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Level lifetimes for the candidate chiral doublet bands of 80 Br were extracted by means of the Doppler-shift attenuation method. The absolute transition probabilities derived from the lifetimes agree well with the M 1 and E2 chiral electromagnetic selection rules, and the calculations reported in the frame- work of triaxial particle rotor model [S.Y. Wang et al., Phys. Lett. B 703 (2011) 40] also support firmly for the chirality in 80 Br. Such good agree- ments among the experimental data, selection rules of chiral doublet bands and theoretical calculations are rare and outstanding in researches of nuclear chirality. Besides odd-odd Cs isotopes, odd-odd Br isotopes in the A ≈ 80 mass region represent another territory that exhibits the ideal selection rules expected for chiral doublet bands.

Level lifetimes for the candidate chiral doublet bands of Br-80 were extracted by means of the Doppler-shift attenuation method. The absolute transition probabilities derived from the lifetimes agree well with the M1 and E2 chiral electromagnetic selection rules, and are well reproduced by the triaxial particle rotor model calculations. Such good agreements among the experimental data, selection rules of chiral doublet bands and theoretical calculations are rare and outstanding in researches of nuclear chirality. Besides odd-odd Cs isotopes, odd-odd Br isotopes in the A approximate to 80 mass region represent another territory that exhibits the ideal selection rules expected for chiral doublet bands. (C) 2022 The Author(s). Published by Elsevier B.V.

The paper shows that a cube of opposition, a structure that generalizes the square of opposition invented in ancient logic, can be generated from the composition of a binary relation with a subset, by the effect of set complementation on the subset, on the relation, or on the result of the composition. Since the composition of relations is encountered in many areas, the structure of opposition exhibited by the cube of opposition has a universal flavor. In particular, it applies to information processing-oriented settings such as rough set theory, possibility theory, or formal concept analysis. We then discuss how this structure extends to a fuzzy relation and a fuzzy subset, and the graded cube of opposition thus obtained provides an organized view of the different existing compositions of fuzzy relations. The paper concludes by pointing out areas of research where the cube of opposition, or its graded version are of interest.

© 2018 Wiley Periodicals, Inc. The classification of a new item may be viewed as a matter of associating it with the class where it is the least at odds w.r.t. the elements already in the class. An oddness measure of an item with respect to a multiset, applicable to Boolean features as well as to numerical ones, has been recently proposed. It has been shown that cumulating this measure over pairs or triples (rather than larger subsets) of elements in a class could provide an accurate estimate of the global oddness of an item with respect to a class. This idea is confirmed and refined in the present paper. Rather than considering all the pairs in a class, one can only deal with the pairs whose an element is one of the nearest neighbors of the item, in the target class. The oddness evaluation computed on this basis still leads to good results in terms of accuracy. One can take a step further and choose the second element in the pair also as another nearest neighbor in the class. Although the method relies on the notion of neighbors, the resulting algorithm is far from being a variant of the classical k-nearest neighbors approach. The oddness with respect to a class computed only on the basis of pairs made of two nearest neighbors leads to a low complexity algorithm. Experiments on a set of UCI benchmarks show that the classifier obtained can compete with other well-known approaches.

© 2018 Analogical proportions are statements of the form a is to b as c is to d. Such expressions compare the pair (a,b) with the pair (c,d). Previous papers have developed logical modelings of such proportions both in Boolean and in multiple-valued settings. They emphasize a reading of the proportion as “the way a and b differ is the same as c and d differ”. The ambition of this paper is twofold. The paper first provides a deeper understanding and further justifications of the Boolean modeling, before introducing analogical inequalities, where “as” is replaced by “as much as” in the comparison of two pairs. From an abstract viewpoint, analogical proportions are supposed to obey at least three postulates expressing reflexivity, symmetry, and stability under central permutation. Nevertheless these postulates are not enough to determine a single model and a minimality condition has to be added as shown in this paper. These models are organized in a complete lattice based on set inclusion. This leads us to discuss lower and upper approximations of the minimal model. Apart from being minimal, this model can also be evaluated in terms of Kolmogorov complexity via an expression reflecting the intended meaning of analogy. We show that the six Boolean patterns of the minimal model that make Boolean analogy true minimize this expression. Besides, analogical proportions extend to 4-tuples of Boolean vectors. This enables us to explain why analogical proportions also reads in terms of similarity (rather than difference, i.e., dissimilarity): a and d share the same presence or absence of features as b and c. Moreover, we establish a link between analogical proportion and Hamming distances between components of the proportion. We also emphasize that analogical proportions are pervasive in any comparison of two vectors a and d that implicitly induce the existence of “intermediary” vectors b and c forming together such a proportion. The similarity reading and the dissimilarity rea

The square of opposition is as old as logic. There has been a recent renewal of interest on this topic, due to the emergence of new structures (hexagonal and cubic) extending the square. They apply to a large variety of representation frameworks, all based on the notions of sets and relations. After a reminder about the structures of opposition, and an introduction to their gradual extensions (exemplified on fuzzy sets), the paper more particularly studies fuzzy rough sets and rough fuzzy sets in the setting of gradual structures of opposition.