Special Issue "Fuzzy Sets, Fuzzy Logic and Their Applications"

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

Deadline for manuscript submissions: 31 December 2019.

Special Issue Editor

Prof. Michael Voskoglou
E-Mail Website
Guest Editor
Graduate Technological Educational Institute (T.E.I.) of Western Greece, School of Technological Applications, 26334 Patras, Greece
Interests: Fuzzy Sets and Logic, Markov Chains, Abstract and Linear Algebra, Artificial Intelligence, Mathematics Education

Special Issue Information

Dear Colleagues,

A few years ago, probability theory was a unique tool in hands of the experts dealing with situations of uncertainty appearing in problems of science and in everyday life. However, nowadays, with the development of fuzzy set theory—introduced by Zadeh in 1965—and the extension of fuzzy logic, the situation has changed. In fact, these new mathematical tools provided scientists with the opportunity to model under conditions that are vague or not precisely defined, thus succeeding in mathematically solving problems whose statements are expressed in our natural language. As a result, the spectrum of application has been rapidly extended, covering all of the physical sciences, economics and management, expert systems like financial planners, diagnostic, meteorological, information retrieval, control systems, etc., industry, robotics, decision making, programming, medicine, biology, humanities, education and almost all the other sectors of the human activity, including human reasoning itself. The first major commercial application of fuzzy logic was in cement kiln control (Zadeh, 1983), followed by a navigation system for automatic cars, a fuzzy controller for the automatic operation of trains, laboratory level controllers, controllers for robot vision, graphics, controllers for automated police sketchers and many others. It should be mentioned that fuzzy mathematics has been also significantly developed on the theoretical level, providing important insights even to branches of the classical mathematics, like algebra, analysis, geometry, etc.

The target of the present Special Issue of the MDPI journal Mathematics is to provide the experts in the field (academics, researchers, practitioners, etc.) the opportunity to present recent theoretical advances on fuzzy sets and fuzzy logic and of their extension/generalization (e.g. intuitionistic fuzzy logic, neutrosophic sets, etc.) and their applications to all fields of human activity.

Prof. Michael Voskoglou
Guest Editor

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Fuzzy Sets and their Generalizations
  • Fuzzy Logic
  • Defuzzification Techniques
  • Fuzzy Numbers
  • Uncertainty in Fuzzy Environments

Published Papers (11 papers)

