ANALYSIS OF CERTAIN L-FUZZY RELATIONAL EQUATIONS AND THE STUDY OF ITS SOLUTIONS BY MEANS OF THE L-FUZZY CONCEPT THEORY

2012 ◽  
Vol 20 (01) ◽  
pp. 21-40 ◽  
Author(s):  
CRISTINA ALCALDE ◽  
ANA BURUSCO ◽  
RAMÓN FUENTES-GONZÁLEZ
Keyword(s):  
Complete Lattice ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Fuzzy Relational Equations ◽  
Fuzzy Concept ◽  
Concept Theory

Given a Brouwerian complete lattice (L,≤) and two referential sets K and E, and using a fuzzy relation R ∈ LE×E which is reflexive and symmetric, certain fuzzy relations [Formula: see text] are characterized as solutions of X ⊲ R = X, proving that they play the role of the blocks in the context of crisp tolerance relations. Moreover, it is verified that these new fuzzy blocks [Formula: see text] can be determinated by means of the L-fuzzy concepts associated with the K -labeled L-fuzzy context (L,K,E,E,R).

scholarly journals Bipolar Fuzzy Relations

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1044 ◽  
Author(s):  
Jeong-Gon Lee ◽  
Kul Hur
Keyword(s):  
Equivalence Class ◽  
Level Set ◽  
Equivalence Relation ◽  
Level Sets ◽  
Equivalence Classes ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Transitive Relation ◽  
Fuzzy Partition

We introduce the concepts of a bipolar fuzzy reflexive, symmetric, and transitive relation. We study bipolar fuzzy analogues of many results concerning relationships between ordinary reflexive, symmetric, and transitive relations. Next, we define the concepts of a bipolar fuzzy equivalence class and a bipolar fuzzy partition, and we prove that the set of all bipolar fuzzy equivalence classes is a bipolar fuzzy partition and that the bipolar fuzzy equivalence relation is induced by a bipolar fuzzy partition. Finally, we define an ( a , b ) -level set of a bipolar fuzzy relation and investigate some relationships between bipolar fuzzy relations and their ( a , b ) -level sets.

scholarly journals On rough sets induced by fuzzy relations approach in semigroups

2018 ◽  
Vol 16 (1) ◽  
pp. 1634-1650
Author(s):  
Rukchart Prasertpong ◽  
Manoj Siripitukdet
Keyword(s):  
Prime Ideal ◽  
Rough Set ◽  
Rough Sets ◽  
Sufficient Conditions ◽  
Unit Interval ◽  
Fuzzy Relation ◽  
Prime Ideals ◽  
Fuzzy Relations ◽  
Completely Prime Ideal

AbstractIn this paper, we introduce a rough set in a universal set based on cores of successor classes with respect to level in a closed unit interval under a fuzzy relation, and some interesting properties are investigated. Based on this point, we propose a rough completely prime ideal in a semigroup structure under a compatible preorder fuzzy relation, including the rough semigroup and rough ideal. Then we provide sufficient conditions for them. Finally, the relationships between rough completely prime ideals (rough semigroups and rough ideals) and their homomorphic images are verified.

Millennial’s engagement with fashion brands

2019 ◽  
Vol 23 (1) ◽  
pp. 2-16 ◽  
Author(s):  
Nagaraj Samala ◽  
Sapna Singh
Keyword(s):  
Self Concept ◽  
Brand Love ◽  
Content Type ◽  
Mediating Role ◽  
Moderated Mediation Model ◽  
Brand Advocacy ◽  
Marketing Variables ◽  
Concept Theory ◽  
Moderating Role

PurposeMillennials are more fashion conscious, relate themselves to the fashion brands they wear. This concept of brand engagement with self-concept (BESC) studies with other marketing variables yields interesting results. The purpose of this paper is to investigate the role of BESC with brand love and brand advocacy of millennials toward their favorite fashion brands. The study also tests the moderating role of millennials’ involvement and knowledge.Design/methodology/approachData are collected from 621 graduate student millennials of a university. Hayes process macros is used to test the moderated-mediation model.FindingsThe study confirms the complementary mediating role of BESC and enhances the moderating role of involvement and knowledge. Millennials with high involvement and knowledge enhance the positive relationship between brand love, BESC and brand advocacy.Originality/valueThe study contributes to the existing literature of self-concept theory and provides useful insights for fashion marketers about millennials.

FUZZY RELATION CALCULUS IN THE COMPRESSION AND DECOMPRESSION OF FUZZY RELATIONS

2002 ◽  
Vol 02 (04) ◽  
pp. 617-631 ◽  
Author(s):  
VINCENZO LOIA ◽  
WITOLD PEDRYCZ ◽  
SALVATORE SESSA
Keyword(s):  
Lossy Compression ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Triangular Norm ◽  
Fuzzy Matrix ◽  
Fuzzy Relation Equations

We firstly review some fundamentals of fuzzy relation calculus and, by recalling some known results, we improve the mathematical contents of our previous papers by using the properties of a triangular norm over [0,1]. We make wide use of the theory of fuzzy relation equations for getting lossy compression and decompression of images interpreted as two-argument fuzzy matrices.The same scope is achieved by decomposing a fuzzy matrix using the concept of Schein rank. We illustrate two algorithms with a few examples.

