Article
Engineering, Multidisciplinary
Changxing Fan, Jihong Chen, Keli Hu, En Fan, Xiuqing Wang
Summary: This paper first proposes the normal Pythagorean neutrosophic set (NPNS), which integrates the distribution of incompleteness, indeterminacy, and inconsistency of the Pythagorean neutrosophic set (PNS) and normal fuzzy number. The properties of NPNS are defined. Two types of NPNS Choquet integral operators are introduced to solve the decision-making problem of nonstrictly independent and interacting attributes. Finally, the stability of the new method is validated using these operators.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2022)
Article
Computer Science, Artificial Intelligence
Li Wang, Yan-Ling Bao
Summary: Single-valued neutrosophic hesitant fuzzy elements are useful for characterizing information, but one of the aggregation operators does not satisfy idempotency and is not suitable for practical applications.
PATTERN ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Sorin G. Gal, Constantin P. Niculescu
Summary: The study establishes the integral representation of Choquet operators on a space C(X) by utilizing the Choquet-Bochner integral of a real-valued function with respect to a vector capacity.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Computer Science, Theory & Methods
Zdenko Takac, Mikel Uriz, Mikel Galar, Daniel Paternain, Humberto Bustince
Summary: In this work, we introduce the concept of d(G)-Choquet integral, which extends the discrete Choquet integral by incorporating a dissimilarity function to represent input differences and replacing the sum with more general functions. We demonstrate that the discrete Choquet integral and the d-Choquet integral are specific cases of the d(G)-Choquet integral. We also define interval-valued fuzzy measures and show their application in defining a monotonic interval-valued discrete Choquet integral using d(G)-Choquet integrals. The validity of this interval-valued Choquet integral is studied through an illustrative example in a classification problem.
FUZZY SETS AND SYSTEMS
(2022)
Article
Computer Science, Information Systems
Michal Boczek, Lenka Halcinova, Ondrej Hutnik, Marek Kaluszka
Summary: This paper defines a novel survival function based on conditional aggregation operators, which generalizes existing integrals, and introduces the Choquet-Stieltjes functional as well as the conditions under which it can be called an integral.
INFORMATION SCIENCES
(2021)
Article
Computer Science, Information Systems
Lin Sha, Yabin Shao
Summary: Fermatean fuzzy hesitant sets are a flexible and powerful decision-making tool that allows decision makers to incorporate uncertainty and hesitation into their decision-making process, resulting in more informed and effective decisions in complex and uncertain environments. The proposed Fermatean hesitant fuzzy Choquet integral ordered aggregation operators handle interdependent decision criteria or preferences and provide decisions under ideal and non-ideal situations. A multi-attribute decision-making method for Fermatean hesitant fuzzy information is presented using these operators, and its practicality and effectiveness are demonstrated through numerical examples.
Article
Computer Science, Theory & Methods
Jun Li, Radko Mesiar, Yao Ouyang
Summary: This paper introduces two types of preorders on the system of all non-empty sets of collections based on a fixed monotone measure mu. By means of these two new preorders, the coincidences of decomposition integrals and superdecomposition integrals are investigated. The generalized integral equivalence theorem is shown in the general framework involving an ordered pair of decomposition systems. This provides a unified approach to the coincidences of several well-known decomposition and superdecomposition integrals.
FUZZY SETS AND SYSTEMS
(2023)
Article
Computer Science, Information Systems
Mikel Uriz, Daniel Paternain, Humberto Bustince, Mikel Galar
Summary: Fuzzy measure-based aggregations consider interactions among input source coalitions, but defining the fuzzy measure is a challenge. This paper proposes a new algorithm for learning fuzzy measure that can optimize any cost function, using advancements from deep learning frameworks. Experimental study with 58 datasets shows the effectiveness of the proposed method in optimizing cross-entropy cost for binary and multi-class classification problems, compared to other state-of-the-art methods for fuzzy measure learning.
INFORMATION SCIENCES
(2023)
Article
Computer Science, Artificial Intelligence
Mehdi Divsalar, Marzieh Ahmadi, Elnaz Ebrahimi, Alessio Ishizaka
Summary: A probabilistic hesitant fuzzy set is introduced as a generalization of the hesitant fuzzy set for handling uncertain information when there is no complete consensus among decision-makers. This paper presents a novel Choquet integral-based TODIM method and validates its effectiveness through a supplier selection problem in the dairy industry.
EXPERT SYSTEMS WITH APPLICATIONS
(2022)
Article
Automation & Control Systems
Hazwani Hashim, Harish Garg, Ashraf Al-Quran, Noor Azzah Awang, Lazim Abdullah
Summary: This paper combines the Shapley fuzzy measure with the improved generalized weighted HM operator to propose two aggregation operators for solving multi-criteria decision-making problems under interval neutrosophic vague sets. The effectiveness of the proposed methods is demonstrated through a numerical example and sensitivity analysis.
