Research

17 pages, 6238 KiB

Open AccessArticle

Generalized Fuzzy Linguistic Bicubic B-Spline Surface Model for Uncertain Fuzzy Linguistic Data

by Mohd Syafiq Bidin, Abd. Fatah Wahab, Mohammad Izat Emir Zulkifly and Rozaimi Zakaria

Symmetry 2022, 14(11), 2267; https://doi.org/10.3390/sym14112267 - 28 Oct 2022

Viewed by 1067

A fuzzy linguistic data set that is uncertain is difficult to analyze and describe in the form of a smooth and continuous generic figure. Therefore, the study aims to develop a new model of a B-spline surface using a different approach of a [...] Read more.

A fuzzy linguistic data set that is uncertain is difficult to analyze and describe in the form of a smooth and continuous generic figure. Therefore, the study aims to develop a new model of a B-spline surface using a different approach of a crisp and fuzzy linguistic point relation with three types of linguistic function: low

L

, medium

M_{i}

and high

H

. These linguistic functions are defined first to introduce the fuzzy linguistic point relation. Then, a new algorithm of the fuzzy linguistic bicubic B-spline surface model is presented to convert fuzzy linguistic data into fuzzy linguistic control points. In addition, a numerical example of fuzzy linguistic data is considered at the end of this study to visualize the suggested model. Thus, the relation between the fuzzy linguistic data points can be analyzed to present another area of knowledge in which symmetry phenomena occur. The symmetry here plays an important role in solving the uncertain fuzzy linguistic data problem by using the suggested model. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications)

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22 pages, 2858 KiB

Open AccessArticle

Prime Cordial Labeling of Generalized Petersen Graph under Some Graph Operations

by Weidong Zhao, Muhammad Naeem and Irfan Ahmad

Symmetry 2022, 14(4), 732; https://doi.org/10.3390/sym14040732 - 03 Apr 2022

Cited by 2 | Viewed by 1916

Abstract

A graph is a connection of objects. These objects are often known as vertices or nodes and the connection or relation in these nodes are called arcs or edges. There are certain rules to allocate values to these vertices and edges. This allocation [...] Read more.

A graph is a connection of objects. These objects are often known as vertices or nodes and the connection or relation in these nodes are called arcs or edges. There are certain rules to allocate values to these vertices and edges. This allocation of values to vertices or edges is called graph labeling. Labeling is prime cordial if vertices have allocated values from 1 to the order of graph and edges have allocated values 0 or 1 on a certain pattern. That is, an edge has an allocated value of 0 if the incident vertices have a greatest common divisor

(\gcd)

greater than 1. An edge has an allocated value of 1 if the incident vertices have a greatest common divisor equal to 1. The number of edges labeled with 0 or 1 are equal in numbers or, at most, have a difference of 1. In this paper, our aim is to investigate the prime cordial labeling of rotationally symmetric graphs obtained from a generalized Petersen graph

P (n, k)

under duplication operation, and we have proved that the resulting symmetric graphs are prime cordial. Moreover, we have also proved that when we glow a Petersen graph with some path graphs, then again, the resulting graph is a prime cordial graph. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications)

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16 pages, 1152 KiB

Open AccessArticle

by Muhammad Nabeel Abid, Miin-Shen Yang, Hanen Karamti, Kifayat Ullah and Dragan Pamucar

Symmetry 2022, 14(2), 410; https://doi.org/10.3390/sym14020410 - 18 Feb 2022

Cited by 22 | Viewed by 1681

Abstract

T-spherical fuzzy set (TSFS) is a fuzzy layout aiming to provide a larger room for the processing of uncertain information-based data where four aspects of unpredictable information are studied. The frame of picture fuzzy sets (PFSs) and intuitionistic fuzzy sets (IFSs) provide limited [...] Read more.

T-spherical fuzzy set (TSFS) is a fuzzy layout aiming to provide a larger room for the processing of uncertain information-based data where four aspects of unpredictable information are studied. The frame of picture fuzzy sets (PFSs) and intuitionistic fuzzy sets (IFSs) provide limited room for processing such kinds of information. On a scale of zero to one, similarity measures (SMs) are a tool for evaluating the degrees of resemblance between various items or phenomena. The goal of this paper is to investigate the shortcomings of picture fuzzy (PF) SMs in order to introduce a new SM in a T-spherical fuzzy (TSF) environment. The newly improved SM has a larger ground for accommodating the uncertain information with three degrees and is also responsible for the reduction of information loss. The proposed SM’s validity is demonstrated mathematically and by examples. To examine the application of the suggested SM two real-life issues are discussed, including the concerns of medical diagnosis and pattern recognition. A comparison of the suggested SMs with current SMs is also made to assess the proposed work’s reliability. Since symmetric triangular fuzzy numbers are quite useful in database acquisition, we will consider the proposed SM for symmetric T-spherical triangular fuzzy numbers in the near future. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications)

