Fuzzy complete lattices

Zhang, Qiye; Wei-xian, Xie; Fan, Lei

doi:10.1016/j.fss.2008.12.001

Cited by 78 publications

(24 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Definition 2.4. ( [12,13]) Let (X, e X ) be a fuzzy poset and A ∈ L X . (1) A point x 0 is called a join of A, denoted by…”

Section: Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

The Properties of Join and Meet Preserving Maps

Kim

2014

Korean Journal of Mathematics

View full text Add to dashboard Cite

show abstract

“…Definition 2.4. ( [12,13]) Let (X, e X ) be a fuzzy poset and A ∈ L X . (1) A point x 0 is called a join of A, denoted by…”

Section: Preliminariesmentioning

confidence: 99%

“…Bělohlávek [1,2] developed the notion of fuzzy contexts using Galois connections with R ∈ L X×Y on a complete residuated lattice. Zhang [12,13] introduced the fuzzy complete lattice which is defined by join and meet on fuzzy posets. It is an important mathematical tool for algebraic structure of fuzzy contexts [1][2][3][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

The Properties of Join and Meet Preserving Maps

Kim

2014

Korean Journal of Mathematics

View full text Add to dashboard Cite

show abstract

“…Some examples are as follows. Zhang et al [24,25] analysed the properties of fuzzy domains and fuzzy complete lattices. Lai [26], Yao [27] and Hao [28] investigated the relationships between fuzzy orders and fuzzy topological spaces.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy ideals of ordered semigroups with fuzzy orderings

Huang

2016

Open Mathematics

View full text Add to dashboard Cite

Abstract:The purpose of this paper is to introduce the notions of .2; 2 _q k /-fuzzy ideals of a fuzzy ordered semigroup with the ordering being a fuzzy relation. Several characterizations of .2; 2 _q k /-fuzzy left (resp. right) ideals and .2; 2 _q k /-fuzzy interior ideals are derived. The lattice structures of all .2; 2 _q k /-fuzzy (interior) ideals on such fuzzy ordered semigroup are studied and some methods are given to construct an .2; 2 _q k /-fuzzy (interior) ideals from an arbitrary fuzzy subset. Finally, the characterizations of generalized semisimple fuzzy ordered semigroups in terms of .2; 2 _q k /-fuzzy ideals (resp. .2; 2 _q k /-fuzzy interior ideals) are developed.

show abstract

“…A number of papers on the topic of sets with fuzzy order relations valuated in a complete lattice with additional structure have been published in recent years. Among many others, articles [9,10,12] may be used as a reference. There are various structures used for fuzzy valuation in the literature, e.g., frames [3] and complete residuated lattices [12], both being just special cases of quantales.…”

Section: Introductionmentioning

confidence: 99%

On some basic constructions in categories of quantale-valued sup-lattices

Šlesinger¹

2016

Math. Appl.

View full text Add to dashboard Cite

Abstract. If the standard concepts of partial-order relation and subset are fuzzified, taking valuation in a unital commutative quantale Q, corresponding concepts of joins and join-preserving mappings can be introduced. We present constructions of limits, colimits and Hom-objects in categories Q-Sup of Q-valued fuzzy joinsemilattices, showing the analogy to the ordinary category Sup of join-semilattices. IntroductionIn the standard concept of a fuzzy set [11], the relation "x is an element of X" is fuzzified, and replaced by a mapping X → [0, 1] assigning to each element of X its "membership degree". As further generalization, the membership degree can be evaluated in structures more general than the real unit interval, typically frames, residuated lattices, or quantales.In our paper, the concept of a set remains unchanged, and it will be the partial order relation and the notion of a subset that will be replaced by suitable mappings to a quantale. Instead of considering on X a partial order relation ≤, we employ a unital quantale Q and mappings M : X → Q and e : X × X → Q, which quantify the "degree of truth" of membership in a subset and of being less or equal.Sets equipped with quantale-valued binary mappings were initially investigated in the so-called quantitative domain theory [4]. A number of papers on the topic of sets with fuzzy order relations valuated in a complete lattice with additional structure have been published in recent years. Among many others, articles [9,10,12] may be used as a reference. There are various structures used for fuzzy valuation in the literature, e.g., frames [3] and complete residuated lattices [12], both being just special cases of quantales. Also terminology has not settled yet, and differs among authors. As the multiplicative unit of a quantale need not be its top element, even truth can have more degrees in Q. This is different from valuation using frames or residuated lattices where the unit is the top element as well.The basic properties of the category of complete join-semilattices as well as the fundamental constructions in this category such as limits and colimits have MSC (2010): primary 08A72, 06F99; secondary 18B35.

show abstract

Fuzzy complete lattices

Cited by 78 publications

References 30 publications

The Properties of Join and Meet Preserving Maps

The Properties of Join and Meet Preserving Maps

Fuzzy ideals of ordered semigroups with fuzzy orderings

On some basic constructions in categories of quantale-valued sup-lattices

Contact Info

Product

Resources

About