci..

[26]  Li-Jun Yang,et al.  An extension of ELECTRE to multi-criteria decision-making problems with multi-hesitant fuzzy sets , 2015, Inf. Sci..

[27]  G. Wei,et al.  Extension of VIKOR method for decision making problem based on hesitant fuzzy set , 2013 .

[28]  Zeshui Xu,et al.  Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making , 2014, Inf. Sci..

[29]  Zeshui Xu,et al.  Qualitative decision making with correlation coefficients of hesitant fuzzy linguistic term sets , 2015, Knowl. Based Syst..

[30]  Florentin Smarandache,et al.  An Extended TOPSIS Method for Multiple Attribute Decision Making based on Interval Neutrosophic Uncertain Linguistic Variables , 2015 .

[31]  Francisco Herrera,et al.  A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets , 2013, Inf. Sci..

[32]  Xiaolu Zhang,et al.  Multicriteria Pythagorean fuzzy decision analysis: A hierarchical QUALIFLEX approach with the closeness index-based ranking methods , 2016, Inf. Sci..

[33]  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.

[34]  Shu-Ping Wan,et al.  Mathematical programming methods for consistency and consensus in group decision making with intuitionistic fuzzy preference relations , 2016, Knowl. Based Syst..

[35]  Gülçin Büyüközkan,et al.  Multi Criteria Group Decision Making Approach for Smart Phone Selection Using Intuitionistic Fuzzy TOPSIS , 2016, Int. J. Comput. Intell. Syst..

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

[37]  Cengiz Kahraman,et al.  Multicriteria Evaluation of Cloud Service Providers Using Pythagorean Fuzzy TOPSIS , 2018, J. Multiple Valued Log. Soft Comput..

[38]  Madhumangal Pal,et al.  Intuitionistic Neutrosophic Set Relations and Some of Its Properties , 2010 .

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

[40]  Jindong Qin,et al.  Multi-attribute group decision making using combined ranking value under interval type-2 fuzzy environment , 2015, Inf. Sci..

[41]  Zeshui Xu,et al.  Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information , 2013, Knowl. Based Syst..

[42]  Shyi-Ming Chen,et al.  Autocratic decision making using group recommendations based on ranking interval type-2 fuzzy sets , 2016, Inf. Sci..

[43]  Shyi-Ming Chen,et al.  Fuzzy multiattribute decision making based on transformation techniques of intuitionistic fuzzy values and intuitionistic fuzzy geometric averaging operators , 2016, Inf. Sci..

[44]  Keqin Li,et al.  Toward trustworthy cloud service selection: A time-aware approach using interval neutrosophic set , 2016, J. Parallel Distributed Comput..

[45]  Witold Pedrycz,et al.  Frank aggregation operators and their application to hesitant fuzzy multiple attribute decision making , 2016, Appl. Soft Comput..

[46]  Ting-Yu Chen,et al.  The interval-valued fuzzy TOPSIS method and experimental analysis , 2008, Fuzzy Sets Syst..

[47]  Shyi-Ming Chen,et al.  Multiattribute decision making based on interval-valued intuitionistic fuzzy values , 2012, Expert Syst. Appl..

[48]  Yan Zhang,et al.  Multi-criteria decision making method based on possibility degree of interval type-2 fuzzy number , 2013, Knowl. Based Syst..

[49]  Cengiz Kahraman,et al.  Extension of WASPAS with Spherical Fuzzy Sets , 2019, Informatica.

[50]  Harish Garg,et al.  A Novel Correlation Coefficients between Pythagorean Fuzzy Sets and Its Applications to Decision‐Making Processes , 2016, Int. J. Intell. Syst..

[51]  Zeshui Xu,et al.  Total orders of extended hesitant fuzzy linguistic term sets: Definitions, generations and applications , 2016, Knowl. Based Syst..

[52]  Petr Hájek,et al.  Integrating TOPSIS with interval-valued intuitionistic fuzzy cognitive maps for effective group decision making , 2019, Inf. Sci..

[53]  Chunqiao Tan,et al.  A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS , 2011, Expert Syst. Appl..

[54]  Jonathan M. Garibaldi,et al.  Uncertain Fuzzy Reasoning: A Case Study in Modelling Expert Decision Making , 2007, IEEE Transactions on Fuzzy Systems.

