Multi-attribute decision analysis under a linguistic hesitant fuzzy environment

In this paper, a new class of fuzzy sets called linguistic hesitant fuzzy sets (LHFSs) is defined, which can address the qualitative preferences of experts as well as reflect their hesitancy, uncertainty and inconsistency. Based on the defined operational laws of LHFSs and the order relationship, two linguistic hesitant fuzzy hybrid aggregation operators are defined: the generalized linguistic hesitant fuzzy hybrid weighted averaging (GLHFHWA) operator and the generalized linguistic hesitant fuzzy hybrid geometric mean (GLHFHGM) operator. Furthermore, to address the situation in which the elements in a set are interdependent, the generalized linguistic hesitant fuzzy hybrid Shapley weighted averaging (GLHFHSWA) operator and the generalized linguistic hesitant fuzzy hybrid Shapley geometric mean (GLHFHSGM) operator are presented, which are extensions of the GLHFHWA and GLHFHGM operators. Models designed to obtain the optimal fuzzy measures and additive measures on an attribute set and on an ordered set are, respectively, constructed. Then, an approach to linguistic hesitant fuzzy multi-attribute decision analysis is developed. Finally, two numerical examples are provided to demonstrate the practicality and efficiency of the proposed procedure.

[1]  B. Farhadinia,et al.  Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets , 2013, Inf. Sci..

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

[3]  I. Turksen.  Type 2 representation and reasoning for CWW , 2002 .

[4]  Yejun Xu,et al.  Group decision making under hesitant fuzzy environment with application to personnel evaluation , 2013, Knowl. Based Syst..

[5]  Egidijus Rytas Vaidogas,et al.  Multi-attribute Decision-making in Economics of Fire Protection , 2011 .

[6]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

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

[8]  Jonathan Lawry,et al.  A methodology for computing with words , 2001, Int. J. Approx. Reason..

[9]  Francisco Herrera,et al.  Linguistic decision analysis: steps for solving decision problems under linguistic information , 2000, Fuzzy Sets Syst..

[10]  Francisco Herrera,et al.  Hesitant Fuzzy Linguistic Term Sets for Decision Making , 2012, IEEE Transactions on Fuzzy Systems.

[11]  Gui-Wu Wei,et al.  A method for multiple attribute group decision making based on the ET-WG and ET-OWG operators with 2-tuple linguistic information , 2010, Expert Syst. Appl..

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

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

[14]  Zeshui Xu,et al.  A method based on linguistic aggregation operators for group decision making with linguistic preference relations , 2004, Inf. Sci..

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

[16]  Francisco Herrera,et al.  An overview on the 2-tuple linguistic model for computing with words in decision making: Extensions, applications and challenges , 2012, Inf. Sci..

[17]  Francisco Herrera,et al.  A 2-tuple fuzzy linguistic representation model for computing with words , 2000, IEEE Trans. Fuzzy Syst..

[18]  Jian-Bo Yang,et al.  The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties , 2006, Eur. J. Oper. Res..

[19]  Michael Margaliot,et al.  Fuzzy control of a benchmark problem: a computing with words approach , 2004, IEEE Transactions on Fuzzy Systems.

[20]  Peide Liu.  Some geometric aggregation operators based on interval intuitionistic uncertain linguistic variables and their application to group decision making , 2013 .

[21]  Humberto Bustince,et al.  Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms , 2014, Inf. Sci..

[22]  Francisco Herrera,et al.  Computing with words in decision making: foundations, trends and prospects , 2009, Fuzzy Optim. Decis. Mak..

[23]  Jin-Hsien Wang,et al.  A new version of 2-tuple fuzzy linguistic representation model for computing with words , 2006, IEEE Trans. Fuzzy Syst..

[24]  Xiaohong Chen,et al.  Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making , 2010, Expert Syst. Appl..

[25]  Robert W. Swezey.  An Application of a Multi-Attribute Utilities Model to Training Analysis , 1979 .

[26]  Yejun Xu,et al.  Approaches based on 2-tuple linguistic power aggregation operators for multiple attribute group decision making under linguistic environment , 2011, Appl. Soft Comput..

[27]  Gui-Wu Wei,et al.  Some generalized aggregating operators with linguistic information and their application to multiple attribute group decision making , 2011, Comput. Ind. Eng..

[28]  Nadire Cavus.  The application of a multi-attribute decision-making algorithm to learning management systems evaluation , 2011, Br. J. Educ. Technol..

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

[30]  Francisco Herrera,et al.  A linguistic decision model for promotion mix management solved with genetic algorithms , 2002, Fuzzy Sets Syst..

[31]  J. Dolan.  Multi-Criteria Clinical Decision Support , 2010, The patient.

[32]  Francisco Herrera,et al.  Theory and Methodology Choice functions and mechanisms for linguistic preference relations , 2000 .

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

[34]  Zeshui Xu,et al.  Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment , 2004, Inf. Sci..

[35]  Michel Grabisch,et al.  K-order Additive Discrete Fuzzy Measures and Their Representation , 1997, Fuzzy Sets Syst..

