Zhen-Yu Xiu | Searcharxiv

arXiv2024

New construction methods for uninorms via functions with q and uninorms on bounded lattices

In this paper, we study the construction methods for uninorms on bounded lattices via functions with the given uninorms and $q\in \mathbb{L_{B}}$ (or $p\in \mathbb{L_{B}}$). Specifically, we investigate the conditions under which these functions can be uninorms on bounded lattices when $q\in (0,\mathfrak{e})\cup I_{\mathfrak{e}}^{\varrho}$ and $q\in I_{\varrho}^{\mathfrak{e}}$ (or $p\in (\mathfrak{e},1)\cup I_{\mathfrak{e}}^σ$ and $p\in I_σ^{\mathfrak{e}}$), respectively. Moreover, some illustrative examples and figures are provided.

math.LO↗

arXiv2017

$(L,M)$-fuzzy convex structures

In this paper, the notion of $(L,M)$-fuzzy convex structures is introduced. It is a generalization of $L$-convex structures and $M$-fuzzifying convex structures. In our definition of $(L,M)$-fuzzy convex structures, each $L$-fuzzy subset can be regarded as an $L$-convex set to some degree. The notion of convexity preserving functions is also generalized to lattice-valued case. Moreover, under the framework of $(L,M)$-fuzzy convex structures, the concepts of quotient structures, substructures and products are presented and their fundamental properties are discussed. Finally, we create a functor $ω$ from $\mathbf{MYCS}$ to $\mathbf{LMCS}$ and show that there exists an adjunction between $\mathbf{MYCS}$ and $\mathbf{LMCS}$, where $\mathbf{MYCS}$ and $\mathbf{LMCS}$ denote the category of $M$-fuzzifying convex structures, and the category of $(L,M)$-fuzzy convex structures, respectively.

math.GN↗