On distance and correlation measures of hesitant fuzzy information

By Zeshui Xu, Meimei Xia. International Journal of Intelligent Systems, 2011

506 citations recorded by the source corpus.

A hesitant fuzzy set, allowing the membership of an element to be a set of several possible values, is very useful to express people's hesitancy in daily life. In this paper, we define the distance and correlation measures for hesitant fuzzy information and then discuss their properties in detail. These measures are all defined under the assumption that the values in all hesitant fuzzy elements (the fundamental units of hesitant fuzzy sets) are arranged in an increasing order and two hesitant fuzzy elements have the same length when we compare them. We can find that the results, by using the developed distance measures, are the smallest ones among those when the values in two hesitant fuzzy elements are arranged in any permutations. In addition, the derived correlation coefficients are based on different linear relationships and may have different results. © 2011 Wiley Periodicals, Inc.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2c6e292d4b00acc60a0662505076b7f42262b9b9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information (2013, background): “It is clear that Xu and Xia's extension rule is consistent with our extension rule when g = 1 and g = 0.”
Probabilistic linguistic term sets in multi-attribute group decision making (2016, methodology): “A summary on the relative techniques for representing linguistic information Representation model Literature Characteristic Probabilistic information HFLTSs [21] A list of several consecutive terms N/A EHFLTSs [25,39] A list of several terms N/A Proportional linguistic terms [26] A proportion of two”
Hesitant Fuzzy Sets: State of the Art and Future Directions (2014, background): “54 Zhou and Li pointed out in Ref.”
Some Hesitant Fuzzy Aggregation Operators with Their Application in Group Decision Making (2011, background): “Xu and Xia (2011c) investigated the induced generalized aggregation operators under intuitionistic fuzzy environments, including the induced generalized intuitionistic fuzzy Choquet integral operators and induced generalized intuitionistic fuzzy Dempster–Shafer operators, etc., and gave their…”
Hesitant fuzzy entropy and cross‐entropy and their use in multiattribute decision‐making (2012, methodology): “Calculate the attribute weight w j of the attribute G j by the maximizing deviation method: where d ( α ij , α kj ) is the distance between α ij and α kj deﬁned by Xu and Xia, 42 , 43 such that for two HFEs α and β , the distance between α and β , denoted as d ( α, β ), is given as Step 3.”
Extension of VIKOR method for decision making problem based on hesitant fuzzy set (2013, background): “Xu and Xia [24,25] proposed a variety of distance measures for hesitant fuzzy sets, based on which the corresponding similarity measures can be obtained, and defined the distance and correlation measures for hesitant fuzzy information and discussed their properties in detail.”
Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis (2013, unknown): “[32–35].”