Mehmet Ünver

Ankara University · Department of Mathematics

The concept of continuous function valued q-rung orthopair fuzzy set (CFVq ROFS) represents an innovative framework within fuzzy set theory, where the assessment of an element’s membership and non-membership degrees is accomplished through continuous functions. This paper introduces a novel entropy measure for CFVq ROFS, employing the Riemann integ...

In this short correspondence, we introduce some novel cosine similarity measures tailored for \(q\)-rung orthopair fuzzy sets (\(q\)-ROFSs), which capture both the direction and magnitude aspects of fuzzy set representations. Traditional cosine similarity measures focus solely on the direction (cosine of the angle) between vectors, neglecting the c...

This paper presents novel concepts in fuzzy topologies, namely q -rung orthopair picture fuzzy ( q -ROPF) topology and q -rung orthopair picture fuzzy point ( q -ROPFP). These concepts extended the existing notions in fuzzy topologies. We introduced a more relaxed form of continuity, called q ε -ROPF continuity, which allows for a flexible analysis...

The paper aims is to present a multi-criteria decision-making algorithm for solving decision-making problems with the utilization of the C-IFSs (circular intuitionistic fuzzy sets) features. In it, the uncertainties present in the data are handled with the help of C-IFSs in which we considers the circular rating of each object within a certain radi...

In this paper, we introduce the concept of circular Pythagorean fuzzy set (value) (C-PFS(V)) as a new generalization of both circular intuitionistic fuzzy sets (C-IFSs) proposed by Atannassov and Pythagorean fuzzy sets (PFSs) proposed by Yager. A circular Pythagorean fuzzy set is represented by a circle that represents the membership degree and the...

This AI-generated visualization of fuzzy set theory takes on a creative approach, transforming the abstract concepts of fuzzy set theory into a visually engaging artwork. The use of colors, shapes, patterns, and other artistic elements likely adds a layer of symbolism or metaphor to convey the essence of fuzzy set theory in a unique and visually st...

As an extension of the concepts of fuzzy set and intuitionistic fuzzy set, the concept of Pythagorean fuzzy set better models some real life problems. Distance, entropy, and similarity measures between Pythagorean fuzzy sets play important roles in decision making. In this paper, we give a new entropy measure for Pythagorean fuzzy sets via the Suge...

The objective of this study is to introduce sine trigonometric weighted arithmetic aggregation operators for multi-criteria group decision making in complex intuitionistic fuzzy environment. Specifically, the study focuses on the Dombi aggregation operators and defines the Euclidean distance and Hamming distance between complex intuitionistic fuzzy...

Fuzzy sets, which have a crucial role in the decision making theory, model uncertainty by means of membership and non-membership functions. q-rung orthopair fuzzy sets, which are the natural extension of fuzzy, intuitionistic fuzzy and Pythagorean fuzzy sets, are quite successful in modeling data thanks to their larger domains. However, in a q-rung...

In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutros...

The primary aim of the notion of consistency fuzzy set (CFS) is to model the uncertain information given in a fuzzy multi environment and so to obtain meaningful data from the fuzzy multi-sets and to present this data in a compact form via some statistical tools. The data collected by fuzzy multi-sets are processed via CFSs and a sort of data scien...

In probability theory, uniform integrability of families of random variables or random elements plays an important role in the mean convergence. In this paper, we introduce a new version of uniform integrability for sequences in normed spaces in the weak sense. We study the relationship of this new concept with summability theory by considering sta...

In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacyand the falsity, which is a new extension of intuitionistic fuzzy valued neutroso...

Korovkin type approximation via summability methods is one of the recent interests of the mathematical analysis. In this paper, we prove some Korovkin type approximation theorems in \(L_{q}[a,b]\), the space of all measurable real valued qth power Lebesgue integrable functions defined on [a, b] for \(q\ge 1\), and C[a, b], the space of all continuo...

In this paper, we introduce the concept of circular Pythagorean fuzzy set (value) (C-PFS(V)) as a new generalization of both circular intuitionistic fuzzy sets (C-IFSs) proposed by Atannassov and Pythagorean fuzzy sets (PFSs) proposed by Yager. A circular Pythagorean fuzzy set is represented by a circle that represents the membership degree and the...

In fuzzy set theory, the aggregation is the process that combines input fuzzy sets into a single output fuzzy set. In this manner, an aggregation operator is an important tool in the fuzzy set theory and its applications. The purpose of this study is to present some algebraic operators among neutrosophic enthalpy values and to provide some aggregat...

In this paper, we establish a relationship between the concepts of P-strong, P-statistical convergences and P-uniform integrability where P stands for a power series method. We also prove that if a power series method has a summability function, then the space of all P-statistically convergent sequences cannot be endowed with a local convex FK-topo...