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14 pages, 705 KiB

Open AccessArticle

Experimental Analysis of a Fuzzy Scheme against a Robust Controller for a Proton Exchange Membrane Fuel Cell System

by Cristian Napole, Mohamed Derbeli and Oscar Barambones

Symmetry 2022, 14(1), 139; https://doi.org/10.3390/sym14010139 - 12 Jan 2022

Cited by 2 | Viewed by 1164

Abstract

Proton exchange membrane fuel cells (PEMFC) are capable of transforming chemical energy into electrical energy with zero emissions. Therefore, these devices had been a point of attention for the scientific community as to provide another solution to renewable sources of energy. Since the [...] Read more.

Proton exchange membrane fuel cells (PEMFC) are capable of transforming chemical energy into electrical energy with zero emissions. Therefore, these devices had been a point of attention for the scientific community as to provide another solution to renewable sources of energy. Since the PEMFC is commonly driven with a power converter, a controller has to be implemented to supply a convenient voltage. This is an important task as it allows the system to be driven at an operative point, which can be related to the maximum power or an user desired spot. Along this research article, a robust controller was compared against a fuzzy logic strategy (with symmetric membership functions) where both were implemented to a commercial PEMFC through a dSPACE 1102 control board. Both proposals were analysed in an experimental test bench. Outcomes showed the advantages and disadvantages of each scheme in chattering reduction, accuracy, and convergence speed. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications)

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16 pages, 342 KiB

Open AccessArticle

Aggregation of Weak Fuzzy Norms

by Tatiana Pedraza, Jorge Ramos-Canós and Jesús Rodríguez-López

Symmetry 2021, 13(10), 1908; https://doi.org/10.3390/sym13101908 - 11 Oct 2021

Cited by 2 | Viewed by 1093

Abstract

Aggregation is a mathematical process consisting in the fusion of a set of values into a unique one and representing them in some sense. Aggregation functions have demonstrated to be very important in many problems related to the fusion of information. This has [...] Read more.

Aggregation is a mathematical process consisting in the fusion of a set of values into a unique one and representing them in some sense. Aggregation functions have demonstrated to be very important in many problems related to the fusion of information. This has resulted in the extended use of these functions not only to combine a family of numbers but also a family of certain mathematical structures such as metrics or norms, in the classical context, or indistinguishability operators or fuzzy metrics in the fuzzy context. In this paper, we study and characterize the functions through which we can obtain a single weak fuzzy (quasi-)norm from an arbitrary family of weak fuzzy (quasi-)norms in two different senses: when each weak fuzzy (quasi-)norm is defined on a possibly different vector space or when all of them are defined on the same vector space. We will show that, contrary to the crisp case, weak fuzzy (quasi-)norm aggregation functions are equivalent to fuzzy (quasi-)metric aggregation functions. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications)

19 pages, 2007 KiB

Open AccessArticle

Applying the Dijkstra Algorithm to Solve a Linear Diophantine Fuzzy Environment

by Mani Parimala, Saeid Jafari, Muhamad Riaz and Muhammad Aslam

Symmetry 2021, 13(9), 1616; https://doi.org/10.3390/sym13091616 - 02 Sep 2021

Cited by 15 | Viewed by 2638

Abstract

Linear Diophantine fuzzy set (LDFS) theory expands Intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PyFS) theories, widening the space of vague and uncertain information via reference parameters owing to its magnificent feature of a broad depiction area for permissible doublets. We codify [...] Read more.

Linear Diophantine fuzzy set (LDFS) theory expands Intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PyFS) theories, widening the space of vague and uncertain information via reference parameters owing to its magnificent feature of a broad depiction area for permissible doublets. We codify the shortest path (SP) problem for linear Diophantine fuzzy graphs. Linear Diophantine fuzzy numbers (LDFNs) are used to represent the weights associated with arcs. The main goal of the presented work is to create a solution technique for directed network graphs by introducing linear Diophantine fuzzy (LDF) optimality constraints. The weights of distinct routes are calculated using an improved score function (SF) with the arc values represented by LDFNs. The conventional Dijkstra method is further modified to find the arc weights of the linear Diophantine fuzzy shortest path (LDFSP) and coterminal LDFSP based on these enhanced score functions and optimality requirements. A comparative analysis was carried out with the current approaches demonstrating the benefits of the new algorithm. Finally, to validate the possible use of the proposed technique, a small-sized telecommunication network is presented. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications)

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14 pages, 295 KiB

Open AccessArticle

Fuzzy Sawi Decomposition Method for Solving Nonlinear Partial Fuzzy Differential Equations

by Atanaska Georgieva and Albena Pavlova

Symmetry 2021, 13(9), 1580; https://doi.org/10.3390/sym13091580 - 27 Aug 2021

Cited by 10 | Viewed by 1534

Abstract

The main goal of this paper is to propose a new decomposition method for finding solutions to nonlinear partial fuzzy differential equations (NPFDE) through the fuzzy Sawi decomposition method (FSDM). This method is a combination of the fuzzy Sawi transformation and Adomian decomposition [...] Read more.

