Concept Of Fuzzy Sets Research Articles

Optimal Procurement of COVID-19 Vaccine with Time-Dependent Holding Cost and Shortages under Cloud Fuzzy Demand Rate

COVID-19 vaccine has emerged as the most powerful weapon against the spread of the coronavirus. Therefore, the management of the vaccine inventory is undoubtedly the most influential and important task for the global distribution of the vaccine. This paper is an attempt to model the vaccine inventory system having time-varying holding costs and partially backlogged shortages. The concept of fuzzy set and cloud pentagonal fuzzy number has been incorporated to make the models more realistic and applicable. Models are solved and validated through numerical examples and graphical representation. Further, sensitivity analysis has been done to identify the most sensitive parameters of all. Finally, managerial insights and conclusions have been drawn to make the vaccine inventory system more robust.

Modified Block Homotopy Perturbation Method for solving triangular linear Diophantine fuzzy system of equations

Numerous real-world applications can be solved using the broadly adopted notions of intuitionistic fuzzy sets, Pythagorean fuzzy sets, and q-rung orthopair fuzzy sets. These theories, however, have their own restrictions in terms of membership and non-membership levels. Because it utilizes benchmark or control parameters relating to membership and non-membership levels, this theory is particularly valuable for modeling uncertainty in real-world problems. We propose the unique concept of linear Diophantine fuzzy set with benchmark parameters to overcome these restrictions. Different numerical, analytical, and semi-analytical techniques are used to solve linear systems of equations with several fuzzy numbers, such as intuitionistic fuzzy number, triangular fuzzy number, bipolar fuzzy number, trapezoidal fuzzy number, and hexagon fuzzy number. The purpose of this research is to solve a fuzzy linear system of equations with the most generalized fuzzy number, such as Triangular linear Diophantine fuzzy number, using an analytical technique called Homotopy Perturbation Method. The linear systems co-efficient are crisp when the right hand side vector is a triangular linear Diophantine fuzzy number. A numerical test examples demonstrates how our newly improved analytical technique surpasses other existing methods in terms of accuracy and CPU time. The triangular linear Diophantine fuzzy systems of equations’ strong and weak visual representations are explored.

On Cohesive Fuzzy Sets, Operations and Properties with Applications in Electromagnetic Signals and Solar Activities

In the present communication, a new concept of a cohesive fuzzy set (CHFS) has been proposed as a synchronized generalization of complex fuzzy sets and hesitant fuzzy sets in a systematic way. The novelty of the introduced notion lies in the selection of the best alternative among the available multiple favorable situations, where the possibility of its range is in the extended unit circle of the complex plane. We study the relationship between the CHFS and the complex intuitionistic fuzzy set (CIFS), along with validation of the obtained results. On the basis of the proposed notion, various properties, operations, and identities have been established with their necessary proof. The applications of CHFS in the process of filtering the signals for obtaining the reference signal using the necessary Fourier cosine transform or inverse Fourier cosine transform and identifying the maximum number of sunspots in a particular interval of solar activity have been suitably discussed with illustrative numerical examples. Some advantages of incorporating the proposed notion have also been tabulated for better understanding.

On Some New Types of Fuzzy Soft Compact Spaces

In this article, we apply the concept of fuzzy soft δ -open sets to define new types of compactness in fuzzy soft topological spaces, namely, δ -compactness and δ ∗ -compactness. We explore some of their basic properties and reveal the relationships between these types and that which are defined by other authors. Also, we show that δ ∗ -compactness is more general than that which is presented in other papers. To clarify the obtained results and relationships, some illustrative examples are given.

Assessing Sustainable Passenger Transportation Systems to Address Climate Change Based on MCDM Methods in an Uncertain Environment

Climate change, the emission of greenhouse gases, and air pollution are some of the most important and challenging environmental issues. One of the main sources of such problems is the field of transportation, which leads to the emission of greenhouse gases. An efficient way to deal with such problems is carrying out sustainable transportation to reduce the amount of air pollution in an efficient way. The evaluation of sustainable vehicles can be considered a multi-criteria decision-making (MCDM) method due to the existence of several criteria. In this paper, we aim to provide an approach based on MCDM methods and the spherical fuzzy set (SFS) concept to evaluate and prioritize sustainable vehicles for a transportation system in Tehran, Iran. Therefore, we have developed a new integrated approach based on the stepwise weight assessment ratio analysis (SWARA) and the measurement of alternatives and ranking according to the compromise solution (MARCOS) methods in SFS to assess the sustainable vehicles based on the criteria identified by experts. The evaluation results show that the main criterion of the environment has a high degree of importance compared to other criteria. Moreover, autonomous vehicles are the best and most sustainable vehicles to reduce greenhouse gas emissions. Finally, by comparing the ranking results with other decision-making methods, it was found that the proposed approach has high validity and efficiency.