The concept of entropy is one of the most important notions of the information theory. Entropy quanties the amount of uncertainty involved in the value of a random variable or the outcome of a random process. Shannon's entropy is one of the most useful entropy types. The notion of enthalpy is the information energy expressed by the complement of Sh...

The notion of trigonometric similarity measure (SM) for spherical fuzzy sets (SFSs) has become very important in solving various problems in pattern recognition and medical diagnosis. This study proposes some trigonometric SMs with the help of Choquet integral for SFSs. The proposed trigonometric SMs clearly satisfy the axiomatic definition of clas...

Равномерная интегрируемость является важным понятием в теории вероятностей и в функциональном анализе, поскольку играет важную роль в установлении законов больших чисел. В литературе можно найти различные варианты понятия равномерной интегрируемости. Некоторые из них определяются с помощью матричных методов суммирования, например суммирования по ма...

A single-valued neutrosophic multi-set is characterized by a sequence of truth membership degrees, a sequence of indeter-minacy membership degrees and a sequence of falsity membership degrees. Nature of a single-valued neutrosophic multi-set allows us to consider multiple information in the truth, indeterminacy and falsity memberships which is pret...

The concept of Choquet integral that a special ordered weighted averaging operator (OWA) is an aggregation function and it generalizes the concepts of arithmetic and the weighted mean. This concept allows us to model interaction between criteria with the help of a fuzzy measure. Our aim is to combine fuzzy set theory and fuzzy measure theory by usi...

In this article, the concept of \({\mathcal {J}}\)-uniform integrability of a sequence of random variables \(\left\{ X_{k}\right\} \) with respect to \(\left\{ a_{nk} \right\} \) is introduced where \({\mathcal {J}}\) is a non-trivial ideal of subsets of the set of positive integers and \(\left\{ a_{nk} \right\} \) is an array of real numbers. We s...

Medical diagnosis is a disease identification process that matches symptoms with diseases based on the symptoms of target patient. In this process, it is necessary to establish a similarity relation between symptoms and diseases so as to determine the correct diagnosis. Similarity measure theory is a beneficial way that is used to model this relati...

In this chapter, we propose ten trigonometric similarity measures based on the Choquet integral for Pythagorean fuzzy sets using the trigonometric functions cosine and cotangent. We show that the proposed trigonometric similarity measures are more sensitive expansions of some existing trigonometric similarity measures. Subsequently, we give applica...

As an extension of the concepts of fuzzy set, intuitionistic fuzzy set, interval valued fuzzy set and interval valued intuitionistic fuzzy set, the concept of neutrosophic set has been developed to represent uncertain, imprecise, incomplete and inconsistent information that exists in the real life problems. The class of simplified neutrosophic sets...

In this paper, we define the concept of Pythagorean fuzzy point. We define a similarity measure between Pythagorean fuzzy points, and we give an application of this similarity measure in pattern recognition. We also introduce a new type of continuity for the functions defined between two Pythagorean fuzzy topological spaces. Moreover, we introduce...

In this correspondence, for a nonnegative regular summability matrix B and an array \(\left\{ a_{nk}\right\} \) of real numbers, the concept of B-statistical uniform integrability of a sequence of random variables \(\left\{ X_{k}\right\} \) with respect to \(\left\{ a_{nk}\right\} \) is introduced. This concept is more general and weaker than the c...

In this correspondence, for an array {Xnk:un≤k≤vn,n∈N} of integrable random elements in a real separable Banach space and an array {ank:un≤k≤vn,n∈N} of real numbers, a new type of compact uniform integrability is introduced and it is used to obtain degenerate mean convergence theorems for the weighted sums ∑k=unvnank(Xnk−EXnk),n∈N. More specificall...

In this paper, we introduce the concept of A-statistical uniform integrability of sequences of random variables which is not only more general than the concept of uniform integrability, but is also weaker than the concept of uniform integrability. We also give some characterizations of A-statistical uniform integrability and prove a law of large nu...

In this paper we investigate the distance of convergence in measure whenever the measure is not σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}...

In this paper we investigate some Korovkin type approximation properties of the q-Meyer-K\"onig and Zeller operators and Durrmeyer variant of the q-Meyer-K\"onig and Zeller operators via Abel summability method which is a sequence-to-function transformation and which extends the ordinary convergence. We show that the approximation results obtained...

In the present paper, we introduce the notion of Pythagorean fuzzy topological space by motivating from the notion of fuzzy topological space. We define Pythagorean fuzzy continuity of a function defined between Pythagorean fuzzy topological spaces and we characterize this concept. Using the concept of continuity, we also give a method to construct...

