Fuzzy Multisets Research Articles

Enhancing decision-making with linear diophantine multi-fuzzy set: application of novel information measures in medical and engineering fields

Enhancing decision-making with linear diophantine multi-fuzzy set: application of novel information measures in medical and engineering fields

Topological Approaches in Characterization of Algebraic Structure of Fuzzy Multiset Finite Automata

Topological Approaches in Characterization of Algebraic Structure of Fuzzy Multiset Finite Automata

Multi-fuzzy sets and neural networks: a collaborative tool for artificial intelligence

Multi-fuzzy sets and neural networks: a collaborative tool for artificial intelligence

Exponential similarity measure of confidence consistency fuzzy cubic sets in fuzzy multiset scenarios and its application in piano performance evaluation

A consistency fuzzy set is composed of mean values and consistency degrees of fuzzy sequences in the transformation process of a fuzzy multiset (FM), but lacks confidence intervals in relation to a confidence level of fuzzy sequences, which shows its deficiency. To solve this deficiency, this paper aims to propose an improved transformation approach from FM to a confidence consistency fuzzy cubic set (CCFCS) and to develop an exponential similarity measure of CCFCSs for modeling piano performance evaluation (PPE) in a FM scenario. Consequently, this study includes the following context. First, a transformation approach from FM to CCFCS is proposed in terms of mean values, consistency degrees (the complement of standard deviation), and confidence intervals of fuzzy sequences subject to a confidence level and normal distribution. Second, the exponential similarity measure of CCFCSs is proposed in the scenario of FMs. Third, a PPE model is developed based on the proposed similarity measure of CCFCSs in the FM scenario. Finally, the developed model is applied to a piano performance competition organized by Shaoxing University in China as an actual evaluation example, and then the rationality and validity of the proposed model in the scenario of FMs are verified through sensitivity and comparison analysis.

A Study on Intuitionistic Multi-Fuzzy Ideals in BH-Algebra

The purpose of this paper is to implement the concept of intuitionistic multi-fuzzy sets to ideals in BH-algebra. In this paper, we introduce the notion of intuitionistic multi-fuzzy ideals, intuitionistic multi-fuzzy closed ideals in BH-algebra and investigate some of their related properties. Also we discuss the relation between intuitionistic multi-fuzzy ideals and intuitionistic multi-fuzzy closed ideals of BH-algebra. Finally we define the upper level subset of intuitionistic multi-fuzzy ideals of BH-algebra and study some of its properties based on (α,β )-cut.

Anti homomorphism and homomorphism of bipolar valued multi Fuzzy HX-subgroups and it’s normal

In this article, homomorphism and anti-homomorphism bipolar valued multi normal fuzzy HX subgroup of a HX group is studied, discussed and their properties are introduced. The theorems presented in this article are considered a generalization of what has been publishedthrough the concept of fuzzy sets. As the concept of fuzzy sets was introduced by Zadeh in 1965, after that this concept, we expanded into more than one types, intuitionistic fuzzy set, bipolar fuzzy sets, tripolar fuzzy set, and bipolar valued multi fuzzy set are one of this.

A Possibilistic Information Fusion-Based Unsupervised Feature Selection Method Using Information Quality Measures

The main goal of most information quality (IQ)-based measures is to combine data provided by multiple information sources to enhance the quality of information essential for decision makers to perform their tasks. However, there is few work to fuse multi-source information from the perspective of possibility distribution (PD) and use IQ as the evaluation criteria for feature selection. The PD is one of important concepts in possibility theory, which is a generally acknowledged method for describing a kind of uncertain knowledge. In this paper, we propose a novel representation model of possibility distributions based on fuzzy multisets, namely, a possibility distribution information system (PDIS). Then, several IQ measures are defined in the PDIS, including Gini entropy, compatibility, conflict, credibility and separability degrees. In view of this, a minimal-separability-minimal-uncertainty-based unsupervised feature selection algorithm (UmSMU) is designed. The proposed UmSMU can sufficiently fuse multiple possibilistic information. Meanwhile, the selected features maintain as much information as possible while minimizing the uncertainty of information. The experimental results show that the proposed algorithm performs well, especially when it comes to selecting fewer features and improving performance.

