جستجوی مقالات مرتبط با کلیدواژه « fuzzy set » در نشریات گروه « ریاضی »

‎When it comes to solving dynamic‎ ‎programming challenges‎, ‎it is essential to have a well-structured ‎‎‎‎decision theory‎. ‎As a result‎, ‎the decision-makers must operate in a‎ ‎dynamically complicated environment where appropriate and rapid‎ ‎reaction in a cooperative way is the fundamental key to effectively‎ ‎completing the task‎. ‎We express a theory of decision modeling and‎ ‎axiomatizing a decision-making process‎. ‎The payoffs and‎ ‎probabilities are represented with simplified neutrosophic sets‎. ‎We‎ ‎therefore‎, ‎provide the theory of choice with the implementation of‎ ‎simplified neutrosophic sets‎. ‎By exploiting the idea of pure‎ ‎strategy‎, ‎we introduce two steps‎: ‎in the first step‎, ‎for each‎ ‎attractive point‎, ‎some particular event is selected that can bring‎ ‎about a relatively neutrosophic upper payoff with a relatively‎ ‎neutrosophic upper probability or a relatively neutrosophic lower‎ ‎payoff with a relatively neutrosophic upper probability‎. ‎A‎ ‎decision-maker selects the most favored attractive point in the‎ ‎second stage‎, ‎based on the focus on all attractive points‎. ‎Neutrosophic focus theory has been introduced to improve overall‎ ‎performance with more flexibility in complex decision-making‎. ‎The‎ ‎approach suggested in this work has been implemented in a real-life‎ ‎example to determine its effectiveness‎. ‎The proposed method is shown to‎ ‎be the most useful for ranking scenarios and addressing dynamic‎ ‎programming problems in decision-making‎.

This article focuses on evaluating the success or failure of kidney transplantation using Shannon entropy‎, ‎fuzzy sets‎, ‎and Scaf‎. ‎The data for Scaf references used in this study for both healthy individuals and kidney transplant recipients have been collected from the relevant literature‎. ‎For both groups‎, ‎Scaf's Shannon entropy values have been calculated using an appropriate probability density function and formulation‎, ‎and sequences have been generated for CAF and Scr biomarkers from entropy values‎, ‎with findings interpreted‎. ‎These sequences are called healing sequences‎. ‎A case study demonstrating whether the transplant procedure was successful or unsuccessful was presented using sequences that we refer to as healing sequences‎. ‎In this context‎, ‎the utilization of mathematical tools such as fuzzy sets‎, ‎Shannon entropy‎, ‎and reference intervals becomes evident‎. ‎These tools provide a systematic and quantitative approach to assessing the outcomes of kidney transplantation‎. ‎By leveraging the principles of Shannon entropy‎, ‎we gain insights into the degree of unpredictability and fuzziness associated with biomarker values‎, ‎which can be indicative of the transplant's success‎.
‎Furthermore‎, ‎the concept of healing sequences provides a valuable framework for tracking the progression of patients post-transplantation‎. ‎By monitoring changes in CAF and Scr biomarkers over time‎, ‎healthcare professionals can make informed decisions and interventions to ensure the well-being of kidney transplant recipients‎.

The present study aims to described the concept of trapezoidal fuzzy multi number aggregation operators and also provide its application in architecture. Our main focus is on the trapezoidal fuzzymulti number weighted arithmetic average (TFMNWAA) operator, the trapezoidal fuzzy multi numberweighted geometric average (TFMNWGA) operator and trapezoidal fuzzy multi-number hybrid aggregation (TFMNHA) operator along with their developable properties. Then the notion of the score function of ranking the trapezoidal fuzzy multi numbers is defined. We apply the TFMNHA operator to multi criteria decision making trapezoidal fuzzy multi number. Finally, a comparative analysis is presented with a numerical example is provided to show its applicability and usefulness.

