Special Issue "Nonlinear Analysis Using Fuzzy Mathematics"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (31 January 2019).

Special Issue Editor

Prof. Dr. Hsien-Chung Wu
Website
Guest Editor
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan
Interests: fuzzy optimization; fuzzy real analysis; fuzzy statistical analysis; operations research; computational intelligence; soft computing; fixed point theory; applied functional analysis
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Special Issue Information

Dear Colleagues,

Many mathematical problems modelled from engineering and economics are categorized as nonlinear problems. The nonlinear analysis plays an important role to solve these nonlinear problems including nonlinear optimization problems, nonlinear ordinary and partial differential equations, equilibrium problems in economics, variational problems in physics, economics, etc. When the data in mathematical problems involve imprecision or fuzziness, the fuzzy sets theory plays another important role to tackle the so-called fuzzy mathematical problems. This Special Issue focuses on using the techniques in fuzzy sets theory to solve the nonlinear problems that are accompanied with fuzzy data. The topics of this Special Issue include:

  • calculus of variation
  • fixed point theorem in fuzzy metric space
  • fuzzy optimization
  • fuzzy variational inequality
  • fuzzy game theory
  • fuzzy differential equation
  • fuzzy integral
  • Nash equilibrium
  • set-valued and variational analysis
  • topological methods in nonlinear analysis
Prof. Dr. Hsien-Chung Wu
Guest Editor

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Keywords

  • Calculus of variation
  • Fixed Point theorems
  • Fuzzy integrals
  • Fuzzy metric spaces
  • Fuzzy games
  • Fuzzy sets
  • Fuzzy variational inequalities
  • Fuzzy optimization
  • Nash equilibrium
  • Nonlinear analysis
  • Set-valued functions
  • Variational analysis

Published Papers (7 papers)