HOMOMORPHISM OF IMAF NORMAL SUBGROUP

ABSTRACT In this article an attempt has been made to study some new algebraic structures of intuitionistic multi-anti fuzzy normal subgroups under homomorphism are discussed. Keywords Intuitionistic multi-fuzzy set (IMFS), Intuitionistic multi-anti fuzzy subgroup (IMAFSG), Intuitionistic multi-anti fuzzy normal subgroup (IMAFNSG). Mathematics Subject Classification 20N25, 03E72, 08A72, 03F55, 06F35, 03G25, 08A05

From Restricted Equivalence Functions on $L^{n}$ to Similarity Measures Between Fuzzy Multisets

Restricted equivalence functions are well-known functions to compare two numbers in the interval between 0 and 1. Despite the numerous works studying the properties of restricted equivalence functions and their multiple applications as support for different similarity measures, an extension of these functions to an n-dimensional space is absent from the literature. In this paper, we present a novel contribution to the restricted equivalence function theory, allowing to compare multivalued elements. Specifically, we extend the notion of restricted equivalence functions from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L^{n}$</tex-math></inline-formula> and present a new similarity construction on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L^{n}$</tex-math></inline-formula> . Our proposal is tested in the context of color image anisotropic diffusion as an example of one of its many applications.

Linear diophantine multi-fuzzy aggregation operators and its application in digital transformation

Digital transformation is the significant phenomena in contemporary global environment. All the conventional fuzzy sets are extended by the Linear Diophantine Fuzzy Set (LDFS). LDFS is the most viable adaptable method for decision makers to choose their grade values as it includes reference parameters. The foremost vision is to promote the resilient integration of Linear Diophantine Multi-Fuzzy Set (LDMFS) as a model for constructing decisions in order to identify the appropriate standards for digital transformation. Aggregation Operators are crucial in fuzzy systems for fusing information. To aggregate the LDMF, a number of operators have been devised, such as the Linear Diophantine Multi-Fuzzy Weighted Geometric Operator (LDMFWGO), Linear Diophantine Multi-Fuzzy Ordered Weighted Geometric Operator (LDMFOWGO), Linear Diophantine Multi-Fuzzy Weighted Averaging Operator (LDMFWGO) and Linear Diophantine Multi-Fuzzy Ordered Weighted Averaging Operator (LDMFOWAO). By integrating preferred aggregating operations, a novel method for MCDM with LDMF data is studied. The best option from the current alternatives can be determined using these operators. Moreover, a comparison of LDMF operators is made. Additionally, the idea of a scoring function for LDF is designed to examine the rank of viable alternaties. Additionally, a novel approach to solving LDMF sets is suggested. The annals on organisational digital transformation is presented as the final section to test the supremacy of the theory. Accurate rankings for digital transformation are provided by the outcome. To exhibit the robustness of the MCDM methodology, a prompt comparative analysis is established between the suggested concept and the currently used approaches.