Some Properties Of Cartesian Product Of Two Fuzzy Normed Spaces

In this paper , the concept of the Cartesian Product of two fuzzy
 normed spaces is presented. Some basic properties and theorems on this
 concept are proved. The main goal of this paper is to prove that the
 Cartesian product of two complete fuzzy normed spaces is a complete
 fuzzy normed space.
 Key words:Fuzzy normed space , Cartesian product , Cauchy sequence ,
 complete fuzzy normed space.
 1- Introduction
 
 The fuzzy set concepts was introduced in mathematics by K.Menger
 in 1942 and reintroduced in the system theory by L.A.Zadeh in 1965.
 In 1984, Katsaras [ 1 ] , first introduced the notation of fuzzy norm on
 linear space, in the same year Wu and Fang [ 4 ] also introduced a notion of
 fuzzy normed space . Later on many other mathematicians like Felbin [ 2 ]
 , Cheng and Mordeson [ 10] , Bag and Samanta [12], J.Xiao and X.Zhu
 [8,9] , Krishna and Sarma [11] , Balopoulos and Papadopoulos [ 13] etc,
 have given different definitions of fuzzy normed spaces .
 J.Kider introduced the definition of fuzzy normed space[ 7 ] , we use this
 definition to prove that the Cartesian product of two fuzzy normed spaces
 is also fuzzy normed space.
 
 The structure of the paper is as follow : In section 2 we
 present some fundamental concepts . In section 3, the definition of fuzzy
 normed space appeared [7] is used to prove that the cartesain product of
 two fuzzy normed spaces is also fuzzy normed space, then we prove that
 the cartesain product of two complete fuzzy normed spaces is complete
 fuzzy normed space.
 
 2. Preliminaries
 In this section, we briefly recall some definitions and preliminary
 results which are used in this paper.

Some Results on Submodules Using (μ,ν,ω)-Single-Valued Neutrosophic Environment

The use of a single-valued neutrosophic set (svns) makes it much easier to manage situations in which one must deal with incorrect, unexpected, susceptible, faulty, vulnerable, and complicated information. This is a result of the fact that the specific forms of material being discussed here are more likely to include errors. This new theory has directly contributed to the expansion of both the concept of fuzzy sets and intuitionistic fuzzy sets, both of which have experienced additional development as a direct consequence of the creation of this new theory. In svns, indeterminacy is correctly assessed in a way that is both subtle and unambiguous. Furthermore, membership in the truth, indeterminacy, and falsity are all completely independent of one another. In the context of algebraic analysis, certain binary operations may be regarded as interacting with algebraic modules. These modules have pervasive and complicated designs. Modules may be put to use in a wide variety of different applications. Modules have applications in a diverse range of industries and market subsets due to their adaptability and versatility. Under the umbrella of the triplet (μ,ν,ω) structure, we investigate the concept of svns and establish a relationship between it and the single-valued neutrosophic module and the single-valued neutrosophic submodule, respectively. The purpose of this study is to gain an understanding of the algebraic structures of single-valued neutrosophic submodules under the triplet structure of a classical module and to improve the validity of this method by analyzing a variety of important facets. In this article, numerous symmetrical features of modules are also investigated, which demonstrates the usefulness and practicality of these qualities. The results of this research will allow for the successful completion of both of these objectives. The tactics that we have devised for use in this article are more applicable to a wide variety of situations than those that have been used in the past. Fuzzy sets, intuitionistic fuzzy sets, and neutrosophic sets are some of the tactics that fall under this category.

Decision Support System Based on Complex Fractional Orthotriple Fuzzy 2-Tuple Linguistic Aggregation Operator

In this research, we provide tools to overcome the information loss limitation resulting from the requirement to estimate the results in the discrete initial expression domain. Through the use of 2-tuples, which are made up of a linguistic term and a numerical value calculated between [0.5,0.5), the linguistic information will be expressed. This model supports continuous representation of the linguistic data within its scope, permitting it to express any information counting received through an aggregation procedure. This study provides a novel approach to develop a linguistic multi-attribute group decision-making (MAGDM) approach with complex fractional orthotriple fuzzy 2-tuple linguistic (CFOF2TL) assessment details. Initially, the concept of a complex fractional orthotriple fuzzy 2-tuple linguistic set (CFO2TLS) is proposed to convey uncertain and fuzzy information. In the meantime, simple aggregation operators, such as CFOF2TL weighted average and geometric operators, are defined. In addition, the CFOF2TL Maclaurin’s symmetric mean (CFOF2TLMSM) operators and their weighted shapes are presented, and their attractive characteristics are also discussed. A new MAGDM approach is built using the developed aggregation operators to address managing economic crises under COVID-19 with the CFOF2TL information. As a result, the effectiveness and robustness of the developed method are accompanied by an empirical example, and a comparative study is carried out by contrasting it with previous approaches.

