Fuzzy Cone Research Articles

A study on fuzzy sphere and fuzzy cone

In this paper, we investigate three different methods to construct a fuzzy sphere. These methods depend on the entities available to form a fuzzy sphere. In the first method, we formulate a fuzzy sphere when the position of the center and the value of the radius are given imprecisely. In the second method, a fuzzy sphere is constructed when the diameter of a fuzzy sphere is known. In the last method, we construct a fuzzy sphere that passes through four given S-type space fuzzy points whose core points are not co-planar. Also, a rotation invariance property of a fuzzy sphere is investigated. In addition, we show that the intersection of a fuzzy sphere with a crisp plane is a fuzzy circle. In a sequel, the idea of a fuzzy cone is developed. The properties concerned with the intersection of a fuzzy cone with a crisp plane are studied sequentially. All the studies are supported with geometrical interpretations and numerical examples.Moreover, we also develop the algorithms to get the membership grade of a number(i)in the diameter form of the fuzzy sphere and(ii)in the four-point form of the fuzzy sphere.

Analytical Analysis of Common Fixed Point Results in Fuzzy Cone Metric Spaces

The concept of fuzzy sets was introduced by Zadeh (1965) which marked the beginning of the evolution of fuzzy mathematics. The introduction of uncertainty in the theory of sets in a non-probabilistic manner opened up new possibilities for research in this field. Since then, many authors have explored the theory of fuzzy sets and its applications, leading to successful advancements in various fields such as mathematical programming, model theory, engineering sciences, image processing, and control theory. In this paper, we aim to improve and generalize some common fixed point theorems in fuzzy cone metric spaces, an extension of the well-known results given by Saif Ur Rahman and Hong Xu-Li (2017).

Novi pristup Lebegovom integralu u prerađenim fazi konusnim metričkim prostorima pomoću teorema jedinstvene spregnute nepokretne tačke

Introduction/purpose: This article introduces the concept of revised fuzzy cone contraction by using the concept of a traiangular conorm and Revised Fuzzy Cone contractive conditions. Methods: This article established new Revised Fuzzy Cone Contraction (RFC-C) type unique coupled Fixed Point theorems (FP theorems) in revised fuzzy cone metric spaces (RFCMS) by using the triangular property of RFCMS. Results: The obtained results on fixed points in revised fuzzy cone metric spaces generalize some known results in the litrature and present illustrative examples to support the main work. Conclusion: The RFC contractive conditions generalize some important contraction types and examine the existence of a fixed point in revised fuzzy cone metric spaces. In addition, the Lebesgue integral type mapping is applied to get the existence result of a unique coupled fixed point in RFCMS to validate the main work.

On Fixed Point Results for Nonlinear Contractions in Fuzzy Cone Metric Space

The study of Fixed Point Theory in various metric space has been on focus of scientific development for many authors. It has been advanced either by generalizing the contractive inequality or by extending the conditions of metric. Fuzzy metric space has been defined as space in which the distance between elements is not an exact number in difference with metric space. Fixed point Theory is an important framework point of view in fuzzy metric spaces. Many studies have been showed the existence and uniqueness of a fixed point for different type of contractions in these spaces. Nonlinear contractions and their generalizations have been under investigations in several metric spaces. The aim of this paper is the study of fixed points for generalized nonlinear contractions in fuzzy metric space. Our results guarantee the existence and uniqueness of a fixed point for these contractions and extend some known theorems in metric space to fuzzy metric space. As an application of main theorem an example is taken.

Characterization of fuzzy order relation by fuzzy cone

Characterization of fuzzy order relation by fuzzy cone

Generalized contraction theorem in M -fuzzy cone metric spaces

This work defines MM-Fuzzy Cone Metric Space, as a new metric space. It also analyzes possible forms of contractive conditions and groups them accordingly to set up generalized contractive conditions for self-mappings defined over MM-fuzzy cone metric spaces. We prove the existence of fixed points of these mappings and exhibit the same through a suitable example.