A Novel Approach in the Light of Fuzzy Multiset Topology

A Novel Approach in the Light of Fuzzy Multiset Topology

(α, γ)-Anti-Multi-Fuzzy Subgroups and Some of Its Properties

Recently, fuzzy multi-sets have come to the forefront of scientists’ interest and have been used in algebraic structures such as multi-groups, multi-rings, anti-fuzzy multigroup and (α, γ)-anti-fuzzy subgroups. In this paper, we first summarize the knowledge about the algebraic structure of fuzzy multi-sets such as (α, γ)-anti-multi-fuzzy subgroups. In a way, the notion of anti-fuzzy multigroup is an application of anti-fuzzy multi sets to the theory of group. The concept of anti-fuzzy multigroup is a complement of an algebraic structure of a fuzzy multi set that generalizes both the theories of classical group and fuzzy group. The aim of this paper is to highlight the connection between fuzzy multi-sets and algebraic structures from an anti-fuzzification point of view. Therefore, in this paper, we define (α, γ)-anti-multi-fuzzy subgroups, (α, γ)-anti-multi-fuzzy normal subgroups, (α, γ)-anti-multi-fuzzy homomorphism on (α, γ)-anti-multi-fuzzy subgroups and these been explicated some algebraic structures. Then, we introduce the concept (α, γ)-anti-multi-fuzzy subgroups and (α, γ)-anti-multi-fuzzy normal subgroups and of their properties. This new concept of homomorphism as a bridge among set theory, fuzzy set theory, anti-fuzzy multi sets theory and group theory and also shows the effect of anti-fuzzy multi sets on a group structure. Certain results that discuss the (α, γ) cuts of anti-fuzzy multigroup are explored.

Multi-attribute Group Decision-making Based on Hesitant Bipolar-valued Fuzzy Information and Social Network

Fuzzy sets have undergone several expansions and generalisations in the literature, including Atanasov’s intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets, to name a few. They can be regarded as fuzzy multisets from a formal standpoint; nevertheless, their interpretation differs from the two other approaches to fuzzy multisets that are currently available. Hesitating fuzzy sets (HFS) are very useful if consultants have hesitation in dealing with group decision-making problems between several possible memberships. However, these possible memberships can be not only crisp values in [0,1], but also interval values during a practical evaluation process. Hesitant bipolar valued fuzzy set (HBVFS) is a generalization of HFS. This paper aims to introduce a general framework of multi-attribute group decision-making using social network. We propose two types of decision-making processes: Type-1 decision-making process and Type-2 decision-making process. In the Type-1 decision-making process, the experts’ original opinion is proces for the final ranking of alternatives. In Type-2 decision making processs, there are two major aspects we consider. First, consistency tests and checking of consensus models are given for detecting that the judgments are logically rational. Otherwise, the framework demands (partial) decision-makers to review their assessments. Second, the coherence and consensus of several HBVFSs are established for final ranking of alternatives. The proposed framework is clarified by an example of software packages selection of a university.

The concept of inverse α-cuts in multi Q-fuzzy set

In various mathematical theories such as fuzzy sets, fuzzy multisets, fuzzy soft sets, the concept of α-Cuts were applied together with their inverses. However, we noticed that in multi Q-fuzzy sets only α-Cuts were studied without their inverses. In this paper the concept of inverse α-Cuts and their properties in multi Q-fuzzy sets were introduced. Some distinctive features of α-Cuts and inverse α-Cuts were demonstrated. It is shown that as both first and second decomposition theorems hold in the former, it actually fails in the latter. Moreover, unlike α-cuts, it was discovered that, a multi Q-fuzzy set cannot be uniquely represented as the family of all its weak inverse α-cuts. Thus, both α-cuts and inverse α-cuts attract applications in many mathematical fields.

Algebraic Hyperstructure of Multi-Fuzzy Soft Sets Related to Polygroups

The combination of two elements in a group structure is an element, while, in a hypergroup, the combination of two elements is a non-empty set. The use of hypergroups appears mainly in certain subclasses. For instance, polygroups, which are a special subcategory of hypergroups, are used in many branches of mathematics and basic sciences. On the other hand, in a multi-fuzzy set, an element of a universal set may occur more than once with possibly the same or different membership values. A soft set over a universal set is a mapping from parameters to the family of subsets of the universal set. If we substitute the set of all fuzzy subsets of the universal set instead of crisp subsets, then we obtain fuzzy soft sets. Similarly, multi-fuzzy soft sets can be obtained. In this paper, we combine the multi-fuzzy soft set and polygroup structure, from which we obtain a new soft structure called the multi-fuzzy soft polygroup. We analyze the relation between multi-fuzzy soft sets and polygroups. Some algebraic properties of fuzzy soft polygroups and soft polygroups are extended to multi-fuzzy soft polygroups. Some new operations on a multi-fuzzy soft set are defined. In addition to this, we investigate normal multi-fuzzy soft polygroups and present some of their algebraic properties.

