scholarly journals Types of Complex Fuzzy Relations with Applications in Future Commission Market

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Madad Khan ◽  
Muhammad Zeeshan ◽  
Seok-Zun Song ◽  
Sohail Iqbal
Keyword(s):  
Fuzzy Sets ◽  
Equivalence Relation ◽  
Order Relation ◽  
Fuzzy Relations ◽  
Inverse Relation ◽  
Transitive Relation ◽  
Temporal Dependence ◽  
Symmetric Relation ◽  
Asymmetric Relation ◽  
Fuzzy Order

In this paper, we introduce types of relations on complex fuzzy sets such as the complex fuzzy (CF) inverse relation, complex fuzzy reflexive relation, complex fuzzy symmetric relation, complex fuzzy antisymmetric relation, complex fuzzy transitive relation, complex fuzzy irreflexive relation, complex fuzzy asymmetric relation, complex fuzzy equivalence relation, and complex fuzzy-order relation. We study some basic results and particular examples of these relations. Moreover, we discuss the applications of complex fuzzy relations in Future Commission Market (FCM). We show that the introduction of CF relations to applications of FCMs can give a significant method for describing the temporal dependence between parameters of a Future Commission Market.

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 Aggregation of Indistinguishability Fuzzy Relations Revisited

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1441
Author(s):  
Juan-De-Dios González-Hedström ◽  
Juan-José Miñana ◽  
Oscar Valero
Keyword(s):  
Equivalence Relation ◽  
Fuzzy Relations ◽  
Measure Of Similarity ◽  
Dual Notion ◽  
The Relationship

Indistinguishability fuzzy relations were introduced with the aim of providing a fuzzy notion of equivalence relation. Many works have explored their relation to metrics, since they can be interpreted as a kind of measure of similarity and this is, in fact, a dual notion to dissimilarity. Moreover, the problem of how to construct new indistinguishability fuzzy relations by means of aggregation has been explored in the literature. In this paper, we provide new characterizations of those functions that allow us to merge a collection of indistinguishability fuzzy relations into a new one in terms of triangular triplets and, in addition, we explore the relationship between such functions and those that aggregate extended pseudo-metrics, which are the natural distances associated to indistinguishability fuzzy relations. Our new results extend some already known characterizations which involve only bounded pseudo-metrics. In addition, we provide a completely new description of those indistinguishability fuzzy relations that separate points, and we show that both differ a lot.

On Convexity of Fuzzy Sets and Fuzzy Relations

1992 ◽  
Vol 59 (1-2) ◽  
pp. 91-102
Author(s):  
Xu Chen-Wei
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Relations

scholarly journals New Hermite–Hadamard-type inequalities for "Equation missing" No EquationSource Format="TEX", only image -convex fuzzy-interval-valued functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Muhammad Bilal Khan ◽  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Yu-Ming Chu
Keyword(s):  
Order Relation ◽  
Interval Space ◽  
Fuzzy Order ◽  
Interval Valued ◽  
Fuzzy Interval

AbstractIn this paper, we introduce the non-convex interval-valued functions for fuzzy-interval-valued functions, which are called "Equation missing"-convex fuzzy-interval-valued functions, by means of fuzzy order relation. This fuzzy order relation is defined level-wise through Kulisch–Miranker order relation given on the interval space. By using the "Equation missing"-convexity concept, we present fuzzy-interval Hermite–Hadamard inequalities for fuzzy-interval-valued functions. Several exceptional cases are debated, which can be viewed as useful applications. Interesting examples that verify the applicability of the theory developed in this study are presented. The results of this paper can be considered as extensions of previously established results.

scholarly journals Some new Jensen, Schur and Hermite-Hadamard inequalities for log convex fuzzy interval-valued functions

2021 ◽  
Vol 7 (3) ◽  
pp. 4338-4358
Author(s):  
Muhammad Bilal Khan ◽  
◽  
Hari Mohan Srivastava ◽  
Pshtiwan Othman Mohammed ◽  
Kamsing Nonlaopon ◽  
...  
Keyword(s):  
Convex Functions ◽  
Optimization Problems ◽  
Fuzzy Optimization ◽  
Order Relation ◽  
Inclusion Relation ◽  
Nonconvex Functions ◽  
New Directions ◽  
Fuzzy Order ◽  
Interval Valued ◽  
Fuzzy Interval

<abstract> <p>The inclusion relation and the order relation are two distinct ideas in interval analysis. Convexity and nonconvexity create a significant link with different sorts of inequalities under the inclusion relation. For many classes of convex and nonconvex functions, many works have been devoted to constructing and refining classical inequalities. However, it is generally known that log-convex functions play a significant role in convex theory since they allow us to deduce more precise inequalities than convex functions. Because the idea of log convexity is so important, we used fuzzy order relation $\left(\preceq \right)$ to establish various discrete Jensen and Schur, and Hermite-Hadamard (H-H) integral inequality for log convex fuzzy interval-valued functions (L-convex F-I-V-Fs). Some nontrivial instances are also offered to bolster our findings. Furthermore, we show that our conclusions include as special instances some of the well-known inequalities for L-convex F-I-V-Fs and their variant forms. Furthermore, we show that our conclusions include as special instances some of the well-known inequalities for L-convex F-I-V-Fs and their variant forms. These results and different approaches may open new directions for fuzzy optimization problems, modeling, and interval-valued functions.</p> </abstract>

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 New fuzzy-interval inequalities in fuzzy-interval fractional calculus by means of fuzzy order relation

2021 ◽  
Vol 6 (10) ◽  
pp. 10964-10988
Author(s):  
Muhammad Bilal Khan ◽  
◽  
Pshtiwan Othman Mohammed ◽  
Muhammad Aslam Noor ◽  
Abdullah M. Alsharif ◽  
...  
Keyword(s):  
Interval Analysis ◽  
Order Relation ◽  
Strong Relationship ◽  
Data Uncertainty ◽  
Hadamard Inequality ◽  
Special Cases ◽  
Fejér Inequality ◽  
Fuzzy Order ◽  
Interval Valued ◽  
Fuzzy Interval

<abstract> <p>It is well-known that interval analysis provides tools to deal with data uncertainty. In general, interval analysis is typically used to deal with the models whose data are composed of inaccuracies that may occur from certain kinds of measurements. In interval analysis and fuzzy-interval analysis, the inclusion relation (⊆) and fuzzy order relation $\left(\preccurlyeq \right)$ both are two different concepts, respectively. In this article, with the help of fuzzy order relation, we introduce fractional Hermite-Hadamard inequality (<italic>HH</italic>-inequality) for <italic>h</italic>-convex fuzzy-interval-valued functions (<italic>h</italic>-convex-IVFs). Moreover, we also establish a strong relationship between <italic>h</italic>-convex fuzzy-IVFs and Hermite-Hadamard Fejér inequality (<italic>HH</italic>-Fejér inequality) via fuzzy Riemann Liouville fractional integral operator. It is also shown that our results include a wide class of new and known inequalities for <italic>h</italic>-convex fuzz-IVFs and their variant forms as special cases. Nontrivial examples are presented to illustrate the validity of the concept suggested in this review. This paper's techniques and approaches may serve as a springboard for further research in this field.</p> </abstract>

On type-2 fuzzy relations and interval-valued type-2 fuzzy sets

2014 ◽  
Vol 236 ◽  
pp. 1-32 ◽  
Author(s):  
Bao Qing Hu ◽  
Chun Yong Wang
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Relations ◽  
Interval Valued
Sign in / Sign up

Export Citation Format

Share Document