Fuzzy parameterized-interval complex neutrosophic soft sets and their applications under uncertainty

Interval complex neutrosophic soft set (ICNSS) is the generalization of complex neutrosophic soft set (CNSS) as it provides an interval-based membership structure to handle the complex neutrosophic soft data. However, in the definition of the ICNSS, parameters set is a classical set, and the parameters have the same degree of importance which is considered as 1. This poses a limitation in modeling of some problems. Therefore, we introduce the concept of fuzzy parameterized interval complex neutrosophic soft set (FP-ICNSS) based on idea that each of elements of parameters set has got an importance degree. The basic theoretical operations and properties are defined and verified on FP-ICNSS. For FP-ICNSS, we conceptualize the relevant mapping and study the properties of the FP-ICNSS images and inverse images. Then, we propose a new algorithm that is applicable in the field of medical diagnosis and decision-making problems for selection right product. Moreover, an illustrative example is presented which depicts its validity for successful application to the problems involving vagueness and uncertainties. Eventually, a comparison between the proposed model and the existing methods is conducted to clarify the importance of this model.

(α1, 2, β1, 2)-complex intuitionistic fuzzy subgroups and its algebraic structure

<abstract> <p>A complex intuitionistic fuzzy set is a generalization framework to characterize several applications in decision making, pattern recognition, engineering, and other fields. This set is considered more fitting and coverable to Intuitionistic Fuzzy Sets (IDS) and complex fuzzy sets. In this paper, the abstraction of (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$) complex intuitionistic fuzzy sets and (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroups were introduced regarding to the concept of complex intuitionistic fuzzy sets. Besides, we show that (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroup is a general form of every complex intuitionistic fuzzy subgroup. Also, each of (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy normal subgroups and cosets are defined and studied their relationship in the sense of the commutator of groups and the conjugate classes of group, respectively. Furthermore, some theorems connected the (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroup of the classical quotient group and the set of all (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy cosets were studied and proved. Additionally, we expand the index and Lagrange's theorem to be suitable under (${{\alpha _{1, 2}}, {\beta _{1, 2}}}$)-complex intuitionistic fuzzy subgroups.</p> </abstract>

Trapezoidal type-2 Pythagorean fuzzy TODIM approach for sensible decision-making with unknown weights in the presence of hesitancy

<abstract> <p>Motivated by the concept of type-2 fuzzy sets, we introduce a novel framework known as trapezoidal type-2 Pythagorean fuzzy sets (TRT-2-PFSs), an extension of triangular fuzzy sets. Basic operations like addition and scalar multiplication of two TRT-2-Pythagorean fuzzy numbers (TRT-2-PFNs) are defined. We also explore comparative analysis and distance measurements between two TRT-2-PFNs. A methodology for evaluating unknown weight vectors and criteria weights is proposed. Building upon TRT-2-PFSs, an extension of the TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method is developed to address intricate decision-making challenges. Ultimately, the newly introduced TRT-2-PFS-based TODIM technique is employed to tackle multi-criteria decision-making (MCDM) problems.</p> </abstract>

Prioritization of Strategies of Digital Transformation of Supply Chain Employing Bipolar Complex Fuzzy Linguistic Aggregation Operators

Digitalization has addressed all parts of organizations together with supply chain management. Innovations like installed RFID, GPS, and sensors have assisted organizations with changing their current conventional supply chain framework into more spry, adaptable, open, and cooperative computerized models. A lot of organizations want to get the advantages of digitalization, particularly in the supply chain But here, the biggest problem, that the organizations are facing is the ambiguities, i.e. how to select and evaluate the best strategy for the supply chain digital transformation (SCDT), on which criteria or attribute they can assess the strategies of SCDT, etc. Multi-attribute decision-making (MADM) procedure is the finest technique to evaluate and find out the finest strategy of the SCDT. To handle these ambiguities and for making the MADM technique, this study first establishes the concept of bipolar complex fuzzy linguistic sets (BCFLSs) and its essential properties. Furthermore, we scrutinize average and geometric AOs for BCFLS such as bipolar complex fuzzy linguistic weighted averaging (BCFLWA) and bipolar complex fuzzy linguistic weighted geometric (BCFLWG) operators along with their idempotency, boundedness, and monotonicity properties. After that, to exhibit the usefulness of our established notion and AOs in real life and the selection and evaluation of the strategy of digital transformation of the supply chain, we interpret a DM technique and explore a numerical example. To exhibit the supremacy of the defined BCFLS and defined AOs we compare them with certain prevailing conceptions.

