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Zhudeng Wang - One of the best experts on this subject based on the ideXlab platform.

  • left right semi uninorms and coimplications on a Complete Lattice
    Fuzzy Sets and Systems, 2016
    Co-Authors: Zhudeng Wang
    Abstract:

    In this paper, we firstly discuss the deresidual operations of left (right) semi-uninorms and show which properties they satisfy. Then, we investigate the left and right semi-uninorms induced by a coimplication and give some conditions such that the operations induced by a coimplication constitute left or right semi-uninorms. Finally, we demonstrate that the meet-semiLattice of all disjunctive right (left) ?-distributive left (right) semi-uninorms is order-reversing isomorphic to the join-semiLattice of all right ?-distributive coimplications, which satisfy the neutrality principle.

  • the relations between implications and left right semi uninorms on a Complete Lattice
    International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 2015
    Co-Authors: Xiaoying Hao, Meixia Niu, Zhudeng Wang
    Abstract:

    Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we study the relations between implications and left (right) semi-uninorms on a Complete Lattice. We firstly investigate the left (right) semi-uninorms induced by implications, give some conditions such that the operations induced by implications constitute left or right semi-uninorms, and demonstrate that the operations induced by a right infinitely ∧-distributive implication, which satisfies the order property, are left (right) infinitely ∨-distributive left (right) semi-uninorms. Then, we discuss the residual operations of left (right) semi-uninorms and show that left (right) residual operators of strict left (right)-conjunctive left (right) infinitely ∨-distributive left (right) semi-uninorms are right infinitely ∧-distributive implications that satisfy the order property. Finally, we reveal the relationships between strict left (right)-conjunctive left (right) infinitely ∨-distributive left (right) semi-uninorms and right infinitely ∧-distributive implications which satisfy the order property.

  • constructing implications and coimplications on a Complete Lattice
    Fuzzy Sets and Systems, 2014
    Co-Authors: Zhudeng Wang
    Abstract:

    Abstract In this paper, we firstly give out the formulas for calculating the upper (lower) approximation implications and coimplications of a binary operation on a Complete Lattice. Then, we discuss some properties of the upper (lower) approximation implications and coimplications. Finally, we investigate the relations between the upper (lower) approximation implications and the lower (upper) approximation coimplications.

  • pseudo uninorms and coimplications on a Complete Lattice
    Fuzzy Sets and Systems, 2013
    Co-Authors: Zhudeng Wang
    Abstract:

    Pseudo-uninorms are a generalization of uninorms by removing the commutativity from the axioms of the uninorms. In this paper, we further study pseudo-uninorms and coimplications on a Complete Lattice. Firstly, we discuss the residual coimplications of pseudo-uninorms and give equivalent conditions for left (right) infinitely @?-distributive pseudo-uninorms. Then, we study some properties of (U,N)-coimplications generated from a pseudo-uninorm and a strong negation. Finally, we investigate the pseudo-uninorms induced by coimplications, present equivalent conditions for right infinitely @?-distributive coimplications, and provide some conditions such that the operators induced by coimplications are uninorms.

  • left and right semi uninorms on a Complete Lattice
    Kybernetika, 2013
    Co-Authors: Zhudeng Wang, Keming Tang
    Abstract:

    Uninorms are important generalizations of triangular norms and conorms, with a neutral element lying anywhere in the unit interval, and left (right) semi-uninorms are non-commutative and non-associative extensions of uninorms. In this paper, we firstly introduce the concepts of left and right semi-uninorms on a Complete Lattice and illustrate these notions by means of some examples. Then, we lay bare the formulas for calculating the upper and lower approximation left (right) semi-uninorms of a binary operation. Finally, we discuss the relations between the upper approximation left (right) semi-uninorms of a given binary operation and the lower approximation left (right) semi-uninorms of its dual operation.

Huawen Liu - One of the best experts on this subject based on the ideXlab platform.

  • coimplications derived from pseudo uninorms on a Complete Lattice
    International Journal of Approximate Reasoning, 2017
    Co-Authors: Huawen Liu, Witold Pedrycz
    Abstract:

    Abstract Coimplications are one of the important connectives used in fuzzy logic and fuzzy inference because they are a generalization of binary coimplications existing in classical logic. In this work, we further study two classes of coimplications derived from pseudo-uninorms on a Complete Lattice. Firstly, we present some characterizations of ( U , N ) -coimplications derived from a pseudo-uninorm and a strong negation. Then, we investigate residual coimplications and ( U , N ) -coimplications jointly rather than separately.

  • characterizations of residual coimplications of pseudo uninorms on a Complete Lattice
    Fuzzy Sets and Systems, 2015
    Co-Authors: Huawen Liu
    Abstract:

    Pseudo-uninorms are a generalization of uninorms by removing the commutativity from the axioms of the uninorms. In this paper, we further study coimplications generated from pseudo-uninorms on a Complete Lattice. Firstly, we further discuss the properties of residual coimplications generated from pseudo-uninorms on a Complete Lattice. Then, we recall the induced operators by coimplications on a Complete Lattice and give conditions such that they are pseudo-uninorms. Finally, we give out some characterizations of the residual coimplications generated from (right) infinitely ?-distributive disjunctive pseudo-uninorms on a Complete Lattice.