In our paper, we continue the study of the theory of fuzzy soft sets and their properties. Based on the singular values of the corresponding matrix, we define the energy of a fuzzy soft set, as well as the $\lambda$-energy of a fuzzy soft set, allowing us to introduce an effective method for decision-making. Then, we consider the limits of the defined energies, which are essentially non-negative numerical values. The paper demonstrates through examples how the introduced method can be successfully applied to many problems containing uncertainties. Additionally, the paper includes comparisons of the introduced method with other methods addressing similar problems.

In 2000, exponential trapezoidal fuzzy numbers were defined for the first time by Chen and Lie [3] without investigating the definition and properties of fuzzy numbers for them.  Therefore, in this paper first, some necessary definitions and the difference between fuzzy numbers and fuzzy quantities are presented. Then, the correctness of the definition of exponential trapezoidal fuzzy numbers is investigated. It is concluded that exponential trapezoidal fuzzy numbers do not satisfy general conditions of fuzzy numbers such as bounded amplitude and continuity. In fact, these are fuzzy quantities not fuzzy numbers. As a result, a ranking method is proposed for such quantities to be examined using common tools and test platforms that exist for ranking fuzzy quantities. Moreover, the strength and weaknesses of the method are reported.

Given a uniform space (X, U), we introduce, from the uniformity U, some uniformities on the set F(X) of all normal, upper semicontinuous with compact support fuzzy sets on X: the Skorokhod uniformity, the level-wise uniformity, the endograph uniformity and the sendograph uniformity. For metric spaces we prove that these uniformities coincide with the uniformities induced by the Skorokhod metric (the level-wise metric, the endograph metric and the sendograph metric, respectively). We study completeness of this class of uniform spaces.

Zadeh extended in 1965 crisp sets to the concept of fuzzy set (FS) on the purpose of tackling mathematically the partial truths and the definitions with no clear boundaries. In a later stage FSs were extensively used for tackling the existing in the real world uncertainty. Neutrosophic sets (NSs) are extensions of FSs in which each element of the universal set is characterized, apart from Zadeh’s membership degree, by the degrees of non-membership and indeterminacy. Grey numbers (GNs) are real numbers with known range, represented by a closed real interval, but with unknown exact value. GNs and NSs are used in this paper as tools for assessment processes under fuzzy conditions. The use of GNs enables the evaluation of the mean performance of a group of objects when qualitative grades (linguistic expressions) are used for the individual assessment of its members. The use of NSs, on the other hand, is useful for assessing the overall performance of a group, when one, due to incomplete assessment data, is not sure about the exactness of the grades assigned to its members. It is concluded that the suitable combination of two or more theories related to FSs give better assessment outcomes in general. Examples are also presented on student assessment illustrating our results.

‎After the introduction of the concept of fuzzy sets‎ ‎by Zadeh‎, ‎several researches were conducted on‎ ‎the generalizations of the notion of fuzzy sets‎. ‎There are many viewpoints on the notion of metric space in fuzzy topology‎. ‎One of the most important problems in fuzzy topology is obtaining an appropriate concept of fuzzy metric space‎. ‎This problem has been investigated by many authors from different points of view‎. ‎Atanassov gives the concept of the intuitionistic fuzzy set as a generalization of the fuzzy set‎. ‎Park introduced the notion of intuitionistic fuzzy metric space as a natural generalization of fuzzy metric spaces due to George and Veeramani‎. ‎This paper introduces the concept of intuitionistic fuzzy modular space‎. ‎Afterward‎, ‎a Hausdorff topology induced by a $\delta$-homogeneous intuitionistic fuzzy modular is defined and some related topological properties are also examined‎. ‎After giving the fundamental definitions and the necessary examples‎, ‎we introduce the definitions of intuitionistic fuzzy boundedness‎, ‎intuitionistic fuzzy compactness‎, ‎and intuitionistic fuzzy convergence‎, ‎and obtain several preservation properties and some characterizations concerning them‎. ‎Also‎, ‎we investigate the relationship between an intuitionistic fuzzy modular and an intuitionistic fuzzy metric‎. ‎Finally‎, ‎we prove some known results of metric spaces including Baire’s theorem and the Uniform limit theorem for intuitionistic fuzzy modular spaces‎.

