We consider rational functions of the form V(x)/U(x), where both V(x) and U(x) are relatively prime polynomials over finite field \(\mathbb {F}_q\). Polynomials that permute elements a field, called permutation (PPs), have been subject research for decades. Let \({\mathcal {P}}^1(\mathbb {F}_q)\) denote {F}_q\cup \{\infty \}\). If function, permutes {F}_q)\), it is function (PRF). \(N_d(q)\) nu...

Stochastic, as well fuzzy uncertainty, can be found in most real-world systems. Considering both types of uncertainties simultaneously makes optimization problems incredibly challenging. In this paper, we analyze the permutation flow shop problem (PFSP) with stochastic and processing times. The main goal is to find solution (permutation jobs) that minimizes expected makespan. However, due exist...

The Halton sequence is one of the classical low-discrepancy sequences. It is effectively used in numerical integration when the dimension is small, however, for larger dimensions, the uniformity of the sequence quickly degrades. As a remedy, generalized (scrambled) Halton sequences have been introduced by several researchers since the 1970s. In a generalized Halton sequence, the digits of the o...

Multiple classifiers combination is a technique that combines the decisions of different classifiers as to reduce the variance of estimation errors and improve the overall classification accuracy. A new multiple classifiers fusion method integrated classifier selection and classifier combination is proposed in this paper. It is base on interval-valued fuzzy permutation. Firstly, normalize all c...

The activation of the Deep Convolutional Neural Networks hidden layers can be successfully used as features, often referred as Deep Features, in generic visual similarity search tasks. Recently scientists have shown that permutation-based methods offer very good performance in indexing and supporting approximate similarity search on large database of objects. Permutation-based approaches repres...

The reconstruction problem for permutations on n elements from their erroneous patterns which are distorted by transpositions is presented in this paper. It is shown that for any n ≥ 3 an unknown permutation is uniquely reconstructible from 4 distinct permutations at transposition distance at most one from the unknown permutation. The transposition distance between two permutations is defined a...

Given the channel routing topology with k tracks, the problem of minimizing crosstalk is intractable, requiring O(k!) time even in the track-based permutation. In this paper, a new approach for track assignment enhancement, minimizing the ●ignal cmsatalk and defect areas between netn, while preserving the number of tracks, is presented. The approach is to allow for the split “nets” to be permut...

Permutation polynomials over finite fields play important roles in finite fields theory. They also have wide applications in many areas of science and engineering such as coding theory, cryptography, combinational design, communication theory and so on. Permutation binomials and trinomials attract people’s interest due to their simple algebraic form and additional extraordinary properties. In t...