Pairwise comparison based multiattribute decision‐making (MADM) methods are widely used and studied in recent years. However, the perception and cognition towards the semantic representation for the linguistic rating scale and the way in which the pairwise comparisons are executed are still open to discuss. The commonly used ratio scale is likely to produce misapplications and the matrix based comparison style needs too many comparisons and is not able to guarantee the consistency of the matrix when the number of objects involved is large. This research proposes a new MADM method CBWM (Cognitive Best Worst Method) which adopts interval scale to represent the pairwise difference and only compares each object to the best object and the worst object rather than all the other objects. CBWM is a vector based method which only needs 2n − 3 pairwise comparisons and is more likely to generate consistent comparisons and reliable results. The theoretical analysis and a real world application demonstrate the effectiveness of CBWM.

The main idea of filter methods in feature selection is constructing a feature-assessing criterion and searching for feature subset that optimizes the criterion. The primary principle of designing such criterion is to capture the relevance between feature subset and the class as precisely as possible. It would be difficult to compute the relevance directly due to the computation complexity when the size of feature subset grows. As a result, researchers adopt approximate strategies to measure relevance. Though these strategies worked well in some applications, they suffer from three problems: parameter determination problem, the neglect of feature interaction information and overestimation of some features. We propose a new feature selection algorithm that could compute mutual information between feature subset and the class directly without deteriorating computation complexity based on the computation of partitions. In light of the specific properties of mutual information and partitions, we propose a pruning rule and a stopping criterion to accelerate the searching speed. To evaluate the effectiveness of the proposed algorithm, we compare our algorithm to the other five algorithms in terms of the number of selected features and the classification accuracies on three classifiers. The results on the six synthetic datasets show that our algorithm performs well in capturing interaction information. The results on the thirteen real world datasets show that our algorithm selects less yet better feature subset.

Aiming at combining the good characteristics of a differential scale in representing human cognition and the favorable properties of interval judgments in expressing decision-makers’ uncertainty, this paper proposes the interval cognitive network process (I-CNP) to extend the primitive cognition network process (P-CNP) to handle interval judgments. The key points of I-CNP include a consistency definition for an interval pairwise opposite matrix (IPOM) and a method to derive interval utilities from an IPOM. This paper defines a feasible region-based consistency definition and a transitivity based consistency definition for an IPOM. Both of the two definitions are equivalent to the consistency definition for a crisp pairwise opposite matrix (POM) when an IPOM is reduced to a POM. Two methods that are able to derive interval utilities from both consistent and inconsistent IPOMs are developed based on the two definitions. Four numerical examples are used to illustrate the proposed methods and to compare I-CNP to interval analytic hierarchy process (IAHP). The results show that I-CNP reflects the decision-makers’ cognition better, and that the suggestions provided by I-CNP are more convincing. I-CNP provides new useful alternative tools for multi-attribute decision-making problems.