A subsethood-based entropy for weight determination in interval-valued fuzzy soft set group decision making

Entropy measure for interval-valued fuzzy soft set (IVFSS) is a formulation that calculates the degree of fuzziness of a particular IVFSS. In this paper, we establish an axiomatic definition of subsethood-based entropy for IVFSS and introduce an entropy measure that satisfies this axiomatic definition. An entropy weight formulation is then presented and applied in aggregating a collection of IVFSSs into a collective IVFSs which is particularly useful in the context of group decision making under IVFSS environment. A numerical example is presented to illustrate its usefulness.Entropy measure for interval-valued fuzzy soft set (IVFSS) is a formulation that calculates the degree of fuzziness of a particular IVFSS. In this paper, we establish an axiomatic definition of subsethood-based entropy for IVFSS and introduce an entropy measure that satisfies this axiomatic definition. An entropy weight formulation is then presented and applied in aggregating a collection of IVFSSs into a collective IVFSs which is particularly useful in the context of group decision making under IVFSS environment. A numerical example is presented to illustrate its usefulness.

[1]  Qiang Zhang,et al.  Multicriteria decision making method based on intuitionistic fuzzy weighted entropy , 2011, Expert Syst. Appl..

[3]  I. J. Myung,et al.  Maximum Entropy Aggregation of Expert Predictions , 1996 .

[4]  Zeshui Xu,et al.  Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment , 2012, Inf. Fusion.

[5]  Bart Kosko,et al.  Fuzzy entropy and conditioning , 1986, Inf. Sci..

[6]  Zheng Pei,et al.  Similarity Measure and Entropy of Fuzzy Soft Sets , 2014, TheScientificWorldJournal.

[7]  Hai Liu,et al.  Entropy on intuitionistic fuzzy soft sets and on interval-valued fuzzy soft sets , 2013, Inf. Sci..

[8]  Shyi-Ming Chen,et al.  Feature subset selection based on fuzzy entropy measures for handling classification problems , 2008, Applied Intelligence.

[9]  B. Farhadinia,et al.  A theoretical development on the entropy of interval-valued fuzzy sets based on the intuitionistic distance and its relationship with similarity measure , 2013, Knowl. Based Syst..

[10]  Virginia R. Young,et al.  Fuzzy subsethood , 1996, Fuzzy Sets Syst..

[11]  R Kuppuchamy,et al.  A threshold fuzzy entropy based feature selection for medical database classification. , 2013, Computers in biology and medicine.

[12]  Weixin Xie,et al.  Distance measure and induced fuzzy entropy , 1999, Fuzzy Sets Syst..

[13]  Changlin Mei,et al.  Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure , 2009, Knowl. Based Syst..

[14]  Weixin Xie,et al.  Subsethood measure: new definitions , 1999, Fuzzy Sets Syst..

[15]  Mehdi Fasanghari,et al.  An intuitionistic fuzzy group decision making method using entropy and association coefficient , 2012, Soft Computing.

[16]  Przemyslaw Grzegorzewski,et al.  Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric , 2004, Fuzzy Sets Syst..

[17]  C. H. Juang Prof.,et al.  AGGREGATING EXPERT OPINIONS BY FUZZY ENTROPY METHOD , 1992 .

[18]  B. K. Tripathy,et al.  A New Approach to Interval-Valued Fuzzy Soft Sets and Its Application in Decision-Making , 2017 .

[19]  Ioannis K. Vlachos,et al.  Subsethood, entropy, and cardinality for interval-valued fuzzy sets - An algebraic derivation , 2007, Fuzzy Sets Syst..

[20]  Ting-Yu Chen,et al.  Determining objective weights with intuitionistic fuzzy entropy measures: A comparative analysis , 2010, Inf. Sci..

[21]  Sheng-Yi Jiang,et al.  A note on information entropy measures for vague sets and its applications , 2008, Inf. Sci..

[22]  Settimo Termini,et al.  A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory , 1972, Inf. Control..

[23]  Jing-nan Sun,et al.  Entropy method for determination of weight of evaluating indicators in fuzzy synthetic evaluation for water quality assessment. , 2006, Journal of environmental sciences.

[24]  Wenyi Zeng,et al.  Normalized distance, similarity measure, inclusion measure and entropy of interval-valued fuzzy sets and their relationship , 2008, Inf. Sci..

[25]  Tsau Young Lin,et al.  Combination of interval-valued fuzzy set and soft set , 2009, Comput. Math. Appl..

[26]  Shaorong Liu,et al.  A method of generating control rule model and its application , 1992 .