INTERNATIONAL JOURNAL OF FUZZY SYSTEMS
(2022)
Article
Computer Science, Information Systems
Michal Boczek, Ondrej Hutnik, Marek Kaluszka
Summary: This study introduces a generalized Choquet-Sugeno-like operator that can extend many existing operators for bounded nonnegative functions and monotone measures. The new operator is based on concepts of dependence relation and conditional aggregation operators, while not depending on a-level sets. Conditions under which the Choquet-Sugeno-like operator coincides with some Choquet-like integrals on finite spaces have been provided, and some basic properties of the operator have been studied.
INFORMATION SCIENCES
(2022)
Article
Computer Science, Theory & Methods
Radko Mesiar, Andrea Stupnanova, LeSheng Jin
Summary: This paper introduces OWA operators and their representation based on Choquet integrals, and proposes a generalization of OWA operators called BIOWA operators. The properties of BIOWA operators are studied and exemplified through various examples.
FUZZY SETS AND SYSTEMS
(2022)
Article
Computer Science, Artificial Intelligence
Michal Boczek, Tomasz Jozefiak, Marek Kaluszka, Andrzej Okolewski
Summary: This paper emphasizes the importance of studying the different forms of monotonicity for various discrete Choquet-like integrals in data aggregation and real-world applications. It provides complete monotonicity characterizations for two operators and offers full characterizations of the operators as aggregation functions.
INTERNATIONAL JOURNAL OF APPROXIMATE REASONING
(2023)
Article
Computer Science, Information Systems
F. Durante, J. Fernandez Sanchez, C. Ignazzi
Summary: In this study, operators defined on bounded functions on the power set of an infinite set X under finitely additive measures are reconsidered with an extended use of the concept of filter, offering new insights into the problem. The obtained results are then applied to the study of the aggregation of infinite sequences.
INFORMATION SCIENCES
(2021)
Article
Computer Science, Artificial Intelligence
Jing Yang, Wei Su
Summary: This paper presents a new method for dealing with imprecise judgment information, combining objective weights and subjective weights, and incorporating a new similarity measurement approach. Through comparative analysis of experimental results, the effectiveness and efficiency of this method have been demonstrated.
JOURNAL OF INTELLIGENT & FUZZY SYSTEMS
(2022)
Article
Mathematics, Applied
Noori Yasir Abdul-Hassan, Ali Hasan Ali, Choonkil Park
Summary: In this recent work, a new two-step iterative method with fifth-order convergence for solving nonlinear equations is suggested and analyzed. The method is free from second derivatives of functions, based on Halley's method and Taylor's expansion using Hermite orthogonal polynomials basis for approximating second derivatives. The convergence order and error equations of the method are proven, and numerical examples show its efficiency compared to Newton's method and other relevant methods.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2022)
Article
Mathematics, Applied
Mohamed Rossafi, Fakhr-Dine Nhari, Choonkil Park, Samir Kabbaj
Summary: This paper introduces the concept of continuous g-frames with C*-valued bounds and establishes some related results. The operator duals and stability problem are also discussed.
COMPLEX ANALYSIS AND OPERATOR THEORY
(2022)
Article
Mathematics, Applied
Wahid Ullah, Huseyin Isik, Nouman Alam, Choonkil Park, Jung Rye Lee
Summary: In this article, a new geometrical structure that combines a cone metric space over Banach algebra and a controlled metric-type space is introduced. A new metric space is proposed, and analogs of Banach-, Kannan- and Reich-type fixed-point theorems are proved. Various concrete examples are provided to validate the results, which generalize many well-known results in the literature.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Divyakumari Pachaiyappan, Ramdoss Murali, Choonkil Park, Jung Rye Lee
Summary: This paper introduces a new generalized p-dimensional multifarious radical reciprocal functional equation and finds its general solution and stability related to the Ulam problem in modular spaces. Furthermore, it discusses the geometrical interpretation and applications of the introduced Pythagorean means multifarious functional equation in connection with parallel circuits and provides a formula for calculating the equivalent resistance of parallel electrical circuits using functional equations.