The main goal of this paper is to propose a new decomposition method for finding solutions to nonlinear partial fuzzy differential equations (NPFDE) through the fuzzy Sawi decomposition method (FSDM). This method is a combination of the fuzzy Sawi transformation and Adomian decomposition method. For this purpose, two new theorems for fuzzy Sawi transformation regarding fuzzy partial gH-derivatives are introduced. The use of convex symmetrical triangular fuzzy numbers creates symmetry between the lower and upper representations of the fuzzy solution. To demonstrate the effectiveness of the method, a numerical example is provided. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications)

18 pages, 320 KiB

Open AccessArticle

Intuitionistic Fuzzy (IF) Overlap Functions and IF-Rough Sets with Applications

by Xiaofeng Wen, Xiaohong Zhang and Tao Lei

Symmetry 2021, 13(8), 1494; https://doi.org/10.3390/sym13081494 - 14 Aug 2021

Cited by 7 | Viewed by 1568

Abstract

Overlap function (which has symmetry and continuity) is widely used in image processing, data classification, and multi-attribute decision making problems. In recent years, theoretical research on overlap function has been extended to interval valued overlap function and lattice valued overlap function, but intuitionistic [...] Read more.

Overlap function (which has symmetry and continuity) is widely used in image processing, data classification, and multi-attribute decision making problems. In recent years, theoretical research on overlap function has been extended to interval valued overlap function and lattice valued overlap function, but intuitionistic fuzzy overlap function (IF-overlap function) has not been studied. In this paper, the concept of IF-overlap function is proposed for the first time, then the generating method of IF-overlap function is given. The representable IF-overlap function is defined, and the concrete examples of representable and unrepresentable IF-overlap functions are given. Moreover, a new class of intuitionistic fuzzy rough set (IF-roght set) model is proposed by using IF-overlap function and its residual implication, which extends the IF-rough set model based on intuitionistic fuzzy triangular norm, and the basic properties of the new intuitionistic fuzzy upper and lower approximate operators are analyzed and studied. At the same time, the established IF-rough set based on IF-overlap function is applied to MCDM (multi-criteria decision-making) problems, the intuitionistic fuzzy TOPSIS method is improved. Through the comparative analysis of some cases, the new method is proved to be flexible and effective. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications)

22 pages, 530 KiB

Open AccessArticle

Bipolar Picture Fuzzy Graphs with Application

by Waheed Ahmad Khan, Babir Ali and Abdelghani Taouti

Symmetry 2021, 13(8), 1427; https://doi.org/10.3390/sym13081427 - 04 Aug 2021

Cited by 13 | Viewed by 3148

Abstract

In this manuscript, we introduce and discuss the term bipolar picture fuzzy graphs along with some of its fundamental characteristics and applications. We also initiate the concepts of complete bipolar picture fuzzy graphs and strong bipolar picture fuzzy graphs. Firstly, we apply different [...] Read more.

In this manuscript, we introduce and discuss the term bipolar picture fuzzy graphs along with some of its fundamental characteristics and applications. We also initiate the concepts of complete bipolar picture fuzzy graphs and strong bipolar picture fuzzy graphs. Firstly, we apply different types of operations to bipolar picture fuzzy graphs and then we introduce various products of bipolar picture fuzzy graphs. Several other terms such as order and size, path, neighbourhood degrees, busy values of vertices and edges of bipolar picture fuzzy graphs are also discussed. These terminologies also lay the foundations for the discussion about the regular bipolar picture fuzzy graphs. Moreover, we also discuss isomorphisms, weak and co-weak isomorphisms and automorphisms of bipolar picture fuzzy graphs. Finally, at the base of bipolar picture fuzzy graph we present the construction of a bipolar picture fuzzy acquaintanceship graph, which would be an important tool to measure the symmetry or asymmetry of acquaintanceship levels of social networks, computer networks etc. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications)

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17 pages, 2259 KiB

Open AccessArticle

A Decision Analysis Model for the Brand Experience of Branded Apps Using Consistency Fuzzy Linguistic Preference Relations

by Tsuen-Ho Hsu, Chun-Hsien Chen and Ya-Wun Yang

Symmetry 2021, 13(7), 1151; https://doi.org/10.3390/sym13071151 - 27 Jun 2021

Cited by 2 | Viewed by 1815

Abstract

Branded apps are not only an important platform for enterprises and customers to have real-time interactions and communicate marketing messages, but also a new business model that encourages value co-creation between the two. In order to explore the impact of branded apps on [...] Read more.