[55]  Zeshui Xu,et al.  Definite integrals of multiplicative intuitionistic fuzzy information in decision making , 2016, Knowl. Based Syst..

[56]  Zeshui Xu,et al.  The interval‐valued hesitant Pythagorean fuzzy set and its applications with extended TOPSIS and Choquet integral‐based method , 2019, Int. J. Intell. Syst..

[57]  Fei Ye,et al.  An extended TOPSIS method with interval-valued intuitionistic fuzzy numbers for virtual enterprise partner selection , 2010, Expert Syst. Appl..

[58]  Huayou Chen,et al.  Continuous interval-valued intuitionistic fuzzy aggregation operators and their applications to group decision making , 2014 .

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

[60]  Jiuping Xu,et al.  A new outranking choice method for group decision making under Atanassov's interval-valued intuitionistic fuzzy environment , 2014, Knowl. Based Syst..

[61]  Cengiz Kahraman,et al.  Spherical fuzzy sets and spherical fuzzy TOPSIS method , 2019, J. Intell. Fuzzy Syst..

[62]  Zeshui Xu,et al.  Pythagorean fuzzy TODIM approach to multi-criteria decision making , 2016, Appl. Soft Comput..

[63]  Jun Ye,et al.  Trapezoidal neutrosophic set and its application to multiple attribute decision-making , 2014, Neural Computing and Applications.

[64]  Hong-yu Zhang,et al.  Multi-Criteria Decision-Making Method Based on induced Intuitionistic Normal Fuzzy Related Aggregation Operators , 2012, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[65]  Yong Yang,et al.  Fundamental Properties of Interval‐Valued Pythagorean Fuzzy Aggregation Operators , 2016, Int. J. Intell. Syst..

[66]  Witold Pedrycz,et al.  An extended VIKOR method based on prospect theory for multiple attribute decision making under interval type-2 fuzzy environment , 2015, Knowl. Based Syst..

[67]  Peide Liu,et al.  Pythagorean uncertain linguistic partitioned Bonferroni mean operators and their application in multi-attribute decision making , 2017, J. Intell. Fuzzy Syst..

[68]  Humberto Bustince,et al.  Construction of interval-valued fuzzy preference relations from ignorance functions and fuzzy preference relations. Application to decision making , 2014, Knowl. Based Syst..

[69]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

[70]  Harish Garg,et al.  Generalized Pythagorean Fuzzy Geometric Aggregation Operators Using Einstein t‐Norm and t‐Conorm for Multicriteria Decision‐Making Process , 2017, Int. J. Intell. Syst..

[71]  Muhammad Akram,et al.  TOPSIS Approach for MAGDM Based on Interval-Valued Hesitant Fuzzy N-Soft Environment , 2018, International Journal of Fuzzy Systems.

[72]  Zeshui Xu,et al.  Intuitionistic Fuzzy density-Based Aggregation operators and their Applications to Group Decision Making with Intuitionistic Preference Relations , 2014, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[73]  Pavel V. Sevastjanov,et al.  An interval type-2 fuzzy extension of the TOPSIS method using alpha cuts , 2015, Knowl. Based Syst..

[74]  Hai Wang,et al.  Generalized hesitant fuzzy sets and their application in decision support system , 2013, Knowl. Based Syst..

[75]  Zeshui Xu,et al.  Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets , 2014, Int. J. Intell. Syst..

[76]  Iqtadar Hussain,et al.  Extension of TOPSIS method base on Choquet integral under interval-valued Pythagorean fuzzy environment , 2018, J. Intell. Fuzzy Syst..

[77]  Chen-Tung Chen,et al.  Extensions of the TOPSIS for group decision-making under fuzzy environment , 2000, Fuzzy Sets Syst..

[78]  Diyar Akay,et al.  A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method , 2009, Expert Syst. Appl..

[79]  Bo Peng,et al.  Some Intuitionist Fuzzy Weighted Geometric Distance Measures and Their Application to Group Decision Making , 2014, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[80]  Zhen He,et al.  Multiple attribute group decision making based on IVHFPBMs and a new ranking method for interval-valued hesitant fuzzy information , 2016, Comput. Ind. Eng..

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

[82]  Zhiming Zhang,et al.  On the use of multiplicative consistency in hesitant fuzzy linguistic preference relations , 2014, Knowl. Based Syst..