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2022)
Article
Mathematics
Xiaohong Zhang, Rong Liang, Benjamin Bedregal
Summary: After investigating naBL-algebras using non-associative t-norms and overlap functions, the study also extended to inflationary BL-algebras as a recent non-associative generalization of BL-algebras, which can be obtained using general overlap functions. In this paper, it is demonstrated through a counterexample that not every inflationary general overlap function can induce an inflationary BL-algebra, leading to the introduction of the concept of weak inflationary BL-algebras. It is then proven that each inflationary general overlap function corresponds to a weak inflationary BL-algebra, allowing a correction of two mistaken results from a previous paper. Additionally, the properties of weak inflationary BL-algebras are discussed, as well as the relationships among various non-classical logic algebras. Furthermore, the theory of filters and quotient algebras of inflationary general residuated lattices (IGRL) and inflationary pseudo-general residuated lattices (IPGRL) is established, along with the characterization of certain types of IGRLs and IPGRLs using naBL-filters, (weak) inflationary BL-filters, and weak inflationary pseudo-BL-filters.
Article
Mathematics
Rong Liang, Xiaohong Zhang
Summary: This article investigates general overlap functions and their applications in classification problems. It introduces the concept of pseudo general overlap functions as a non-commutative generalization, explores their relationship with other aggregation functions, and characterizes some construction methods. The article also discusses the residuated implications induced by inflationary pseudo general overlap functions and presents the definitions of inflationary pseudo general residuated lattices (IPGRLs) and weak inflationary pseudo BL-algebras. Furthermore, it examines the properties of these algebraic structures and their relations with other structures, such as non-commutative residuated lattice-ordered groupoids.
Article
Mathematics
Rajesh Kumar, Sanjay Kumar, Choonkil Park
Summary: This paper proves some common fixed point theorems for pairs of compatible mappings of specific types, while discussing the existence and uniqueness of common solutions for a class of functional equations in dynamic programming.
JOURNAL OF ANALYSIS
(2023)
Article
Mathematics, Applied
Divyakumari Pachaiyappan, Murali Ramdoss, Choonkil Park
Summary: This paper investigates the general solution and stabilities of generalized functional equations and proposes a new method for image security system based on the introduced functional equation.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Xiaohong Zhang, Rong Liang
Summary: This paper investigates the interval-valued general, residuated, lattice-ordered groupoids and their relevance to IPOFs. It also proposes the notions of expanded interval-valued general, residuated lattice-ordered groupoids and expanded triangle algebras. The one-to-one correspondence between them is explained through a specific proposition. The paper also analyzes the properties of these structures and defines filters, congruence, and quotient structures on the expanded triangle algebras.
Article
Mathematics, Applied
Yamin Sayyari, Mehdi Dehghanian, Choonkil Park
Summary: The main goal of this work is to establish the stabilities of the Mittag-Leffler-Hyers-Ulam type and Hyers-Ulam type of system of first order linear differential equations with constant coefficients using the Laplace transform.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Mathematics
Mehdi Dehghanian, Choonkil Park, Yamin Sayyari
Summary: This paper proves the Ulam stability of ternary hom-der in ternary Banach algebras using the fixed point method.
RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO
(2023)
Article
Engineering, Multidisciplinary
Yamin Sayyari, Mehdi Dehghanian, Choonkil Park
Summary: In this paper, the general solution and the Hyers-Ulam stability of the system of biadditive functional equations in complex Banach spaces are obtained. Furthermore, the Hyers-Ulam stability of f-biderivations in complex Banach algebras is proved.
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING
(2023)
Article
Mathematics, Applied
Mehdi Dehghanian, Choonkil Park, Yamin Sayyari
Summary: In this paper, we introduce the concept of ternary antiderivation on ternary Banach algebras and investigate the stability of ternary antiderivation in ternary Banach algebras.
CUBO-A MATHEMATICAL JOURNAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Mojtaba Sajjadmanesh, Hassen Aydi, Eskandar Ameer, Choonkil Park
Summary: This paper discusses an inverse geometric problem for the three-dimensional Laplace equation to recover an inner boundary of an annular domain using the method of fundamental solutions (MFS). It works by imposing the boundary Cauchy data in a least-square sense and minimizing the objective function. The simplicity and efficiency of this method is demonstrated in several numerical examples.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Interdisciplinary Applications
Khadijeh Sadri, Kamyar Hosseini, Dumitru Baleanu, Soheil Salahshour, Choonkil Park
Summary: This work addresses the numerical solution of fractional delay integro-differential equations with weakly singular kernels using a Vieta-Fibonacci collocation method. The existence and uniqueness of the solution is investigated and proved, and a new formula for extracting the Vieta-Fibonacci polynomials and their derivatives is given. The orthogonality of the derivatives of the polynomials is easily proved, and an error bound for the residual function is estimated. The designed algorithm is examined on four equations, showing its simplicity and accuracy compared to previous methods.
FRACTAL AND FRACTIONAL
(2022)