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Research

Open AccessArticle
Switching Point Solution of Second-Order Fuzzy Differential Equations Using Differential Transformation Method
Mathematics 2019, 7(3), 231; https://doi.org/10.3390/math7030231 - 01 Mar 2019
Cited by 1
Abstract
The first-order fuzzy differential equation has two possible solutions depending on the definition of differentiability. The definition of differentiability changes as the product of the function and its first derivative changes its sign. This switching of the derivative’s definition is handled with the [...] Read more.
The first-order fuzzy differential equation has two possible solutions depending on the definition of differentiability. The definition of differentiability changes as the product of the function and its first derivative changes its sign. This switching of the derivative’s definition is handled with the application of min, max operators. In this paper, a numerical technique for solving fuzzy initial value problems is extended to solving higher-order fuzzy differential equations. Fuzzy Taylor series is used to develop the fuzzy differential transformation method for solving this problem. This leads to a single solution for higher-order differential equations. Full article
(This article belongs to the Special Issue Nonlinear Analysis Using Fuzzy Mathematics)
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Open AccessArticle
Consensus-Based Multi-Person Decision Making with Incomplete Fuzzy Preference Relations Using Product Transitivity
Mathematics 2019, 7(2), 185; https://doi.org/10.3390/math7020185 - 16 Feb 2019
Cited by 1
Abstract
In this paper, a consensus-based method for multi-person decision making (MPDM) using product transitivity with incomplete fuzzy preference relations (IFPRs) is proposed. Additionally, an average aggregation operator has been used at the first level to estimate the missing preference values and construct the [...] Read more.
In this paper, a consensus-based method for multi-person decision making (MPDM) using product transitivity with incomplete fuzzy preference relations (IFPRs) is proposed. Additionally, an average aggregation operator has been used at the first level to estimate the missing preference values and construct the complete fuzzy preference relation (FPR). Then it is confirmed to be product consistent by using the transitive closure formula. Following this, weights of decision makers (DMs) are evaluated by merging consistency weights and predefined priority weights (if any). The consistency weights for the DMs are estimated through product consistency investigation of the information provided by each DM. The consensus process determines whether the selection procedure should be initiated or not. The hybrid comprises of a quitting process and feedback mechanism, and is used to enhance the consensus level amongst DMs in case of an inadequate state. The quitting process arises when some DMs decided to leave the course, and is common in MPDM while dealing with a large number of alternatives. The feedback mechanism is the main novelty of the proposed technique which helps the DMs to improve their given preferences based on this consistency. At the end, a numerical example is deliberated to measure the efficiency and applicability of the proposed method after the comparison with some existing models under the same assumptions. The results show that proposed method can offer useful comprehension into the MPDM process. Full article
(This article belongs to the Special Issue Nonlinear Analysis Using Fuzzy Mathematics)
Open AccessArticle
Some Interval-Valued Intuitionistic Fuzzy Dombi Hamy Mean Operators and Their Application for Evaluating the Elderly Tourism Service Quality in Tourism Destination
Mathematics 2018, 6(12), 294; https://doi.org/10.3390/math6120294 - 01 Dec 2018
Cited by 52
Abstract
In this paper, we expand the Hamy mean (HM) operator and Dombi operations with interval-valued intuitionistic fuzzy numbers (IVIFNs) to propose the interval-valued intuitionistic fuzzy Dombi Hamy mean (IVIFDHM) operator, interval-valued intuitionistic fuzzy weighted Dombi Hamy mean (IVIFWDHM) operator, interval-valued intuitionistic fuzzy dual [...] Read more.
In this paper, we expand the Hamy mean (HM) operator and Dombi operations with interval-valued intuitionistic fuzzy numbers (IVIFNs) to propose the interval-valued intuitionistic fuzzy Dombi Hamy mean (IVIFDHM) operator, interval-valued intuitionistic fuzzy weighted Dombi Hamy mean (IVIFWDHM) operator, interval-valued intuitionistic fuzzy dual Dombi Hamy mean (IVIFDDHM) operator, and interval-valued intuitionistic fuzzy weighted dual Dombi Hamy mean (IVIFWDDHM) operator. Then the MADM models are designed with IVIFWDHM and IVIFWDDHM operators. Finally, we gave an example for evaluating the elderly tourism service quality in tourism destination to show the proposed models. Full article
(This article belongs to the Special Issue Nonlinear Analysis Using Fuzzy Mathematics)
Open AccessArticle
Models for Multiple Attribute Decision Making with Some 2-Tuple Linguistic Pythagorean Fuzzy Hamy Mean Operators
Mathematics 2018, 6(11), 236; https://doi.org/10.3390/math6110236 - 31 Oct 2018
Cited by 46
Abstract
The Hamy mean (HM) operator, as a useful aggregation tool, can capture the correlation between multiple integration parameters, and the 2-tuple linguistic Pythagorean fuzzy numbers (2TLPFNs) are a special kind of Pythagorean fuzzy numbers (PFNs), which can easily describe the fuzziness in actual [...] Read more.