Circular Pythagorean Fuzzy Sets and Applications to Multi-Criteria Decision Making

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 non-membership degree and whose centre consists of non-negative real numbers μ and ν with the condition ${\mu ^{2}}+{\nu ^{2}}\leqslant 1$. A C-PFS models the fuzziness of the uncertain information more properly thanks to its structure that allows modelling the information with points of a circle of a certain centre and a radius. Therefore, a C-PFS lets decision makers to evaluate objects in a larger and more flexible region and thus more sensitive decisions can be made. After defining the concept of C-PFS we define some fundamental set operations between C-PFSs and propose some algebraic operations between C-PFVs via general triangular norms and triangular conorms. By utilizing these algebraic operations, we introduce some weighted aggregation operators to transform input values represented by C-PFVs to a single output value. Then to determine the degree of similarity between C-PFVs we define a cosine similarity measure based on radius. Furthermore, we develop a method to transform a collection of Pythagorean fuzzy values to a C-PFS. Finally, a method is given to solve multi-criteria decision making problems in circular Pythagorean fuzzy environment and the proposed method is practiced to a problem about selecting the best photovoltaic cell from the literature. We also study the comparison analysis and time complexity of the proposed method.

Spherical q-linear Diophantine fuzzy aggregation information: Application in decision support systems

<abstract><p>The main goal of this article is to reveal a new generalized version of the q-linear Diophantine fuzzy set (q-LDFS) named spherical q-linear Diophantine fuzzy set (Sq-LDFS). The existing concepts of intuitionistic fuzzy set (IFS), q-rung orthopair fuzzy set (q-OFS), linear Diophantine fuzzy set (LDFS), and spherical fuzzy set have a wide range of applications in decision-making problems, but they all have strict limitations in terms of membership degree, non-membership degree, and uncertainty degree. We moot the article of the spherical q-linear Diophantine fuzzy set (Sq-LDFS) with control factors to alleviate these limitations. A Spherical q-linear Diophantine fuzzy number structure is independent of the selection of the membership grades because of its control parameters in three membership grades. An Sq-LDFS with a parameter estimation process can be extremely useful for modeling uncertainty in decision-making (DM). By using control factors, Sq-LDFS may classify a physical system. We highlight some of the downsides of q-LDFSs. By using algebraic norms, we offer some novel operational laws for Sq-LDFSs. We also introduced the weighted average and weighted geometric aggregation operators and their fundamental laws and properties. Furthermore, we proposed the algorithms for a multicriteria decision-making approach with graphical representation. Moreover, a numerical illustration of using the proposed methodology for Sq-LDF data for emergency decision-making is presented. Finally, a comparative analysis is presented to examine the efficacy of our proposed approach.</p></abstract>

A study of quadratic Diophantine fuzzy sets with structural properties and their application in face mask detection during COVID-19

<abstract><p>During the COVID-19 pandemic, identifying face masks with artificial intelligence was a crucial challenge for decision support systems. To address this challenge, we propose a quadratic Diophantine fuzzy decision-making model to rank artificial intelligence techniques for detecting masks, aiming to prevent the global spread of the disease. Our paper introduces the innovative concept of quadratic Diophantine fuzzy sets (QDFSs), which are advanced tools for modeling the uncertainty inherent in a given phenomenon. We investigate the structural properties of QDFSs and demonstrate that they generalize various fuzzy sets. In addition, we introduce essential algebraic operations, set-theoretical operations, and aggregation operators. Finally, we present a numerical case study that applies our proposed algorithms to select a unique face mask detection method and evaluate the effectiveness of our techniques. Our findings demonstrate the viability of our mask identification methodology during the COVID-19 outbreak.</p></abstract>

An integrated group decision-making technique under interval-valued probabilistic linguistic T-spherical fuzzy information and its application to the selection of cloud storage provider

