A note on information entropy measures for vague sets and its applications

Improved Cross Entropy Measures of Single Valued Neutrosophic Sets and Interval Neutrosophic Sets and Their Multicriteria Decision Making Methods

“…As a generalization of D e L u c a and T e r m i n i [7] nonprobabilistic entropy, V l a c h o s and S e r g i a d i s [8] have proposed an intuitionistic fuzzy cross entropy measure and applied it to pattern recognition, medical diagnosis and image segmentation. Then, Z h a n g and J i a n g [9] defined a vague cross entropy measure by analogy with the cross entropy of probability distributions and applied it to pattern recognition and medical diagnosis and then Y e [10] further applied the cross entropy of vague sets to the fault diagnosis problem of turbine. Also, Y e [11] has applied the intuitionistic fuzzy cross entropy to multicriteria fuzzy decisionmaking problems.…”

“…Also, Y e [11] has applied the intuitionistic fuzzy cross entropy to multicriteria fuzzy decisionmaking problems. As a generalization of the vague cross-entropy [9], Y e [12] proposed an interval-valued intuitionistic fuzzy cross-entropy measure and applied it to multicriteria decision-making problems. Since a Single Valued Neutrosophic Set (SVNS) is an extension of an intuitionistic fuzzy set, Y e [13] extended the intuitionistic fuzzy cross entropy to SVNSs and proposed a single valued neutrosophic cross entropy measure, and then applied it to multicriteria decisionmaking problems with single valued neutrosophic information.…”

δ-equality of intuitionistic fuzzy sets: a new proximity measure and applications in medical diagnosis

“…De et al [9] extended the Sanchez's method with the theory of intuitionistic fuzzy sets (IFSs). Samuel and Balamurugan [31], Szmidt and Kacprzyk [53], Zhang et al [71], Hung and Yang [19], Wang and Xin [63], Vlachos and Sergiadis [62], Zhang and Jiang [70], Wei and Ye [64] and Hung [18], Junjun et al [20], Maheshwari and Srivastava [24] continued to work on the IFS theory to improve the method of De et al [9], i.e., by using new score functions, new distance functions, or new measures instead of the score function in the method of De et al [9]. In this paper, the proposed algorithm combines the δ-equalities with the extended Sanchez's approach for intuitionistic fuzzy sets.…”

Hybrid Multiattribute Group Decision Making Based on Intuitionistic Fuzzy Information and GRA Method

“…So far, a number of literatures have discussed the topic of IFVs theory which has been widely used in many fields such as multiattribute decision making [11][12][13][14][15][16][17][18][19][20], medical diagnosis [21][22][23], pattern recognition [24][25][26][27][28][29], and clustering analysis [30]. Many research achievement have been made to enrich the IFSs theory from different points of view, including interval-valued intuitionistic fuzzy sets (IVIFSs) [31,32], intuitionistic fuzzy entropy measures [33][34][35][36][37][38][39][40][41][42][43], distance and similarity measures [44][45][46][47] [48][49][50][51][52][53], and intuitionistic fuzzy aggregation operators [54][55][56][57]. In th...…”