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Authors: He, Peng | Wang, Xue-ping

Article Type: Research Article

Abstract: This paper deals with strongly atomic algebraic lattices. Two necessary and sufficient conditions that a strongly atomic algebraic lattice is semimodular are shown by using the locally sublattice, called a WAGC sublattice, of the lattice.

Keywords: Strongly atomic lattice, algebraic lattice, semimodular lattice, WAGC lattice

DOI: 10.3233/JIFS-162168

Citation: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 2, pp. 913-920, 2017

Authors: Sourisse, Arnaud | Wang, Xue Ping

Article Type: Research Article

Abstract: On étudie l'asymptotique des valeurs propres de l'opérateur de Dirac en dimension deux avec un champ magnétique variable qui tend vers l'infini. On utilise la structure supersymétique de cet opérateur pour se ramener à l'étude des valeurs propres de l'opérateur de Schrödinger avec un potentiel électrique égal au champ magnétique.

Keywords: opérateur de Dirac, champ magnétique, valeur propre

Citation: Asymptotic Analysis, vol. 55, no. 3-4, pp. 203-228, 2007

Authors: Wang, Xue Ping | Zhu, Lu

Article Type: Research Article

Abstract: We determine the range of the incoming wave operator for the pair of operators (−Δ,−Δ+V1 (x)−iεV2 (x)) on L2 (Rn ) under the conditions n≥3 and 0 is a regular point of −Δ+V1 , V2 ≥0 and ε>0 is small enough. This implies that the dissipative scattering operator is bijective.

Keywords: dissipative quantum scattering, asymptotic completeness, non-selfadjoint Schrödinger operators

DOI: 10.3233/ASY-131190

Citation: Asymptotic Analysis, vol. 86, no. 1, pp. 49-57, 2014

Authors: He, Peng | Wang, Xue-ping

Article Type: Research Article

Abstract: This paper first describes a characterization of a lattice L which can be represented as the collection of all up-sets of a poset. It then obtains a representation of a complete distributive lattice L 0 which can be embedded into the lattice L such that all infima, suprema, the top and bottom elements are preserved under the embedding by defining a monotonic operator on a poset. This paper finally studies the algebraic characterization of a finite distributive.

Keywords: 03E72, 06D05, L-fuzzy set, cut set, complete distributive lattice, embedding, monotonic operator

DOI: 10.3233/JIFS-201430

Citation: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 5, pp. 9021-9030, 2021

Authors: He, Peng | Wang, Xue-Ping

Article Type: Research Article

Abstract:  This paper deals with L -fuzzy up-sets by using terminologies of closure operators. It first gives a condition that a family of some subsets of a nonempty set can be represented by L -fuzzy up-sets, and it finally discusses the L -fuzzy sets on quotient sets under closure operators.

Keywords: Complete lattice, L-fuzzy up-set, closure operator, 03B52, 03E72, 06A15

DOI: 10.3233/JIFS-191388

Citation: Journal of Intelligent & Fuzzy Systems, vol. 38, no. 4, pp. 4667-4673, 2020

Authors: He, Peng | Wang, Xue-Ping

Article Type: Research Article

Abstract: Let D be a finite distributive lattice with n join-irreducible elements. It is well-known that D can be represented as the congruence lattice of a rectangular lattice L which is a special planer semimodular lattice. In this paper, we shall give a better upper bound for the size of L by a function of n , improving a 2009 result of G. Grätzer and E. Knapp.

Keywords: Distributive lattice, Congruence lattice, Rectangular lattice AMS classification: 06C10; 06B10, 06C10, 06B10

DOI: 10.3233/JIFS-191220

Citation: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 3, pp. 2831-2843, 2020

Authors: Mi, Xiao | Wang, Xue-ping

Article Type: Research Article

Abstract: This paper investigates minimal solutions of fuzzy relation inequalities with addition-min composition. It first shows the conditions that an element is a minimal solution of the inequalities, and presents the conditions that the inequalities have a unique minimal solution. It then proves that every solution of the inequalities has a minimal one and proposes an algorithm to searching for a minimal solution with computational complexity O  (n 2 ) where n is the number of unknown variables of the inequalities. This paper finally describes all minimal solutions of the inequalities.

Keywords: Fuzzy relation inequality, addition-min composition, minimal solution, algorithm

DOI: 10.3233/JIFS-202590

Citation: Journal of Intelligent & Fuzzy Systems, vol. 41, no. 6, pp. 6089-6095, 2021

Authors: Li, Meng | Wang, Xue-ping

Article Type: Research Article

Abstract: In order to guarantee the downloading quality requirements of users and improve the stability of data transmission in a BitTorrent-like peer-to-peer file sharing system, this article deals with eigenproblems of addition-min algebras. First, it provides a sufficient and necessary condition for a vector being an eigenvector of a given matrix, and then presents an algorithm for finding all the eigenvalues and eigenvectors of a given matrix. It further proposes a sufficient and necessary condition for a vector being a constrained eigenvector of a given matrix and supplies an algorithm for computing all the constrained eigenvectors and eigenvalues of a given …matrix. This article finally discusses the supereigenproblem of a given matrix and presents an algorithm for obtaining the maximum constrained supereigenvalue and depicting the feasible region of all the constrained supereigenvectors for a given matrix. It also gives some examples for illustrating the algorithms, respectively. Show more

Keywords: Fuzzy relation inequality, Addition-min composition, Eigenvalue, Eigenvector, Algorithm

DOI: 10.3233/JIFS-234499

Citation: Journal of Intelligent & Fuzzy Systems, vol. 46, no. 1, pp. 91-103, 2024

Authors: Chen, Meng | Wang, Xue-ping

Article Type: Research Article

Abstract: In this article, we characterize triangular norms that have not the limit property, which are applied for exploring the characterizations of function f  : [0, 1] → [0, 1] with f ( x ) = lim n → ∞ x T ( n ) for a triangular norm T when the function f is continuous. In particular, we prove that a continuous t-norm T satisfies that f  (x ) >0 for all x  ∈ (0, 1) if and only if 0 is an accumulation point of its non-trivial idempotent elements, and the function f is continuous on [0,1] if and only if T  = T M …. Show more

Keywords: Triangular norm, the limit property, the contrary limit property, Archimedean property, continuity

DOI: 10.3233/JIFS-237999

Citation: Journal of Intelligent & Fuzzy Systems, vol. Pre-press, no. Pre-press, pp. 1-7, 2024

Authors: Sun, Feng | Wang, Xue-ping | Qu, Xiao-bing

Article Type: Research Article

Abstract: This paper deals with fuzzy clique covers in fuzzy graphs. The definition of a fuzzy clique is modified so that the fuzzy subgraph induced by each fuzzy clique is complete. Then, fuzzy cliques and maximal fuzzy cliques are characterized. Finally, fuzzy clique covers and minimum fuzzy clique covers in fuzzy graphs are introduced and characterized, and an algorithm to find a minimum fuzzy clique cover of a given fuzzy graph is also presented.

Keywords: Fuzzy graph, fuzzy clique, fuzzy clique cover, minimum fuzzy clique cover

DOI: 10.3233/IFS-162189

Citation: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 3, pp. 1245-1256, 2016