Interval numbers BON ^r,q ‐OWA operator and its application to multiattribute decision‐making

Abstract

Interval numbers multiple attribute decision‐making (MADM) is an important branch of uncertainty decision theory, and the decision result largely depends on the selection of the aggregation operator. In this paper, we analyze the ordered weighted average (OWA) operator, which is an averaging aggregation operator. The OWA operator provides an aggregation method between the minimum and maximum operators. Moreover, we further analyze some of extensions about OWA operator, and pay special attention to the Bonferroni means and OWA (BON‐OWA) operator. Note that the BON‐OWA operator only aggregate the input arguments which are exact numbers. Under normal circumstances, decision makers is difficult to provide a clear evaluation value for attribute and most of them are described by vague information. When the decision information is an interval numbers, the BON‐OWA operator cannot describe decision result accurately. Under these environments, we proposed the interval numbers BON‐OWA (IBr,q‐OWA) operator to deal with the vague decision information in this paper. Then we consider their main properties, such as idempotence, monotonicity, and boundedness and prove them. Besides, a wide range of special aggregation operators are found in changing parameter values, such as the square mean and max operator, and so on. We also compare the ranking method of the interval numbers based on Boolean matrix. As a result, the combination of IBr,q‐OWA operator makes the decision result more scientific. Finally, a new approach for decision‐making problem is developed based on the IBr,q‐OWA operator, which shows the effectiveness in practical examples.

Bonferroni Weighted Logarithmic Averaging Distance Operator Applied to Investment Selection Decision Making

“…With the limitations outlined above, new approaches to guide future research can focus on modeling other complex and uncertain phenomena that can be represented with fuzzy numbers [44,45] (to be able to use crisp numbers), linguistic variables [46,47] (to be able to use endecadary scales), Pythagorean membership [48,49] (Pythagorean principles) and interval numbers [50,51], and induced [43,52] and heavy aggregations [53,54] (taking into account the attitude of the decision maker), where these methods have the potential to provide solutions for the treatment of highly complex scenarios.…”

Interval‐valued Pythagorean fuzzy linguistic KPCA model based on TOPSIS and its application for emergency group decision making

“…In addition, to describe the evaluation information more scientifically, Yager 11 extended it under the constraint of IFSs and proposed Pythagorean fuzzy sets (PFSs), which can make the sum of membership degree and nonmembership degree greater than 1, but the sum of squares less than 1. Peng and Yang 12 further extended the PFSs to interval values and defined interval‐valued Pythagorean fuzzy sets (IVPFSs), which are widely used and dealt with some imprecise and uncertain problems 13 . However, the above‐mentioned FSs only corresponded numerical transformations of membership and nonmembership to give certain fuzzy concepts.…”

“…Peng and Yang 12 further extended the PFSs to interval values and defined interval-valued Pythagorean fuzzy sets (IVPFSs), which are widely used and dealt with some imprecise and uncertain problems. 13 However, the above-mentioned FSs only corresponded numerical transformations of membership and nonmembership to give certain fuzzy concepts. It is only suitable for quantitative decision-making evaluation.…”