A ranking function for the permutations on n symbols assigns a unique integer in the range [0, n! − 1] to each of the n! permutations. The corresponding unranking function is the inverse: given an integer between 0 and n! − 1, the value of the function is the permutation having this rank. We present simple ranking and unranking algorithms for permutations that can be computed using O(n) arithme...

We study generalization properties of ranking algorithms in the setting of the k-partite ranking problem. In the k-partite ranking problem, one is given examples of instances labeled with one of k ordered ‘ratings’, and the goal is to learn from these examples a real-valued ranking function that ranks instances in accordance with their ratings. This form of ranking problem arises naturally in a...

Ranking functions are instrumental for the success of an information retrieval (search engine) system. However nearly all existing ranking functions are manually designed based on experience, observations and probabilistic theories. This paper tested a novel ranking function discovery technique proposed in [Fan 2003a, Fan2003b] – ARRANGER (Automatic geneRation of RANking functions by GEnetic pR...

Learning To Rank (LTR) techniques aim to learn an effective document ranking function by combining several document features. While the function learned may be uniformly applied to all queries, many studies have shown that different ranking functions favour different queries, and the retrieval performance can be significantly enhanced if an appropriate ranking function is selected for each indi...

In this work, we propose an approach for computing the compromised solution of an LR fuzzy linear system by using of a ranking function when the coefficient matrix is a crisp mn matrix. To do this, we use expected interval to find an LR fuzzy vector, X , such that the vector (AX ) has the least distance from (b) in 1 norm and the 1 cut of X satisfies the crisp linear system AX = b ...

Ranking function is instrumental in affecting the performance of a search engine. Designing and optimizing a search engine’s ranking function remains a daunting task for computer and information scientists. Recently, genetic programming (GP), a machine learning technique based on evolutionary theory, has shown promise in tackling this very difficult problem. Ranking functions discovered by GP h...

in this paper, we propose the least-squares method for computing the positive solution of a m  n fully fuzzy linear system (ffls) of equations, where m > n, based on kaman's arithmetic operations on fuzzy numbers that introduced in [18]. first, we consider all elements of coecient matrix are non-negative or non-positive. also, we obtain 1-cut of the fuzzy number vector solution of the n...

We examine the role of hyperplane ranking during genetic search by developing a metric for measuring the degree of ranking that exists with respect to static hyperplane averages taken directly from the function, as well as the dynamic ranking of hyperplanes during genetic search. The metric applied to static rankings subsumes the concept of deception but the metric provides a more precise chara...