The uncertain OWA operator

By Zeshui Xu, Qingli Da. International Journal of Intelligent Systems, 2002

548 citations recorded by the source corpus.

The ordered weighted averaging (OWA) operator was introduced by Yager 1 to provide a method for aggregating several inputs that lie between the max and min operators. In this article, we investigate the uncertain OWA operator in which the associated weighting parameters cannot be specified, but value ranges can be obtained and each input argument is given in the form of an interval of numerical values. The problem of ranking a set of interval numbers and obtaining the weights associated with the uncertain OWA operator is studied. © 2002 Wiley Periodicals, Inc.

Subfields: Control and Systems Engineering, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6ba847b2d6fd80d7d4493bccd63c3bfd34368ff0

How researchers see this paper

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

In Control and Systems Engineering

1. Zeshui Xu
2. Meimei Xia
3. Weize Wang
4. Xinwang Liu
5. Xiaolu Zhang
6. Ronald R. Yager
7. Na Chen
8. Guiwu Wei

In Management Science and Operations Research

1. Zeshui Xu
2. Meimei Xia
3. Xiaolu Zhang
4. Peide Liu
5. Weize Wang
6. Harish Garg
7. Xinwang Liu
8. Na Chen

In Statistics and Probability

1. Zeshui Xu
2. Meimei Xia
3. Weize Wang
4. Xinwang Liu
5. Xiaolu Zhang
6. Peide Liu
7. Na Chen
8. Ronald R. Yager

Citations in the corpus

• A social network analysis trust-consensus based approach to group decision-making problems with interval-valued fuzzy reciprocal preference relations (2014, unknown): “(5) Given two interval numbers ã1 = [a − 1 , a + 1 ] and ã2 = [a − 2 , a + 2 ], Xu and Da [48] proposed the following possibility degree (PD) to measure the degree up to which the ordering relation ã1 ã2 holds: P (ã1 ã2) = max { 1−max { a2 − a − 1 a1 − a − 1 + a + 2 − a − 2 , 0 } , 0 } (6)”
• An Overview of Distance and Similarity Measures of Intuitionistic Fuzzy Sets (2008, background): “Other kinds of aggregation operators, such as the ordered weighted averaging (OWA) operator [35], the weighted OWA operator [36,37], the uncertain OWA operator [38,39], and Sugeno integral [40], etc.”
• Hesitant fuzzy information aggregation in decision making (2011, background): “Xu and Da [29] obtained the OWA weights under partial weight information by establishing a linear objective-programming model.”
• Power-Geometric Operators and Their Use in Group Decision Making (2010, background): “The investigation on information aggregation has been receiving extensive attention from researchers and practitioners over the past decades, and a variety of operators have been developed to aggregate data information under various environments [1]–[5], such as the weighted-average operator [6], we”
• Hesitant fuzzy multi-attribute decision making based on TOPSIS with incomplete weight information (2013, methodology): “For convenience, let l 1⁄4maxfl~ a; l~ bg, where l~ a and l~ b are the numbers of intervals in IVHFEs ~ a and ~ b, respectively, and we arrange the interval values in any order based on a possibility degree formula [39].”
• Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis (2013, background): “This can be achieved based on a possibility degree formula [57] for the comparison between two interval numbers.”
• Intuitionistic Fuzzy Information Aggregation Using Einstein Operations (2012, methodology): “Xu and Da [64] obtained the OWA weights under partial weight information by establishing a linear objectiveprogramming model.”
• An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations (2006, unknown): “Then we construct a complementary matrix [2,19,27, 21,29,23,25] P=( pij)n n, where: pijz0; pijþpji1⁄41; pii 1⁄4 0:5; i; j 1⁄4 1; 2; .”
• Intuitionistic Fuzzy Aggregation Operators (2007, background): “The WA and OWA operators, however, have usually been used in situations where the input arguments are the exact values [31] and extended to accommodate uncertain environment [36]–[39] or linguistic environment [40]–[45].”
• Generation of linear orders for intervals by means of aggregation functions (2013, background): “However, some situations, e.g., the definition of interval-valued ordered weighted means [12], require a linear order of intervals.”
• Induced uncertain linguistic OWA operators applied to group decision making (2006, methodology): “; nÞ by using (1), for simplicity, let pij 1⁄4 pð~si P~sjÞ, then, we develop a complementary matrix [29–36] as”