Ranking of fuzzy sets based on the concept of existence

AbstractVarious approaches have been proposed for the comparison or ranking of fuzzy sets. However, due to the complexity of the problem, a general method which can be used for any situation still does not exist. This paper formalizes the concept of existence for the ranking of fuzzy sets. Many of the existing fuzzy ranking methods are shown to be some application of this concept. An improved fuzzy ranking method is then introduced, based on this concept. This newly introduced method is expanded for treating both normal and nonnormal, convex and nonconvex fuzzy sets. Emphasis is placed on the use of the subjectivity of the decision maker, such as the optimistic or the pessimistic view points. An improved procedure for obtaining linguistic conclusions is also developed. Finally, some numerical examples are given to illustrate the approach

The estimation of normalized fuzzy weights

AbstractThe estimation of a normalized set of positive fuzzy weights constitutes the most important aspects in the fuzzy multiple attribute decision making process. A systematic treatment of this problem is carried out in this paper. The concept of fuzzy normalization is first defined and the meaning of consistency in a fuzzy environment is discussed. Based on these definitions and discussions, the various approaches in the literature are examined and several improvements or new approaches are proposed. Numerical examples are used to evaluate and to compare the various existing and the newly proposed approaches

Effective action in spherical domains

The effective action on an orbifolded sphere is computed for minimally coupled scalar fields. The results are presented in terms of derivatives of Barnes zeta-functions and it is shown how these may be evaluated. Numerical values are shown. An analytical, heat-kernel derivation of the Ces\`aro-Fedorov formula for the number of symmetry planes of a regular solid is also presented.Comment: 18 pages, Plain TeX (Mailer oddities possibly corrected.

Some Additive Combinatorics Problems in Matrix Rings

We study the distribution of singular and unimodular matrices in sumsets in matrix rings over finite fields. We apply these results to estimate the largest prime divisor of the determinants in sumsets in matrix rings over the integers

State sampling dependence of the Hopfield network inference

The fully connected Hopfield network is inferred based on observed magnetizations and pairwise correlations. We present the system in the glassy phase with low temperature and high memory load. We find that the inference error is very sensitive to the form of state sampling. When a single state is sampled to compute magnetizations and correlations, the inference error is almost indistinguishable irrespective of the sampled state. However, the error can be greatly reduced if the data is collected with state transitions. Our result holds for different disorder samples and accounts for the previously observed large fluctuations of inference error at low temperatures.Comment: 4 pages, 1 figure, further discussions added and relevant references adde

DsJ(2860)D_{sJ}(2860) and DsJ(2715)D_{sJ}(2715)

Recently Babar Collaboration reported a new $c\bar{s}$ state $D_{sJ}(2860)$ and Belle Collaboration observed $D_{sJ}(2715)$. We investigate the strong decays of the excited $c\bar{s}$ states using the $^{3}P_{0}$ model. After comparing the theoretical decay widths and decay patterns with the available experimental data, we tend to conclude: (1) $D_{sJ}(2715)$ is probably the $1^{-}(1^{3}D_{1})$ $c\bar{s}$ state although the $1^{-}(2^{3}S_{1})$ assignment is not completely excluded; (2) $D_{sJ}(2860)$ seems unlikely to be the $1^{-}(2^{3}S_{1})$ and $1^{-}(1^{3}D_{1})$ candidate; (3) $D_{sJ}(2860)$ as either a $0^{+}(2^{3}P_{0})$ or $3^{-}(1^{3}D_{3})$ $c\bar{s}$ state is consistent with the experimental data; (4) experimental search of $D_{sJ}(2860)$ in the channels $D_s\eta$, $DK^{*}$, $D^{*}K$ and $D_{s}^{*}\eta$ will be crucial to distinguish the above two possibilities.Comment: 18 pages, 7 figures, 2 tables. Some discussions added. The final version to appear at EPJ

Charmonium states in QCD-inspired quark potential model using Gaussian expansion method

We investigate the mass spectrum and electromagnetic processes of charmonium system with the nonperturbative treatment for the spin-dependent potentials, comparing the pure scalar and scalar-vector mixing linear confining potentials. It is revealed that the scalar-vector mixing confinement would be important for reproducing the mass spectrum and decay widths, and therein the vector component is predicted to be around 22%. With the state wave functions obtained via the full-potential Hamiltonian, the long-standing discrepancy in M1 radiative transitions of $J/\psi$ and $\psi^{\prime}$ are alleviated spontaneously. This work also intends to provide an inspection and suggestion for the possible $c\bar{c}$ among the copious higher charmonium-like states. Particularly, the newly observed X(4160) and X(4350) are found in the charmonium family mass spectrum as $M(2^1D_2)= 4164.9$ MeV and $M(3^3P_2)= 4352.4$ MeV, which strongly favor the $J^{PC}=2^{-+}, 2^{++}$ assignments respectively. The corresponding radiative transitions, leptonic and two-photon decay widths have been also predicted theoretically for the further experimental search.Comment: 16 pages,3 figure

Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

It is known that actions of field theories on a noncommutative space-time can be written as some modified (we call them $\theta$-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and usual quantum mechanical features of the corresponding field theory. The $\theta$-modification for arbitrary finite-dimensional nonrelativistic system was proposed by Deriglazov (2003). In the present article, we discuss the problem of constructing $\theta$-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract $\theta$-modified actions of the relativistic particles from path integral representations of the corresponding noncommtative field theory propagators. We consider Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as $\theta$-modified actions of the relativistic particles. To confirm the interpretation, we quantize canonically these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The $\theta$-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case