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Research

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Open AccessArticle
Fuzzy Counterparts of Fischer Diagonal Condition in ⊤-Convergence Spaces
Mathematics 2019, 7(8), 685; https://doi.org/10.3390/math7080685 - 31 Jul 2019
Abstract
Fischer diagonal condition plays an important role in convergence space since it precisely ensures a convergence space to be a topological space. Generally, Fischer diagonal condition can be represented equivalently both by Kowalsky compression operator and Gähler compression operator. ⊤-convergence spaces are fundamental [...] Read more.
Fischer diagonal condition plays an important role in convergence space since it precisely ensures a convergence space to be a topological space. Generally, Fischer diagonal condition can be represented equivalently both by Kowalsky compression operator and Gähler compression operator. ⊤-convergence spaces are fundamental fuzzy extensions of convergence spaces. Quite recently, by extending Gähler compression operator to fuzzy case, Fang and Yue proposed a fuzzy counterpart of Fischer diagonal condition, and proved that ⊤-convergence space with their Fischer diagonal condition just characterizes strong L-topology—a type of fuzzy topology. In this paper, by extending the Kowalsky compression operator, we present a fuzzy counterpart of Fischer diagonal condition, and verify that a ⊤-convergence space with our Fischer diagonal condition precisely characterizes topological generated L-topology—a type of fuzzy topology. Hence, although the crisp Fischer diagonal conditions based on the Kowalsky compression operator and the on Gähler compression operator are equivalent, their fuzzy counterparts are not equivalent since they describe different types of fuzzy topologies. This indicates that the fuzzy topology (convergence) is more complex and varied than the crisp topology (convergence). Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)
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Open AccessArticle
An Interactive Data-Driven (Dynamic) Multiple Attribute Decision Making Model via Interval Type-2 Fuzzy Functions
Mathematics 2019, 7(7), 584; https://doi.org/10.3390/math7070584 - 30 Jun 2019
Abstract
A new multiple attribute decision making (MADM) model was proposed in this paper in order to cope with the temporal performance of alternatives during different time periods. Although dynamic MADM problems are enjoying a more visible position in the literature, majority of the [...] Read more.
A new multiple attribute decision making (MADM) model was proposed in this paper in order to cope with the temporal performance of alternatives during different time periods. Although dynamic MADM problems are enjoying a more visible position in the literature, majority of the applications deal with combining past and present data by means of aggregation operators. There is a research gap in developing data-driven methodologies to capture the patterns and trends in the historical data. In parallel with the fact that style of decision making evolving from intuition-based to data-driven, the present study proposes a new interval type-2 fuzzy (IT2F) functions model in order to predict current performance of alternatives based on the historical decision matrices. As the availability of accurate historical data with desired quality cannot always be obtained and the data usually involves imprecision and uncertainty, predictions regarding the performance of alternatives are modeled as IT2F sets. These estimated outputs are transformed into interpretable forms by utilizing the vocabulary matching procedures. Then the interactive procedures are employed to allow decision makers to modify the predicted decision matrix based on their perceptions and subjective judgments. Finally, ranking of alternatives are performed based on past and current performance scores. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)
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Open AccessArticle
Distance Measures between the Interval-Valued Complex Fuzzy Sets
Mathematics 2019, 7(6), 549; https://doi.org/10.3390/math7060549 - 16 Jun 2019
Cited by 1
Abstract
Complex fuzzy set (CFS) is a recent development in the field of fuzzy set (FS) theory. The significance of CFS lies in the fact that CFS assigned membership grades from a unit circle in the complex plane, i.e., in the form of a [...] Read more.
Complex fuzzy set (CFS) is a recent development in the field of fuzzy set (FS) theory. The significance of CFS lies in the fact that CFS assigned membership grades from a unit circle in the complex plane, i.e., in the form of a complex number whose amplitude term belongs to a [ 0 , 1 ] interval. The interval-valued complex fuzzy set (IVCFS) is one of the extensions of the CFS in which the amplitude term is extended from the real numbers to the interval-valued numbers. The novelty of IVCFS lies in its larger range comparative to CFS. We often use fuzzy distance measures to solve some problems in our daily life. Hence, this paper develops some series of distance measures between IVCFSs by using Hamming and Euclidean metrics. The boundaries of these distance measures for IVCFSs are obtained. Finally, we study two geometric properties include rotational invariance and reflectional invariance of these distance measures. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)
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Open AccessArticle
New Concepts of Picture Fuzzy Graphs with Application
Mathematics 2019, 7(5), 470; https://doi.org/10.3390/math7050470 - 24 May 2019
Cited by 1
Abstract
The picture fuzzy set is an efficient mathematical model to deal with uncertain real life problems, in which a intuitionistic fuzzy set may fail to reveal satisfactory results. Picture fuzzy set is an extension of the classical fuzzy set and intuitionistic fuzzy set. [...] Read more.
The picture fuzzy set is an efficient mathematical model to deal with uncertain real life problems, in which a intuitionistic fuzzy set may fail to reveal satisfactory results. Picture fuzzy set is an extension of the classical fuzzy set and intuitionistic fuzzy set. It can work very efficiently in uncertain scenarios which involve more answers to these type: yes, no, abstain and refusal. In this paper, we introduce the idea of the picture fuzzy graph based on the picture fuzzy relation. Some types of picture fuzzy graph such as a regular picture fuzzy graph, strong picture fuzzy graph, complete picture fuzzy graph, and complement picture fuzzy graph are introduced and some properties are also described. The idea of an isomorphic picture fuzzy graph is also introduced in this paper. We also define six operations such as Cartesian product, composition, join, direct product, lexicographic and strong product on picture fuzzy graph. Finally, we describe the utility of the picture fuzzy graph and its application in a social network. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)
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Open AccessArticle
Counterintuitive Test Problems for Distance-Based Similarity Measures Between Intuitionistic Fuzzy Sets
Mathematics 2019, 7(5), 437; https://doi.org/10.3390/math7050437 - 17 May 2019
Abstract
This paper analyzes the counterintuitive behaviors of adopted twelve distance-based similarity measures between intuitionistic fuzzy sets. Among these distance-based similarity measures, the largest number of components of the distance in the similarity measure is four. We propose six general counterintuitive test problems to [...] Read more.