The Hamy mean (HM) operator, as a useful aggregation tool, can capture the correlation between multiple integration parameters, and the 2-tuple linguistic Pythagorean fuzzy numbers (2TLPFNs) are a special kind of Pythagorean fuzzy numbers (PFNs), which can easily describe the fuzziness in actual decision making by 2-tuple linguistic terms (2TLTs). In this paper, to consider both Hamy mean (HM) operator and 2TLPFNs, we combine the HM operator, weighted HM (WHM) operator, dual HM (DHM) operator, and dual WHM (DWHM) operator with 2TLPFNs to propose the 2-tuple linguistic Pythagorean fuzzy HM (2TLPFHM) operator, 2-tuple linguistic Pythagorean fuzzy WHM (2TLPFWHM) operator, 2-tuple linguistic Pythagorean fuzzy DHM (2TLPFDHM) operator and 2-tuple linguistic Pythagorean fuzzy DWHM (2TLPFDWHM) operator. Then some multiple attribute decision making (MADM) procedures are developed based on these operators. At last, an applicable example for green supplier selection is given. Full article
(This article belongs to the Special Issue Nonlinear Analysis Using Fuzzy Mathematics)
Open AccessArticle
Prioritized Linguistic Interval-Valued Aggregation Operators and Their Applications in Group Decision-Making Problems
Mathematics 2018, 6(10), 209; https://doi.org/10.3390/math6100209 - 17 Oct 2018
Cited by 8
Abstract
The linguistic interval-valued intuitionistic fuzzy (LIVIF) set is an efficient tool to represent data in the form of interval membership degrees in a qualitative rather than a quantitative manner. The LIVIF set combines the features of interval-valued intuitionistic fuzzy sets (IFSs) and the [...] Read more.
The linguistic interval-valued intuitionistic fuzzy (LIVIF) set is an efficient tool to represent data in the form of interval membership degrees in a qualitative rather than a quantitative manner. The LIVIF set combines the features of interval-valued intuitionistic fuzzy sets (IFSs) and the linguistic variables (LV) and hence provides more freedom to decision-makers. Under this environment, the main objective of this manuscript is to propose some new aggregation operators by capturing the prioritized relationship between the objects. For this, different weighted averaging and geometric aggregation operators are proposed in which preferences related to each object are expressed in terms of LIVIF numbers. Desirable properties of the proposed operators are studied. Further, a group decision-making (DM) approach is presented to solve the multi-attribute DM problems, and its efficiency has been verified with an illustrative example. Full article
(This article belongs to the Special Issue Nonlinear Analysis Using Fuzzy Mathematics)
Open AccessArticle
Convergence in Fuzzy Semi-Metric Spaces
Mathematics 2018, 6(9), 170; https://doi.org/10.3390/math6090170 - 17 Sep 2018
Cited by 1
Abstract
The convergence using the fuzzy semi-metric and dual fuzzy semi-metric is studied in this paper. The infimum type of dual fuzzy semi-metric and the supremum type of dual fuzzy semi-metric are proposed in this paper. Based on these two types of dual fuzzy [...] Read more.
The convergence using the fuzzy semi-metric and dual fuzzy semi-metric is studied in this paper. The infimum type of dual fuzzy semi-metric and the supremum type of dual fuzzy semi-metric are proposed in this paper. Based on these two types of dual fuzzy semi-metrics, the different types of triangle inequalities can be obtained. We also study the convergence of these two types of dual fuzzy semi-metrics. Full article
(This article belongs to the Special Issue Nonlinear Analysis Using Fuzzy Mathematics)
Open AccessArticle
Near Fixed Point Theorems in the Space of Fuzzy Numbers
Mathematics 2018, 6(7), 108; https://doi.org/10.3390/math6070108 - 25 Jun 2018
Cited by 2
Abstract
The fuzzy numbers are fuzzy sets owning some elegant mathematical structures. The space consisting of all fuzzy numbers cannot form a vector space because it lacks the concept of the additive inverse element. In other words, the space of fuzzy numbers cannot be [...] Read more.
The fuzzy numbers are fuzzy sets owning some elegant mathematical structures. The space consisting of all fuzzy numbers cannot form a vector space because it lacks the concept of the additive inverse element. In other words, the space of fuzzy numbers cannot be a normed space even though the normed structure can be defined on this space. This also says that the fixed point theorems established in the normed space cannot apply directly to the space of fuzzy numbers. The purpose of this paper is to propose the concept of near fixed point in the space of fuzzy numbers and to study its existence. In order to consider the contraction of fuzzy-number-valued function, the concepts of near metric space and near normed space of fuzzy numbers are proposed based on the almost identical concept. The concepts of Cauchy sequences in near metric space and near normed space of fuzzy numbers are also proposed. Under these settings, the existence of near fixed points of fuzzy-number-valued contraction function in complete near metric space and near Banach space of fuzzy numbers are established. Full article
(This article belongs to the Special Issue Nonlinear Analysis Using Fuzzy Mathematics)
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