A new contribution in fuzzy cone metric spaces by strong fixed point techniques with supportive application

In this manuscript, the concept of a cyclic tripled type fuzzy cone contraction mapping in the setting of fuzzy cone metric spaces is introduced. Also, some theoretical results concerned with tripled fixed points are given without a mixed monotone property in the mentioned space. Moreover, under this concept, some strong tripled fixed point results are obtained. Ultimately, to support the theoretical results non-trivial examples are listed and the existence of a unique solution to a system of integral equations is presented as an application.

Characterization on fuzzy soft ordered Banach algebra

In this paper, we define fuzzy soft ordered Banach algebra with fuzzy soft algebra cone, and introduce the character on fuzzy soft ordered Banach algebra in both cases real and complex. Also, we deduce some of its basic properties and we define a new concept which is a maximal fuzzy soft algebra cone and showing that the set of all fuzzy soft character is isomorphism to the set of all maximal fuzzy soft algebra cone. we prove that the set of all real characters is convex and extreme point, we applied Gelfand- Mazur theorem on fuzzy soft Banach algebra, we showed that character (the set of all complex continuous character) is fuzzy soft ordered Banach algebra. with inverse –closed algebra cone ̆ and a non-zero element in ̆ has inverse we have is an isomorphism to Banach space ( ̆)

Fixed point approach for solving a system of Volterra integral equations and Lebesgue integral concept in F$ _{\text{CM}} $-spaces

<abstract><p>The goal of this manuscript is to obtain some tripled fixed point results under a new contractive condition and triangular property in the context of fuzzy cone metric spaces (F$ _{\text{CM}} $-spaces). Moreover, two examples and corollaries are given to validate our work. Ultimately, as applications, the notion of Lebesgue integral is represented by the fuzzy method to discuss the existence of fixed points. Also, the existence and uniqueness solution for a system of Volterra integral equations are studied by the theoretical results.</p></abstract>

Some Compatible and Weakly-Compatible Four Self-Mapping Results Approach to Nonlinear Integral Equations in Fuzzy Cone Metric Spaces

This paper is aimed at proving some unique common fixed point theorems by using the compatible and weakly-compatible four self-mappings in fuzzy cone metric (FCM) space. We prove the results under the generalized rational contraction conditions in FCM spaces with the help of one self-map are continuous. Furthermore, we prove some rational contraction results with the weaker condition of the self-mapping continuity. Ultimately, our theoretical work has been utilized to prove the existence solution of the two nonlinear integral equations. This is an illustrative application of how FCM spaces can be used in other integral type operators.

Some α − ϕ -Fuzzy Cone Contraction Results with Integral Type Application

In this paper, we define α -admissible and α - ϕ -fuzzy cone contraction in fuzzy cone metric space to prove some fixed point theorems. Some related sequences with contraction mappings have been discussed. Ultimately, our theoretical results have been utilized to show the existence of the solution to a nonlinear integral equation. This application is also illustrative of how fuzzy metric spaces can be used in other integral type operators.

$mathcal{I}$-convergence in Fuzzy Cone Normed Spaces

The aim of this paper is to define and study the concept of $mathcal{I}$-convergence in fuzzy cone normed space which is a generalization of R. Saadati and S. M. Vaezpour type fuzzy normal space. We also obtained some basic properties of $mathcal{I}$-convergence. In fuzzy cone normed space, $mathcal{I}$-limit point and $mathcal{I}$-cluster point were defined and studied.

Fuzzy Cone Normed Linear Space and Some Fixed Point Results for Weakly Compatible Mappings

In this paper, an idea of fuzzy cone normed linear space is introduced with underlying space is Felbin’s type fuzzy Banach space. Some basic results as well as results in finite dimensional fuzzy cone normed linear space are studied. Lastly, some fixed point theorems for weakly compatible mappings are established in such spaces.