This paper analyzes the counterintuitive behaviors of adopted twelve distance-based similarity measures between intuitionistic fuzzy sets. Among these distance-based similarity measures, the largest number of components of the distance in the similarity measure is four. We propose six general counterintuitive test problems to analyze their counterintuitive behaviors. The results indicate that all the distance-based similarity measures have some counterintuitive test problems. Furthermore, for the largest number of components of the distance-based similarity measure, four types of counterintuitive examples exist. Therefore, the counterintuitive behaviors are inevitable for the distance-based similarity measures between intuitionistic fuzzy sets. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)
Open AccessArticle
p-Regularity and p-Regular Modification in ⊤-Convergence Spaces
Mathematics 2019, 7(4), 370; https://doi.org/10.3390/math7040370 - 24 Apr 2019
Cited by 1
Abstract
Fuzzy convergence spaces are extensions of convergence spaces. ⊤-convergence spaces are important fuzzy convergence spaces. In this paper, p-regularity (a relative regularity) in ⊤-convergence spaces is discussed by two equivalent approaches. In addition, lower and upper p-regular modifications in ⊤-convergence spaces [...] Read more.
Fuzzy convergence spaces are extensions of convergence spaces. ⊤-convergence spaces are important fuzzy convergence spaces. In this paper, p-regularity (a relative regularity) in ⊤-convergence spaces is discussed by two equivalent approaches. In addition, lower and upper p-regular modifications in ⊤-convergence spaces are further investigated and studied. Particularly, it is shown that lower (resp., upper) p-regular modification and final (resp., initial) structures have good compatibility. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)
Open AccessArticle
On (α,β)-US Sets in BCK/BCI-Algebras
Mathematics 2019, 7(3), 252; https://doi.org/10.3390/math7030252 - 11 Mar 2019
Cited by 1
Abstract
Molodtsov originated soft set theory, which followed a general mathematical framework for handling uncertainties, in which we encounter the data by affixing the parameterized factor during the information analysis. The aim of this paper is to establish a bridge to connect a soft [...] Read more.
Molodtsov originated soft set theory, which followed a general mathematical framework for handling uncertainties, in which we encounter the data by affixing the parameterized factor during the information analysis. The aim of this paper is to establish a bridge to connect a soft set and the union operations on sets, then applying it to B C K / B C I -algebras. Firstly, we introduce the notion of the ( α , β ) -Union-Soft ( ( α , β ) -US) set, with some supporting examples. Then, we discuss the soft B C K / B C I -algebras, which are called ( α , β ) -US algebras, ( α , β ) -US ideals, ( α , β ) -US closed ideals, and ( α , β ) -US commutative ideals. In particular, some related properties and relationships of the above algebraic structures are investigated. We also provide the condition of an ( α , β ) -US ideal to be an ( α , β ) -US closed ideal. Some conditions for a Union-Soft (US) ideal to be a US commutative ideal are given by means of ( α , β ) -unions. Moreover, several characterization theorems of (closed) US ideals and US commutative ideals are given in terms of ( α , β ) -unions. Finally, the extension property for an ( α , β ) -US commutative ideal is established. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)
Open AccessArticle
The “Generator” of Int-Soft Filters on Residuated Lattices
Mathematics 2019, 7(3), 236; https://doi.org/10.3390/math7030236 - 06 Mar 2019
Abstract
In this paper, we give the “generator” of int-soft filters and propose the notion of t-int-soft filters on residuated lattices. We study the properties of t-int-soft filters and obtain some commonalities (e.g., the extension property, quotient characteristics, and a triple of equivalent characteristics). [...] Read more.
In this paper, we give the “generator” of int-soft filters and propose the notion of t-int-soft filters on residuated lattices. We study the properties of t-int-soft filters and obtain some commonalities (e.g., the extension property, quotient characteristics, and a triple of equivalent characteristics). We also use involution-int-soft filters as an example and show some basic properties of involution-int-soft filters. Finally, we investigate the relations among t-int-soft filters and give a simple method for judging their relations. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)
Open AccessArticle
p-Topologicalness—A Relative Topologicalness in ⊤-Convergence Spaces
Mathematics 2019, 7(3), 228; https://doi.org/10.3390/math7030228 - 01 Mar 2019
Cited by 5
Abstract
In this paper, p-topologicalness (a relative topologicalness) in ⊤-convergence spaces are studied through two equivalent approaches. One approach generalizes the Fischer’s diagonal condition, the other approach extends the Gähler’s neighborhood condition. Then the relationships between p-topologicalness in ⊤-convergence spaces and p [...] Read more.
In this paper, p-topologicalness (a relative topologicalness) in ⊤-convergence spaces are studied through two equivalent approaches. One approach generalizes the Fischer’s diagonal condition, the other approach extends the Gähler’s neighborhood condition. Then the relationships between p-topologicalness in ⊤-convergence spaces and p-topologicalness in stratified L-generalized convergence spaces are established. Furthermore, the lower and upper p-topological modifications in ⊤-convergence spaces are also defined and discussed. In particular, it is proved that the lower (resp., upper) p-topological modification behaves reasonably well relative to final (resp., initial) structures. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)
Open AccessArticle
A Partial-Consensus Posterior-Aggregation FAHP Method—Supplier Selection Problem as an Example
Mathematics 2019, 7(2), 179; https://doi.org/10.3390/math7020179 - 15 Feb 2019
Cited by 2
Abstract
Existing fuzzy analytic hierarchy process (FAHP) methods usually aggregate the fuzzy pairwise comparison results produced by multiple decision-makers (DMs) rather than the fuzzy weights estimations. This is problematic because fuzzy pairwise comparison results are subject to uncertainty and lack consensus. To address this [...] Read more.
Existing fuzzy analytic hierarchy process (FAHP) methods usually aggregate the fuzzy pairwise comparison results produced by multiple decision-makers (DMs) rather than the fuzzy weights estimations. This is problematic because fuzzy pairwise comparison results are subject to uncertainty and lack consensus. To address this problem, a partial-consensus posterior-aggregation FAHP (PCPA-FAHP) approach is proposed in this study. The PCPA-FAHP approach seeks a partial consensus among most DMs instead of an overall consensus among all DMs, thereby increasing the possibility of reaching a consensus. Subsequently, the aggregation result is defuzzified using the prevalent center-of-gravity method. The PCPA-FAHP approach was applied to a supplier selection problem to validate its effectiveness. According to the experimental results, the PCPA-FAHP approach not only successfully found out the partial consensus among the DMs, but also shrunk the widths of the estimated fuzzy weights to enhance the precision of the FAHP analysis. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)
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Review