  • semi uninorms and implications on a Complete Lattice
    Fuzzy Sets and Systems, 2012
    Co-Authors: Huawen Liu
    Abstract:

    An extension of a uninorm called a semi-uninorm is introduced and discussed in this paper. First, we introduce the concept of semi-uninorms on a Complete Lattice. Then, we discuss two kinds of residual operators of semi-uninorms and give conditions such that the operators are implications. We also give equivalent conditions for infinitely @?-distributive left- and right-conjunctive semi-uninorms. Furthermore, we define two classes of induced operators by implications on a Complete Lattice and give conditions such that they are semi-uninorms. We also provide the equivalent conditions for the infinitely @?-distributive implications in their second variables.

Witold Pedrycz - One of the best experts on this subject based on the ideXlab platform.

  • coimplications derived from pseudo uninorms on a Complete Lattice
    International Journal of Approximate Reasoning, 2017
    Co-Authors: Huawen Liu, Witold Pedrycz
    Abstract:

    Abstract Coimplications are one of the important connectives used in fuzzy logic and fuzzy inference because they are a generalization of binary coimplications existing in classical logic. In this work, we further study two classes of coimplications derived from pseudo-uninorms on a Complete Lattice. Firstly, we present some characterizations of ( U , N ) -coimplications derived from a pseudo-uninorm and a strong negation. Then, we investigate residual coimplications and ( U , N ) -coimplications jointly rather than separately.

Glad Deschrijver - One of the best experts on this subject based on the ideXlab platform.

  • interval valued and intuitionistic fuzzy mathematical morphologies as special cases of mathbb l fuzzy mathematical morphology
    Journal of Mathematical Imaging and Vision, 2012
    Co-Authors: Peter Sussner, Mike Nachtegael, Tom Mélange, Glad Deschrijver, Estevao Esmi, Etienne Kerre
    Abstract:

    Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a Complete Lattice. Recall that Complete Lattices provide for the most general framework in which MM can be conducted. The concept of $\mathbb{L}$ -fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov's intuitionistic fuzzy set. In addition, the class of $\mathbb{L}$ -fuzzy sets forms a Complete Lattice whenever the underlying set $\mathbb{L}$ constitutes a Complete Lattice. Based on these observations, we develop a general approach towards $\mathbb{L}$ -fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of $\mathbb{L}$ -fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction techniques in terms of interval-valued fuzzy image processing.

  • a representation of t norms in interval valued l fuzzy set theory
    Fuzzy Sets and Systems, 2008
    Co-Authors: Glad Deschrijver
    Abstract:

    In this paper we consider the Lattice L^I which has the closed subintervals of a Complete Lattice as elements. We give a representation theorem of t-norms on this Lattice for which the partial mappings are join-morphisms in terms of t-norms on the underlying Lattice. In fuzzy logic, t-norms which satisfy the residuation principle play an important role. Using our representation theorem, we represent t-norms on L^I which satisfy the residuation principle and two border conditions in terms of t-norms on the underlying Lattice. In the case that the underlying Lattice of L^I is the unit interval, we obtain characterizations of continuous t-norms which are natural extensions of t-norms on the unit interval and which have join-morphisms as partial mappings or alternatively satisfy the residuation principle.

Jinxuan Fang - One of the best experts on this subject based on the ideXlab platform.

  • residual coimplicators of left and right uninorms on a Complete Lattice
    Fuzzy Sets and Systems, 2009
    Co-Authors: Zhudeng Wang, Jinxuan Fang
    Abstract:

    Uninorms are an important generalization of triangular norms and conorms, having a neutral element lying anywhere in the unit interval, and left and right uninorms are a non-commutative extension of uninorms. In this paper, we further study left and right uninorms on a Complete Lattice. First we introduce the concepts of residual coimplicators of left and right uninorms. Then we discuss some basic properties of the residual coimplicators of infinitely @?-distributive left (right) uninorms and pseudo-uninorms. Finally we investigate the relations between residual implicators and residual coimplicators of left (right) uninorms.

  • residual operations of left and right uninorms on a Complete Lattice
    Fuzzy Sets and Systems, 2009
    Co-Authors: Zhudeng Wang, Jinxuan Fang
    Abstract:

    Uninorms are an important generalization of triangular norms and conorms, having a neutral element lying anywhere in the unit interval. In this paper, we introduce the concepts of left and right uninorms on a Complete Lattice. We discuss the residual operations of left and right uninorms, and study some basic properties of the residual operations of infinitely @?-distributive left (right) uninorms and pseudo-uninorms.