In this paper, the notion of fuzzy $(\theta, \mathcal {L})$-weak contraction in $\mathbb{G}-$metric space is introduced, and sufficient conditions for the existence of fuzzy fixed points for such mappings are investigated. Relevant illustrative examples are constructed to support the assumptions of our established theorems. It is observed that the principal ideas obtained herein extend and subsume some well-known results in the corresponding literature. A few of these special cases of our results are noted and discussed as corollaries

The picture fuzzy sets are very useful in those uncertain problems which could not be solved by fuzzy sets, intuitionistic fuzzy sets, Pythagorean fuzzy sets, fermatean fuzzy sets, and q-rung orthopair fuzzy sets. For example, medical diagnosis, personnel selection, human voting, etc. All of these problems require answers of the type no, yes, abstain, and refusal. To compare two picture fuzzy sets, the distance measures play an important role. There are a lot of studies about the distance measures of picture fuzzy sets available in the literature. However, all of these distance measures lead to unreasonable results in most of the problems. So, we in this paper suggest a new distance measure for picture fuzzy sets that is more effective than all of the available distance measures. We also demonstrate its utility in classification and diagnostic problems and contrast its performance with the available ones.

In this paper, we have characterized big data fuzzy sets and shown that topological data points form singleton fuzzy sets which are closed. Besides, fuzzy sets of topological data points are compact and have at least one closed point. We have also shown that the fuzzy set of all condensation points of a fuzzy Hausdor  space is in nite and the cardinality of a topological data fuzzy set is also in nite and arbitrarily distributed in fuzzy Hausdor  spaces.

In this work, we develop a reasoning mechanism under uncertainty for a typical class of decision making problems based on the theory of fuzzy soft set. Accordingly, we consider a logic of fuzzy soft sets. In the sequel, implication operations dealing with fuzzy soft sets over different universal sets and different sets of parameters have been studied extensively. An algorithm for rule based reasoning has been developed for a modus ponens type rule of inference using the proposed logical structure. The entire proposal is illustrated with an example. Results of application of our proposed inference are compared with those obtained by Mondal and Raha on the problem of management of hypertension using a medical diagnostic support system.

The aim of this paper is to introduce the concepts of $alpha$-continuity, $eta$-admissible pair for fuzzy set-valued maps and define a notion of fuzzy $eta-(psi, F)$-contraction. The existence of common fuzzy fixed points for such contraction is investigated in the setting of a complete metric space. The ideas presented herein complement the results of Wardowski, Banach, Heilpern and other results on point-to-point and point-to-set-valued mappings in the comparable literature of metric and fuzzy fixed point theory. A few important of these consequences of our results are highlighted and discussed. Some nontrivial examples and an application to a system of integral inclusions of Fredholm type are considered to support our theorems and to illustrate a usability of the results obtained herein.

Ranking generalized fuzzy numbers plays an important role in many applied models and, in particular, decision-making procedures. In ranking process of two generalized fuzzy numbers, it is natural to compare the sets of values in support of two generalised fuzzy numbers. Accordingly, the comparison of a real number and a generalised fuzzy number as well as two generalised fuzzy numbers have to be considered. On the other hand, it is seen that a definitive process of comparison of a real number and a generalised fuzzy number, as well as two generalised fuzzy numbers, is not possible. So in this study, a method for comparing a real number and a generalised fuzzy number with a degree of accuracy (between a zero and one) is defined and then the method is generalized to compare two generalised fuzzy numbers. In general, an index to rank a real number and generalised fuzzy number is constructed. Eventually, this index is extended to rank two generalised fuzzy numbers based on the concept of accuracy of comparison. The advantage of our method is that it can compare two generalised fuzzy numbers with an accuracy of comparison. Also, a definition is introduced to make a definitive comparison. Finally, the proposed method is illustrated by some numerical examples.

In this paper, two novel extensions of Banach and Meir-Keeler fixed point theorems for $L$-fuzzy set-valued map defined on a complete metric space are presented by using new general contractive conditions under suitable assumptions. In the case when the $L$-fuzzy set-valued map is reduced to its crisp counterparts, our obtained concepts herein generalize several significant fixed point theorems of point-to-point and point-to-set valued mappings in the comparable literature. We provide non-trivial examples to validate the hypotheses of our results.