[36]  Lotfi A. Zadeh,et al.  Fuzzy logic = computing with words , 1996, IEEE Trans. Fuzzy Syst..

[37]  N. Bryson,et al.  An action learning evaluation procedure for multiple criteria decision making problems , 1997 .

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

[39]  Zeshui Xu,et al.  Choquet integrals of weighted intuitionistic fuzzy information , 2010, Inf. Sci..

[40]  Zhiming Zhang,et al.  Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making , 2013, Inf. Sci..

[41]  Francisco Herrera,et al.  A fusion approach for managing multi-granularity linguistic term sets in decision making , 2000, Fuzzy Sets Syst..

[42]  M. Grabisch.  Fuzzy integral in multicriteria decision making , 1995 .

[43]  L. Shapley.  A Value for n-person Games , 1988 .

[44]  Qiang Zhang,et al.  Approaches to multiple-criteria group decision making based on interval-valued intuitionistic fuzzy Choquet integral with respect to the generalized λ-Shapley index , 2013, Knowl. Based Syst..

[45]  Hisao Ishibuchi,et al.  Classification and modeling with linguistic information granules - advanced approaches to linguistic data mining , 2004, Advanced information processing.

[46]  Xiaohong Chen,et al.  Induced intuitionistic fuzzy Choquet integral operator for multicriteria decision making , 2011, Int. J. Intell. Syst..

[47]  Witold Pedrycz,et al.  Granular Computing: Analysis and Design of Intelligent Systems , 2013 .

[48]  Jerry M. Mendel,et al.  Historical reflections and new positions on perceptual computing , 2009, Fuzzy Optim. Decis. Mak..

[49]  Zeshui Xu,et al.  Hesitant fuzzy geometric Bonferroni means , 2012, Inf. Sci..

[50]  Lotfi A. Zadeh,et al.  The concept of a linguistic variable and its application to approximate reasoning-III , 1975, Inf. Sci..

[51]  Luis Martínez,et al.  Sensory evaluation based on linguistic decision analysis , 2007 .

[52]  Peide Liu,et al.  Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making , 2012, Inf. Sci..

[53]  Z. S. Xu,et al.  Eowa And Eowg Operators For Aggregating Linguistic Labels Based On Linguistic Preference Relations , 2004, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[54]  Ronald R. Yager,et al.  On the retranslation process in Zadeh's paradigm of computing with words , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[55]  John Farr,et al.  Evaluation of multi-attribute decision making systems applied during the concept design of new microplasma devices , 2013, Expert Syst. Appl..

[56]  Enrique Herrera-Viedma,et al.  A Fuzzy Linguistic IRS Model Based on a 2-Tuple Fuzzy Linguistic Approach , 2007, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[57]  Zeshui Xu,et al.  Interval-valued hesitant preference relations and their applications to group decision making , 2013, Knowl. Based Syst..

[58]  Yin-Feng Xu,et al.  Computing the Numerical Scale of the Linguistic Term Set for the 2-Tuple Fuzzy Linguistic Representation Model , 2009, IEEE Transactions on Fuzzy Systems.

[59]  Jerry M. Mendel,et al.  Computing with words and its relationships with fuzzistics , 2007, Inf. Sci..

[60]  Yin-Feng Xu,et al.  Consistency and consensus measures for linguistic preference relations based on distribution assessments , 2014, Inf. Fusion.

[61]  Shui Yu,et al.  Linguistic Computational Model Based on 2-Tuples and Intervals , 2013, IEEE Transactions on Fuzzy Systems.

[62]  Gui-Wu Wei,et al.  Extension of TOPSIS method for 2-tuple linguistic multiple attribute group decision making with incomplete weight information , 2010, Knowledge and Information Systems.

[63]  Jian-Bo Yang,et al.  Environmental impact assessment using the evidential reasoning approach , 2006, Eur. J. Oper. Res..

[64]  Luis Martínez-López,et al.  A multi-granular linguistic model for management decision-making in performance appraisal , 2009, Soft Comput..

[65]  Zeshui Xu,et al.  A method for multiple attribute decision making with incomplete weight information in linguistic setting , 2007, Knowl. Based Syst..

[66]  Zeshui Xu,et al.  An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations , 2006, Decis. Support Syst..

[67]  Guiwu Wei,et al.  Hesitant fuzzy prioritized operators and their application to multiple attribute decision making , 2012, Knowl. Based Syst..

[68]  Qiang Zhang,et al.  The induced generalized interval-valued intuitionistic fuzzy hybrid Shapley averaging operator and its application in decision making , 2013, Knowl. Based Syst..

[69]  Lotfi A. Zadeh,et al.  Outline of a New Approach to the Analysis of Complex Systems and Decision Processes , 1973, IEEE Trans. Syst. Man Cybern..

[70]  Na Chen,et al.  Some Hesitant Fuzzy Aggregation Operators with Their Application in Group Decision Making , 2011, Group Decision and Negotiation.