Ranking of fuzzy numbers play an important role in decision making, optimization, forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples it is proved that ranking method proposed by Chen and Chen (Expert Systems with Applications 36 (2009) 6833-6842) is incorrect. The main aim of this paper is to prop...

Predicate abstraction has become one of the most successful methodologies for proving safety properties of programs. Recently, several abstraction methodologies have been proposed for proving liveness properties. This paper studies “ranking abstraction” where a program is augmented by a non-constraining progress monitor, and further abstracted by predicate-abstraction, to allow for automatic ve...

Differing from [6] this paper reduces non-linear ranking function discovering for polynomial programs to semi-algebraic system solving, and demonstrates how to apply the symbolic computation tools, DISCOVERER and QEPCAD, to some interesting examples. keywords: Program Verification, Loop Termination, Ranking Function, Polynomial Programs, Semi-Algebraic Systems, Computer Algebra, DISCOVERER, QEPCAD

The problem of ranking, in which the goal is to learn a real-valued ranking function that induces a ranking or ordering over an instance space, has recently gained much attention in machine learning. We study generalization properties of ranking algorithms using the notion of algorithmic stability; in particular, we derive generalization bounds for ranking algorithms that have good stability pr...

The Spohnian paradigm of ranking functions is in many respects like an order-of-magnitude reverse of subjective probability theory. Unlike probabilities, however, ranking functions are only indirectly—via a pointwise ranking function on the underlying set of possibilities W—defined on a field of propositions A over W . This research note shows under which conditions ranking functions on a field...

A lexicographic ranking function for the set of all permutations of n ordered symbols translates permutations to their ranks in the lexicographic order of all permutations. This is frequently used for indexing data structures by permutations. We present algorithms for computing both the ranking function and its inverse using O(n) arithmetic operations.

A variant of the ranking aggregation problem is considered in this work. The goal is to find an approximation of an unknown true ranking given a set of rankings. We devise a solution called Belief Ranking Estimator (BRE), based on the belief function framework that permits to represent beliefs on the correctness of the rankings position as well as uncertainty on the quality of the rankings from...

Recursive Feature Elimination RFE combined with feature-ranking is an effective technique for eliminating irrelevant features. In this paper, an ensemble of MLP base classifiers with feature-ranking based on the magnitude of MLP weights is proposed. This approach is compared experimentally with other popular feature-ranking methods, and with a Support Vector Classifier SVC. Experimental results...

Label ranking aims to map instances to an order over a predefined set of labels. It is ideal that the label ranking model is trained by directly maximizing performance measures on training data. However, existing studies on label ranking models mainly based on the minimization of classification errors or rank losses. To fill in this gap in label ranking, in this paper a novel label ranking mode...

The term “preference learning” refers to the application of machine learning methods for inducing preference models from empirical data. In the recent literature, corresponding problems appear in various guises. After a brief overview of the field, this work focuses on a particular learning scenario called label ranking, where the problem is to learn a mapping from instances to rankings over a ...