Conventional mathematical tools which require all inferences to be exact, are not always sufficient to handle imprecisions in a wide variety of practical fields. Thus, among various developments in fuzzy mathematics, enormous efforts have been in process to produce new fuzzy analogues of the classical fixed point results and their various applications. Following this line in this paper, a new type of set-valued mapping whose range set lies in a family of soft sets is examined. To this effect, we introduce a few fixed point theorems which are generalizations of several significant fixed point results of point-to-point and point-to-set valued mappings in the comparable literature. Some of these particular cases are noted and analyzed. Moreover, nontrivial examples are provided to support the assumptions of our main results.

We prove that every fuzzy generalized bi-Γ-ideal and every fuzzy interior Γ-ideal in a right weakly regular ordered Γ-semigroup is a fuzzy Γ-ideal. We also show that every fuzzy generalized bi-Γ-ideal in a duo right weakly regular ordered Γ-semigroup is a fuzzy interior Γ-ideal. Then, by using fuzzy Γ-ideals, fuzzy bi-Γ-ideals, fuzzy generalized bi-Γ-ideals and fuzzy interior Γ-ideals, left simple, right simple and simple ordered Γ-semigroups have been characterized. Finally we characterize right weakly regular ordered Γ-semigroup by its fuzzy Γ-ideals, fuzzy bi-Γ-ideals, fuzzy generalized bi-Γ-ideals and fuzzy interior Γ-ideals.

Hypersoft set is an extension of the soft set where there is more than one set of attributes occur and it is very much helpful in multi-criteria group decision making problem. In a hypersoft set, the function F is a multi-argument function. In this paper, we have used the notion of Fuzzy Hypersoft Set (FHSS), which is a combination of fuzzy set and hypersoft set. In earlier research works the concept of Fuzzy Soft Set (FSS) was introduced and it was applied successfully in various fields. The FHSS theory gives more flexibility as compared to FSS to tackle the parameterized problems of uncertainty. To overcome the issue where FSS failed to explain uncertainty and incompleteness there is a dire need for another environment which is known as FHSS. It works well when there is more complexity involved in the parametric data i.e the data that involves vague concepts. This work includes some basic set-theoretic operations on FHSSs and for the reliability and the authenticity of these operations, we have shown its application with the help of a suitable example. This example shows that how FHSS theory plays its role to solve real decision-making problems.

In this article, first the aggregation operator and the operational waves in the oscillators are introduced. Next, we choose a demanded Electrical waveform in the demanded oscillator using a model have been done. We use the fuzzy soft aggregation operator in the oscillators on L2 space at the method can be successfully applied to many problems that contain uncertainties. Our simulation is done with R software.

Given a metric space X, we consider the family of all normal upper semicontinuous fuzzy sets on X, denoted by $mathcal{F}(X)$, and a discrete dynamical system $(X,f)$. In this paper, we study when $(mathcal{F}(X), widehat{f})$ is (strongly) sensitive, where $widehat{f}$ is the Zadeh's extension of f and $mathcal{F}(X)$ is equipped with different metrics: The uniform metric, the Skorokhod metric, the sendograph metric and the endograph metric. We prove that the sensitivity in the induced dynamical system $(mathcal{K}(X),overline{f})$ is equivalent to the sensitivity in $ widehat{f} :mathcal{F}(X)to mathcal{F}(X) $ with respect to the uniform metric, the Skorokhod metric and the sendograph metric. We also show that the following conditions are equivalent:item {rm a)} $(X,f)$ is strongly sensitive;item {rm b)} $(mathcal{F}(X), widehat{f})$ is strongly sensitive, where $mathcal{F}(X)$ is equipped with the uniform metric;item {rm c)} $(mathcal{F}(X), widehat{f})$ is strongly sensitive, where $mathcal{F}(X)$ is equipped with the Skorokhod metric;item {rm d)} $(mathcal{F}(X), widehat{f})$ is strongly sensitive, where $mathcal{F}(X)$ is equipped with the sendograph metric.