scholarly journals Interval Information Content of Fuzzy Relation and the Application in the Fuzzy Implication Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yiying Shi
Keyword(s):  
Information Content ◽  
Similarity Measure ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Fuzzy Implication ◽  
Solid Foundation ◽  
Rule Optimization ◽  
Interval Comparison

In rule optimization, some rule characteristics were extracted to describe the uncertainty correlations of fuzzy relations, but the concrete numbers cannot express correlations with uncertainty, such as “at least 0.1 and up to 0.5.” To solve this problem, a novel definition concerning interval information content of fuzzy relation has been proposed in this manuscript to realize the fuzziness measurement of the fuzzy relation. Also, its definition and expressions have also been constructed. Meanwhile based on the interval information content, the issues of fuzzy implication ranking and clustering were analyzed. Finally, utilizing the combination of possibility’s interval comparison equations and interval value’s similarity measure, the classifications of implication operators were proved to be realizable. The achievements in the presented work will provide a reasonable index to measure the fuzzy implication operators and lay a solid foundation for further research.

scholarly journals Fuzzy Functional and Multivalued Dependencies for Frank’s Class of Additive Generators

2021 ◽  
Vol 15 ◽  
pp. 8-22
Author(s):  
Sanela Nesimovic ◽  
Dzenan Gusic
Keyword(s):  
Fuzzy Relation ◽  
Inference Rules ◽  
Fuzzy Relations ◽  
Fuzzy Implication ◽  
Resolution Principle ◽  
Multivalued Dependency

In this paper we consider all possible dependencies that can be built upon similarity-based fuzzy relations, that is, fuzzy functional and fuzzy multivalued dependencies. Motivated by the fact that the classical obtaining of new dependencies via inference rules may be tedious and uncertain, we replace it by the automated one, where the key role is played by the resolution principle techniques and the fuzzy formulas in place of fuzzy dependencies. We prove that some fuzzy multivalued dependency is actively correct with respect to given fuzzy relation instance if and only if the corresponding fuzzy formula is in line with the attached interpretation. Additionally, we require the tuples of the instance to be conformant (up to some extent) on the leading set of attributes. The equivalence as well as the conclusion are generalized to sets of attributes. The research is conducted by representing the attributes and fuzzy dependencies in the form of fuzzy formulas, and the application of fuzzy implication operators derived from carefully selected Frank’s classes of additive generators

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.

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 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.

Generating Fuzzy Sets and Fuzzy Relations Based on Information

2021 ◽  
Vol 20 ◽  
pp. 178-185
Author(s):  
Radwan Abu- Gdairi ◽  
Ibrahim Noaman
Keyword(s):  
Fuzzy Sets ◽  
Knowledge Discovery ◽  
Set Theory ◽  
Membership Function ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Relation ◽  
Knowledge Discovery In Databases ◽  
Fuzzy Relations

Fuzzy set theory and fuzzy relation are important techniques in knowledge discovery in databases. In this work, we presented fuzzy sets and fuzzy relations according to some giving Information by using rough membership function as a new way to get fuzzy set and fuzzy relation to help the decision in any topic . Some properties have been studied. And application of my life on the fuzzy set was introduced

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