Branded apps are not only an important platform for enterprises and customers to have real-time interactions and communicate marketing messages, but also a new business model that encourages value co-creation between the two. In order to explore the impact of branded apps on customers, this study constructs a fuzzy multi-criteria decision making (FMCDM) analysis model, and it uses consistent fuzzy linguistic preference relations (CFLPR) to set up a symmetric pairwise comparison matrix, which greatly reduces the complexity and error rate of calculations. Empirical research findings show that brand experience attributes and the influence of brand experience on customer loyalty and satisfaction can be more accurately measured. As a consequence of this study, we show that, among the brand experience facets of two retail chain branded apps, behavioral experience is the most favored, while affective experience is the least favored. Furthermore, brand attachment and active participation should be strengthened to enhance customer loyalty. Through the analytical model employed in this study, enterprises can regularly monitor changes in the brand experience preferences of branded app users and evaluate app performance to flexibly adjust mobile device-based marketing campaigns and strategies. It can also aid enterprises in using mobile devices effectively to improve customer loyalty and address the issue of diminishing brand loyalty. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications)

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21 pages, 413 KiB

Open AccessArticle

An Extension TOPSIS Method Based on the Decision Maker’s Risk Attitude and the Adjusted Probabilistic Fuzzy Set

by Donghai Liu, An Huang, Yuanyuan Liu and Zaiming Liu

Symmetry 2021, 13(5), 891; https://doi.org/10.3390/sym13050891 - 17 May 2021

Cited by 5 | Viewed by 1747

Abstract

The paper studies an extension TOPSIS method with the adjusted probabilistic linguistic fuzzy set in which the decision maker’s behavior tendency is considered. Firstly, we propose a concept of probabilistic linguistic q-rung orthopair set (PLQROS) based on the probability linguistic fuzzy set (PLFS) [...] Read more.

The paper studies an extension TOPSIS method with the adjusted probabilistic linguistic fuzzy set in which the decision maker’s behavior tendency is considered. Firstly, we propose a concept of probabilistic linguistic q-rung orthopair set (PLQROS) based on the probability linguistic fuzzy set (PLFS) and linguistic q-rung orthopair set (LQROS). The operational laws are introduced based on the transformed probabilistic linguistic q-rung orthopair sets (PLQROSs) which have the same probability. Through this adjustment method, the irrationality of the existing methods in the aggregation process is avoided. Furthermore, we propose a comparison rule of PLQROS and the aggregated operators. The distance measure of PLQROSs is also defined, which can deal with the symmetric information in multi-attribute decision making problems. Considering that the decision maker’s behavior has a very important impact on decision-making results, we propose a behavioral TOPSIS decision making method for PLQROS. Finally, we apply the practical problem of investment decision to demonstrate the validity of the extension TOPSIS method, and the merits of the behavior decision method is testified by comparing with the classic TOPSIS method. The sensitivity analysis results of decision-maker’s behavior are also given. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications)

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12 pages, 300 KiB

Open AccessArticle

A New Representation of Semiopenness of L-fuzzy Sets in RL-fuzzy Bitopological Spaces

by Ibtesam Alshammari, Omar H. Khalil and A. Ghareeb

Symmetry 2021, 13(4), 611; https://doi.org/10.3390/sym13040611 - 06 Apr 2021

Cited by 1 | Viewed by 1322

Abstract

In this paper, we introduce a new representation of semiopenness of L-fuzzy sets in

R L

-fuzzy bitopological spaces based on the concept of pseudo-complement. The concepts of pairwise

R L

-fuzzy semicontinuous and pairwise

R L

-fuzzy irresolute functions are extended [...] Read more.

In this paper, we introduce a new representation of semiopenness of L-fuzzy sets in

R L

-fuzzy bitopological spaces based on the concept of pseudo-complement. The concepts of pairwise

R L

-fuzzy semicontinuous and pairwise

R L

-fuzzy irresolute functions are extended and discussed based on the

(i, j)

-

R L

-semiopen gradation. Further, pairwise

R L

-fuzzy semi-compactness of an L-fuzzy set in

R L

-fuzzy bitopological spaces are given and characterized. As

R L

-fuzzy bitopology is a generalization of L-bitopology,

R L

-bitopology, L-fuzzy bitopology, and

R L

-fuzzy topology, the results of our paper are more general. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications)

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