Single and Interval-Valued Hybrid Enthalpy Fuzzy Sets and a TOPSIS Approach for Multicriteria Group Decision Making

The concept of entropy is one of the most important notions of the information theory. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. Shannon’s entropy is one of the most useful entropy types. The notion of enthalpy is the information energy expressed by the complement of Shannon’s entropy. In this paper, we propose the concept of interval-valued hybrid enthalpy fuzzy set by modifying single and interval-valued fuzzy multisets. In this context, an interval-valued hybrid enthalpy fuzzy set contains information about both the data and their entropy. We also provide a cosine similarity measure between interval-valued hybrid enthalpy fuzzy sets. Using this cosine similarity measure, we propose a TOPSIS approach for multicriteria group decision making. Moreover, we apply the proposed TOPSIS method to a research assistant selection problem, and we compare the result with the result of a classical TOPSIS method.

SOME PROPERTIES OF FUZZY MULTIGROUPS

The concept of fuzzy multigroup is an algebraic structure of a fuzzy multiset that generalizes both the classical group and fuzzy group. In fact, fuzzy multigroup constitutes an application of fuzzy multiset to the elementary theory of classical group. In this paper, some notions of fuzzy multigroup such as normal series and its properties, fuzzy multigroupoid, fuzzy multimonoid, centralizer of fuzzy multigroup etc., were presented. Some theorems on these together with their proofs were formulated. Some related results on fuzzy multigroups were established

FP-intuitionistic multi fuzzy N-soft set and its induced FP-Hesitant N soft set in decision-making

Intuitionistic fuzzy sets (IFSs) can effectively represent and simulate the uncertainty and diversity of judgment information offered by decision-makers (DMs). In comparison to fuzzy sets (FSs), IFSs are highly beneficial for expressing vagueness and uncertainty more accurately. As a result, in this research work, we offer an approach for solving group decision-making problems (GDMPs) with fuzzy parameterized intuitionistic multi fuzzy N-soft set (briefly, FPIMFNSS) of dimension q by introducing its induced fuzzy parameterized hesitant N-soft set (FPHNSS) as an extension of the multi-fuzzy N-soft set (MFNSS) based group decision-making method (GDMM). In this study, we use the proposed GDMM to solve a real-life GDMP involving candidate eligibility for a single vacant position advertised by an IT firm and compare the ranking performances of the proposed GDMM with the Fatimah-Alcantud method.

On Triangular Multisets and Triangular Fuzzy Multisets

The basic set operations between fuzzy sets are defined using the min and max functions; however, later on, new operators were introduced that used other functions, which, nevertheless, had similar properties to functions min and max. The resulting fuzzy set theories are more suitable for the description and processing of specific data sets. Crisp and fuzzy multisets have found numerous applications but still the basic operations are based on functions min and max. It is straightforward to replace these functions in the fuzzy part of fuzzy multisets; however, it is not as easy but is feasible to do the same with the multisets and the “crisp” part of fuzzy multisets. The new mathematical structures are called triangular multisets and triangular fuzzy multisets, respectively. The aim is to facilitate the processing of certain data sets so they can be used in multi-criteria decision making and computing.

Einstein-operations on fuzzy soft multi sets and decision making

In this paper, we define Einstein product and Einstein sum of fuzzy soft multi sets (FSM-sets) and using these products, we introduce an adjustable approach to FSM-set based decision-making, for solving decision-making in an uncertain situation. The feasibility of our proposed FSM-set based decision-making procedure in practical application is shown by some numerical examples.