scholarly journals A study on orderings based on fuzzy quasi- order relations

2021 ◽  
Author(s):  
Zhonglin Chai
Keyword(s):  
Partial Order ◽  
Order Relation ◽  
Fuzzy Relation ◽  
Partial Order Relation ◽  
Fuzzy Relations ◽  
Fuzzy Graph ◽  
Feasible Method ◽  
Order Relations ◽  
Finite Set ◽  
Quasi Order

Abstract This paper further studies orderings based on fuzzy quasi-order relations using fuzzy graph. Firstly, a fuzzy relation on a finite set is represented equivalently by a fuzzy graph. Using the graph, some new results on fuzzy relations are derived. In ranking those alternatives, we usually obtain a quasi-order relation, which often has inconsistencies, so it cannot be used for orderings directly. We need to remake it into a reasonable partial order relation for orderings. This paper studies these inconsistencies, and divides them into two types: framework inconsistencies and degree inconsistencies. For the former, a reasonable and feasible method is presented to eliminate them. To eliminate the latter, the concept of complete partial order relation is presented, which is more suitable than partial order relation to rank the alternatives. A method to obtain a reasonable complete partial order relation for a quasi-order relation is given also. An example is given as well to illustrate these discussions. Lastly, the paper discusses the connection between quasi-order relations and preference relations for orderings and some other related problems.

scholarly journals The Lattice Structures of Approximation Operators Based on L-Fuzzy Generalized Neighborhood Systems

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Qiao-Ling Song ◽  
Hu Zhao ◽  
Juan-Juan Zhang ◽  
A. A. Ramadan ◽  
Hong-Ying Zhang ◽  
...  
Keyword(s):  
Complete Lattice ◽  
Lattice Isomorphism ◽  
Double Negative ◽  
Lattice Structures ◽  
Fuzzy Relations ◽  
Lower Approximation ◽  
Upper Approximation ◽  
Approximation Operators ◽  
Neighborhood System ◽  
Generalized Neighborhood System

Following the idea of L -fuzzy generalized neighborhood systems as introduced by Zhao et al., we will give the join-complete lattice structures of lower and upper approximation operators based on L -fuzzy generalized neighborhood systems. In particular, as special approximation operators based on L -fuzzy generalized neighborhood systems, we will give the complete lattice structures of lower and upper approximation operators based on L -fuzzy relations. Furthermore, if L satisfies the double negative law, then there exists an order isomorphic mapping between upper and lower approximation operators based on L -fuzzy generalized neighborhood systems; when L -fuzzy generalized neighborhood system is serial, reflexive, and transitive, there still exists an order isomorphic mapping between upper and lower approximation operators, respectively, and both lower and upper approximation operators based on L -fuzzy relations are complete lattice isomorphism.

scholarly journals Use of Fuzzy Relation Equations for Evaluating Mathematical Modelling Skills

2018 ◽  
Vol 3 (2) ◽  
pp. 102-107 ◽  
Author(s):  
Michael Gr. Voskoglou
Keyword(s):  
Mathematical Modelling ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Fuzzy Relation Equations ◽  
Assessment Approach

In the present paper a new assessment approach is developed involving the use of fuzzy relation equations, which are associated with the composition of binary fuzzy relations, for evaluating student mathematical modelling skills. A classroom application and other examples are also presented illustrating our results, and useful conclusions are obtained.

scholarly journals Intuitionistic fuzzy relations compatible with the group Zn

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
E. G. Emam
Keyword(s):  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Fundamental Properties ◽  
Intuitionistic Fuzzy

AbstractIn this paper, we define the compatibility of finite intuitionistic fuzzy relations with the group Zn and prove some of their fundamental properties. We show that some compositions of Zn-compatible intuitionistic fuzzy relations are also Zn-compatible intuitionistic fuzzy relation. Also, from any given finite intuitionistic fuzzy relation ρ, we can construct two intuitionistic fuzzy relations denoted by ρL and ρU which are compatible with Zn. We have also provided some examples to clarify the notions and results.

Hardly Speaking

2021 ◽  
pp. 96-114
Author(s):  
Aurora Donzelli
Keyword(s):  
Fuzzy Relations ◽  
Folk Theory ◽  
Conventional View

Within anthropological folk theory, rapport has often been understood as pivoting on unproblematic notions of co-presence, fuzzy relations of friendship, and the centrality of denotation—that is, what people talk about, rather than how they talk (see Goebel, Chapters 1 and 2, this volume). Contrary to this conventional view, this chapter focuses on the semiotic and meta-pragmatic components of the ethnographic encounter. Drawing on her gradual and unplanned involvement in the domestic chores of the household where she was hosted, the author describes how during her fieldwork in upland Sulawesi she learned how to make offers and elicit preferences in a pragmatically acceptable way. As her role shifted from being a guest to being a host of her host’s guests, she discovered, through a series of misunderstandings, the role of food-mediated commensality in the reproduction of local hierarchies and developed a new understanding of how ethnographic rapport is built through minute, yet meaningful, instances of conversational exchange.

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