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Open AccessReview
Methods for Assessing Human–Machine Performance under Fuzzy Conditions
Mathematics 2019, 7(3), 230; https://doi.org/10.3390/math7030230 - 01 Mar 2019
Cited by 1
Abstract
The assessment of a system’s performance is a very important task, enabling its designer/user to correct its weaknesses and make it more effective. Frequently, in practice, a system’s assessment is performed under fuzzy conditions, e.g., using qualitative instead of numerical grades, incomplete information [...] Read more.
The assessment of a system’s performance is a very important task, enabling its designer/user to correct its weaknesses and make it more effective. Frequently, in practice, a system’s assessment is performed under fuzzy conditions, e.g., using qualitative instead of numerical grades, incomplete information about its function, etc. The present review summarizes the author’s research on building assessment models for use in a fuzzy environment. Those models include the measurement of a fuzzy system’s uncertainty, the application of the center of gravity defuzzification technique, the use of triangular fuzzy or grey numbers as assessment tools, and the application of the fuzzy relation equations. Examples are provided of assessing human (students and athletes) and machine (case-based reasoning systems in computers) capacities, illustrating our results. The outcomes of those examples are compared to the outcomes of the traditional methods of calculating the mean value of scores assigned to the system’s components (system’s mean performance) and of the grade point average index (quality performance) and useful conclusions are obtained concerning their advantages and disadvantages. The present review forms a new basis for further research on systems’ assessment in a fuzzy environment. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications)
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