In this article we introduce the concepts of Pp-statistical convergence and Pp-strong convergence that are introduced via power series methods. Introducing a new type of uniform integrability with the help of power series method we obtain a relationship between these concepts which is actually a characterization of the concept of Pp-strong converge...

Most of the summability methods cannot be defined in an arbitrary Hausdorff topological space unless one introduces a linear or a group structure. In the present paper, using distribution functions over the Borel ?-field of the topology and lacunary sequences we define a new type of convergencemethod in an arbitrary Hausdorff topological space and...

The main goal of the present paper is to study the general structure and theoretical properties of a particular type of a fuzzy measure that can be used to model multi criteria decision making problems in which there exist some sub criteria. After constructing the general form of the non-additive set function, we deal with the interaction coefficie...

In this paper a particular set function which depends on densities of single- tons with interdependence coefficients and which provides redundancy among singletons is considered. The Mo ̈bius representation of this function is obtained. Then a necessary and sufficient condition is presented to attain a fuzzy measure from this set function.

Study of summability theory in an arbitrary topological space is not always an easy issue as many of the convergence methods need linear structure in the space. The concept of statistical convergence is one of the exceptional concepts of summability theory that can be considered in a topological space. There is a strong relationship between this co...

As the concept of uniform integrability has an essential role in the convergence of moments and martingales in the probability theory it is important to study this concept. In the present paper using Bochner integral we define a new type of uniform integrability for sequences of random elements. We give some independent necessary and sufficient con...

Korovkin type approximation theory is concerned with the convergence of the sequences of positive linear operators to the identity operator. In this paper, we deal with the Korovkin type approximation properties of the Cheney–Sharma operators by using A-statistical convergence and Abel convergence that are some well known methods of summability the...

In this note, using the idea of the late Professor Gadjiev (Mat Zametki 20(5):781–786, 1976), we give new, direct and easy proofs of the Korovkin theorems for positive linear operators acting on weighted spaces. Recent improvements and new applications are also presented.

The concept of statistical convergence in an arbitrary topological space is nothing new, it is actually a self-evident concept that comes through the structure of that space. In this paper, by considering the well known topologies on hyperspaces, we investigate the characterizations of statistical convergence of sequences of sets in the realm of th...

A spliced sequence is formed by combining all of the terms of two or more convergent sequences, in their original order, into a new spliced sequence. In this paper replacing convergent sequences by bounded sequences, we study the summability of spliced sequences and give some inequalities that provide us with approximation of the core of transforma...

The aim of this study is to measure the effects of the global warming in the cities in Turkey. The results of the global warming such as drought, temperature changes and rainfall changes are considered as criteria and the evaluation of the impacts of global warming in the cities in Turkey is handled as a multi-criteria decision-making model. A hybr...

The classical Korovkin approximation theory deals with the convergence of a given sequence {Ln} of positive linear operators on C[a,b]. When the sequence of positive linear operators does not converge to the identity operator it may be useful to use some summability methods. In this paper, we study some Korovkin type approximation theorems for the...

The classical summability theory can not be used in the topological spaces as it needs addition operator. Recently some authors have studied the summability theory in the topological spaces by assuming the topological space to have a group structure or a linear structure or introducing some summability methods those do not need a linear structure i...

In the present paper we introduce a new concept of $A$ -distributional convergence in an arbitrary Hausdorff topological space which is equivalent to $A$ -statistical convergence for a degenerate distribution function. We investigate $A$ -distributional convergence as a summability method in an arbitrary Hausdorff topological space. We also s...

The classical Korovkin approximation theory deals with the convergence of a sequence of positive linear operators. When the sequence of positive linear operators does not converge it will be useful to use some summability methods. In this paper we use the Abel method, a sequence-to-function transformation, to study a Korovkin type approximation the...

We characterize the multiplier space of summability fields of four dimensional RH-regular matrices and show that the space of multipliers of a nonnegative RH-regular matrix over an algebra \(\mathcal{U} \) is the space of A-statistically convergent double sequences. For this purpose we prove a variant of the Brudno–Mazur–Orlicz bounded consistency...

Recently Khan and Orhan have proved that an ordinary (single) sequence is A-strongly convergent if and only if it is A-statistically convergent and A-uniformly integrable. In this paper we consider the similar problem for multidimensional sequences when A is a multivariable-to-single matrix. We also study the same question when A is a multivariable...

Using the concept of A-statistical convergence, we give Korovkin-type approximation theorems for a sequence of A-statistically uniformly bounded positive linear operators acting from L p [a,b;c,d] into itself.