<abstract> <p>Cloud storage is crucial in today's digital era due to its accessibility, scalability, cost savings, collaboration and enhanced security features. The selection of a reliable cloud storage provider is a significant multi-attribute group decision-making (MAGDM) problem that involves intrinsic relationships among the various alternatives, attributes and decision DMs. Due to the uncertain and incomplete nature of the evaluation data for cloud storage providers, i.e., quality of service and user feedback, the identification of appropriate cloud storage providers with accurate service ranking remains an open research challenge. To address the above-mentioned challenge, this work proposes the concept of interval-valued probabilistic linguistic T-spherical fuzzy set (IVPLt-SFS). Then, some basic operations and a score function are defined to compare two or more IVPLt-SF numbers (IVPLt-SFNs). For information fusion, two aggregation operators for IVPLt-SFN are also developed. Next, an extended TOPSIS method-based group decision-making technique under interval-valued probabilistic linguistic T-spherical fuzzy information is established to solve the MAGDM problem. Finally, a numerical example is given to illustrate the practicability and usefulness of the designed approach and its suitability as a decision-making tool for selecting a cloud storage provider. Comparative and sensitivity analysis confirmed that this paper enriches the theory and methodology of the selection problem of cloud storage provider and MAGDM analysis.</p> </abstract>

Properties of Fuzzy Semi-Open Sets with Regards to Fuzzy Ideals

This paper introduces a broadened concept of fuzzy semi-open sets by framing them in the context of fuzzy ideals. Where many of their elementary properties will be presented in terms of theorems and lemmas. Also, many related examples about the validity of semi-open sets and their relationships with fuzzy ideals will be provided and discussed.

Two Integral Models and Applications of Hesitant Fuzzy Information Fusion

The existing fuzzy multiattribute decision making methods rely too much on discrete information fusion operators. In the context of big data, it cannot meet the needs of rapid fusion of massive data, nor can it reflect the continuous change of decision-makers thinking over time. In this article, we study how to integrate large-scare continuous hesitant fuzzy information more efficiently. We define the concepts of continuous hesitant fuzzy sets and continuous hesitant fuzzy functions. Based on these, we further explore definite line integrals of continuous hesitant fuzzy functions and their related properties. Two continuous hesitant fuzzy information integration models based on the hesitant fuzzy calculus are proposed. We also commit to revealing the internal connections between the first line integral model, the second line integral model, and the hesitant fuzzy weighted operator. We state why it is necessary to introduce novel aggregation models based on definite line integrals, and then provide applications of the proposed models to prove their validity and rationality. Finally, we compare the proposed models with other aggregation operators to further demonstrate their effectiveness and rationality.

An inclusive study on the fundamentals of interval-valued fuzzy hypersoft set

When compared to its extension, hypersoft set, a soft set only deals with a single set of attributes, while a hypersoft set deals with several attribute-valued disjoint sets that correspond to various attributes. Several researchers have developed models based on soft sets, but the majority of these models suffer from limitations since they are inappropriate for interval-type data or uncertain data. In order to address these issues, a novel model interval-valued fuzzy hypersoft set (IV F HS -set) is presented in this research article. This model not only resolves the inadequacy of soft set for distinct attributes for non-overlapping attribute-valued sets, but also addresses the limitations of soft set-like models with having data in interval environment. This work modifies the current fuzzy hypersoft set concept and introduces certain fundamental ideas, such as subset, not set, whole set, and absolute relative null set, relative absolute set and aggregation operations e.g. intersection, union, extended intersection, restricted union, complement, OR, AND, difference, restricted difference are discussed under IV F HS -set environment with illustrated examples. Some new hybrids of fuzzy hypersoft set under interval-valued settings are also discussed. Moreover, some extensions of IV F HS -set are presented along with different operations.

Intuitionistic Fuzzy Modulus Similarity Measure

The concept of intuitionistic fuzzy sets (IFSs) is an expected explanation for finding the appropriate information. It originated from concept of fuzzy set (FS) theory, which extends the classical conception of a fuzzy set. This paper examines a number of widely employed similarity measures then proposes an IFSs modulus similarity measure and a weight similarity measure. Initially, the authors have discussed numerous existing similarity measures, some of which are unable to justify the axioms of being a similarity measure. Furthermore, some numerical examples are presented to compare the existing similarity measures with the proposed similarity measure. The proposed similarity measure is a practical and effective method for determining the qualitative similarity between IFSs, which do not have any paradoxical nature. In addition, the proposed similarity measure has been demonstrated practically in pattern recognition and medical diagnosis problem. Suggestions for future research comprise the conclusions of the paper.