He paper is organized as follows. Fmoc-leucine-d3 PPAR Section two reviewes some notions briefly. In

He paper is organized as follows. Fmoc-leucine-d3 PPAR Section two reviewes some notions briefly. In Section three, we propose the variety II-dual intersectable formal context and investigate the relations among some notion lattices such as notion lattice, the object oriented notion lattice and OEOL when the formal context is definitely the variety II-dual intersectable context. In Section 4, the inverse proposition of connected conclusions in Section 3 are given. Also, various theorems and examples are given. Ultimately, the summary is provided by using a diagram in Section 5. two. Preliminaries two.1. Notion Lattice Firstly, some fundamental definitions are provided. Definition 1. [2] Let G and M be two finite sets and I be a binary relation in between G and M, we contact ( G, M, I) a formal context. Also, g G and m M are referred to as the object plus the attribute, respectively. ( g, m) I implies that the object g has the attribute m. A pair of dual operators for any X G plus a M and the definitions of formal notion and notion lattice are provided as follows. X = m M , A = g G .( X, A), X as well as a are, respectively, named a formal idea, an extent and an intent when X = A plus a = X. If X = m plus a = g, then m and g are abbreviated to m and g , respctively. If g G, g = , g = M, and m M, m = , m = G, we contact ( G, M, I) the canonical context. If g, h G, g = h , and m, n M, m = n , we contact ( G, M, I) the clarified context. The set of all formal ideas is named the concept lattice denoted by L( G, M, I). For any ( X, A), (Y, B) L( G, M, I), the partial order is defined by:Entropy 2021, 23,three of( X, A)(Y, B) X Y ( A B).And it is actually simple to prove it can be a full lattice using the above partial order. Remark 1. (1) Extent (intent) Amidepsine D References continues to be extent (intent) after the intersection of sets. And the properties of operators are shown in the literature [2]; (2) Just about every set within a lattice except G, M and can also be expressed straight by listing its components. Instance 1. Let G = 1, 2, 3 and M = a, b, c, I is represented in Table 1. We get a formal context. Based on Definition 1, The concepts are calculated simply, then the correspoding notion lattice is represented by Figure 1.Table 1. A formal context ( G, M, I). G 1 2 3 a b c( G ,)(1, a)(2, b)( 3, c)(, M)Figure 1. L( G, M, I) of Table 1.2.2. The Object Oriented Idea Lattice The object oriented idea lattice was proposed by Yao in [16]. Also, it’s recalled as follows. Definition two. [16] Let a formal context be ( G, M, I). For any X G and also a M, a pair of operators : P ( G) P ( M) and : P ( M) P ( G) as follows. X = m M , A = g A = .( X, A) is known as an object oriented concept. X in addition to a are, respectively, called the extent plus the intent of ( X, A) when X = A in addition to a = X. The set of all object oriented concepts kind a complete lattice which is known as the object oriented idea lattice and is denoted by Lo ( G, M, I). The partial order on it can be defined as follows: ( X, A) (Y, B) X Y ( A B).Remark 2. Extent continues to be extent soon after the union of sets. As well as the properties of operators are shown inside the literature [16]. Example 2. Lo ( G, M, I) of Table 1 is shown in Figure two in accordance with Definition two.Entropy 2021, 23,4 of(G , M) (13, ac) (12, ab) (1, a)(23, bc)(3, c)(two, b) (,)Figure two. Lo ( G, M, I) of Table 1.2.three. The Three-Way Object Oriented Notion Lattice Inspired by 3WCA, Wei and Qian [26,27] proposed OEPL and OEOL. The relevant definitions are as follows. Firstly, the adverse oper.