Exciting Fixed Point Results under a New Control Function with Supportive Application in Fuzzy Cone Metric Spaces

The objective of this paper is to present a new notion of a tripled fixed point (TFP) findings by virtue of a control function in the framework of fuzzy cone metric spaces (FCM-spaces). This function is a continuous one-to-one self-map that is subsequentially convergent (SC) in FCM-spaces. Moreover, by using the triangular property of a FCM, some unique TFP results are shown under modified contractive-type conditions. Additionally, two examples are discussed to uplift our work. Ultimately, to examine and support the theoretical results, the existence and uniqueness solution to a system of Volterra integral equations (VIEs) are obtained.

Some Rational Coupled Fuzzy Cone Contraction Theorems in Fuzzy Cone Metric Spaces with an Application

In this paper, we establish the new concept of rational coupled fuzzy cone contraction mapping in fuzzy cone metric spaces and prove some unique rational-type coupled fixed-point theorems in the framework of fuzzy cone metric spaces by using “the triangular property of fuzzy cone metric.” To ensure the existence of our results, we present some illustrative unique coupled fixed-point examples. Furthermore, we present an application of a Lebesgue integral-type contraction mapping in fuzzy cone metric spaces and to prove a unique coupled fixed-point theorem.

An Approach of Lebesgue Integral in Fuzzy Cone Metric Spaces via Unique Coupled Fixed Point Theorems

In the theory of fuzzy fixed point, many authors have been proved different contractive type fixed point results with different types of applications. In this paper, we establish some new fuzzy cone contractive type unique coupled fixed point theorems (FP-theorems) in fuzzy cone metric spaces (FCM-spaces) by using “the triangular property of fuzzy cone metric” and present illustrative examples to support our main work. In addition, we present a Lebesgue integral type mapping application to get the existence result of a unique coupled FP in FCM-spaces to validate our work.

Some New Coupled Fixed-Point Findings Depending on Another Function in Fuzzy Cone Metric Spaces with Application

In this paper, we introduce the new concept of coupled fixed-point (FP) results depending on another function in fuzzy cone metric spaces (FCM-spaces) and prove some unique coupled FP theorems under the modified contractive type conditions by using “the triangular property of fuzzy cone metric.” Another function is self-mapping continuous, one-one, and subsequently convergent in FCM-spaces. In support of our results, we present illustrative examples. Moreover, as an application, we ensure the existence of a common solution of the two Volterra integral equations to uplift our work.

Some set-valued and multi-valued contraction results in fuzzy cone metric spaces

This paper aims to present the concept of multi-valued mappings in fuzzy cone metric spaces and prove some basic lemmas, a Hausdorff metric, and fixed point results for set-valued fuzzy cone-contraction and for multi-valued fuzzy cone-contraction mappings. We prove a fixed point theorem for multi-valued rational type fuzzy cone-contractions in fuzzy cone metric spaces. Our results extend and improve some results given in the literature.

Rational Fuzzy Cone Contractions on Fuzzy Cone Metric Spaces with an Application to Fredholm Integral Equations

This paper is aimed at proving some common fixed point theorems for mappings involving generalized rational-type fuzzy cone-contraction conditions in fuzzy cone metric spaces. Some illustrative examples are presented to support our work. Moreover, as an application, we ensure the existence of a common solution of the Fredholm integral equations: μ τ = ∫ 0 τ Γ τ , v , μ v d v and ν τ = ∫ 0 τ Γ τ , v , ν v d v , for all μ ∈ U , v ∈ 0 , η , and 0 < η ∈ ℝ , where U = C 0 , η , ℝ is the space of all ℝ -valued continuous functions on the interval 0 , η and Γ : 0 , η × 0 , η × ℝ ⟶ ℝ .

Integrable functions of fuzzy cone and ξ - fuzzy cone and their application in the fixed point theorem

The purpose of this study is to present the idea of an f-partition for a closed interval. Additionally, we introduce a new notion for fuzzy cone metric spaces called a fuzzy cone integrable function and prove fundamental fixed-point theorems. Moreover, we develop the concept of a ξ -fuzzy cone integrable function. Finally, we present new results of the fixed- point theorem for ξ -fuzzy cone integrable functions.