Fuzzy Algebra Research Articles

Multi-attribute approach for selection of polymeric materials for manufacturing gears: A case study in the automotive industry

Automotive industry is characterized by mass production, a large share in the gross national income and high employment of workers with different knowledge and skills. Improving the production process, as well as product quality, is one of the most important tasks of automotive enterprise as well as government management. This research promotes a new fuzzy hybrid model for determining the priority of polymeric materials for manufacturing gears in an exact manner, which leads to an incremental improvement in the quality of the considered product. The analysis of polymeric materials and their characteristic is based on data from the relevant literature and experiences of the best practice. The relative importance of material characteristics is stated as fuzzy group decision making problem. The weights vector is determined by using the fuzzy Analytic Hierarchical Process and fuzzy geometric mean. The rank of polymeric materials is obtained by employing the proposed Technique for Order Preference by Similarity to Ideal Solution with triangular fuzzy numbers. The fuzzy algebra rules have been used for determining: (i) distances from Fuzzy Positive Ideal Solutions and Fuzzy Negative Ideal Solutions and (ii) closeness coefficient values. The proposed fuzzy hybrid model testing and verification are performed on real data in an automotive enterprise.

Theoretical Foundation, Topological Technique, and Decision-Making Application of Intuitionistic Fuzzy D-Algebra

Intuitionistic fuzzy D-algebra introduces a novel framework extending classical fuzzy algebra by incorporating degrees of membership and non-membership. This approach addresses the inherent uncertainty and imprecision in real-world systems. Topological techniques facilitate the analysis of convergence and continuity properties, ensuring the robustness of mathematical models. The need for such a framework arises from the limitations of classical fuzzy algebra in capturing nuanced degrees of uncertainty. Real-world decision-making processes often involve complex, ambiguous information that cannot be adequately represented by binary membership functions alone. Intuitionistic fuzzy D-algebra offers a more nuanced representation, expressing hesitation and uncertainty inherent in decision-making contexts. The proposed work comprehensively explores intuitionistic fuzzy D-algebra, including the formal definition of core structures, mathematical modelling, validation strategies through examples and counterexamples, and the development of interactive visualizations. By integrating computational tools and theoretical insights, this framework provides a versatile platform for addressing uncertainty in various domains, from decision-making systems to artificial intelligence, thus paving the way for innovative solutions and improved decision outcomes. The results provide an immersive exploration into the intricacies of intuitionistic fuzzy D-algebra. From the transformation of fuzzy sets into topological spaces to the dynamic manipulation of algebraic operations, each visualization offers an intense dive into understanding uncertainty and imprecision. The visuals serve as powerful educational tools, enabling a profound grasp of complex mathematical concepts and their practical implications in decision-making systems and artificial intelligence.

LATTICE OF A FUZZY PRIME IDEALS IN AN ORDERED SEMIGROUP

This paper introduces the concept of lattices of prime fuzzy ideals, which extends the classical theory of lattices of prime ideals in ring theory to the fuzzy setting. In this paper, we propose some examples and properties related to lattices of prime fuzzy ideals, contributing to the knowledge in fuzzy algebra. Think about an ordered semigroup ℛ. Plotting the function f from ℛ to the closed interval [0,1] defines a fuzzy subset of ℛ, where [0,1] ϵ ℛ. In order to explore prime ideals in rings, semigroups, and ordered semigroups in terms of fuzzy subsets, we build an ordered semigroup ℛ with ordered fuzzy points. To study, we presented the thoughts of ℒ-fuzzy prime ideals of an ordered semigroups ℛ, which forms a completelattice obeying the law relating the operations of multiplication and addition.

SIFAT SUBGRUP NORMAL DARI ANTI SUBGRUP NORMAL FUZZY

A fuzzy set is a concept theory that provide a solution of problem that cannot be explained by crisp set. Along with time, research of a fuzzy set are combined with algebra that produce fuzzy algebra. One of the research is a fuzzy subgroup and fuzzy level subset. The other research is an anti fuzzy subgroup that is inspired by a fuzzy subgroup. The purpose of this research is to write further study of anti fuzzy subgroup properties by induction of properties of fuzzy algebra such as fuzzy set, fuzzy subgroup, and anti fuzzy subgroup. The research procedure is to study the basic concept of fuzzy set, fuzzy subgroup, and anti fuzzy subgroup. Using that concept to proof the properties of the anti fuzzy subgroup. The conclusions are in the anti fuzzy subgroup, set with anti fuzzy subgroup is a subgroup of a group that can be applied to complement of and normal anti fuzzy subgroup closely related to anti fuzzy left coset, right coset, and middle coset.

Multiple-Attribute Decision Making Based on the Probabilistic Dominance Relationship with Fuzzy Algebras

In multiple-attribute decision-making (MADM) problems, ranking the alternatives is an important step for making the best decision. Intuitionistic fuzzy numbers (IFNs) are a powerful tool for expressing uncertainty and vagueness in MADM problems. However, existing ranking methods for IFNs do not consider the probabilistic dominance relationship between alternatives, which can lead to inconsistent and inaccurate rankings. In this paper, we propose a new ranking method for IFNs based on the probabilistic dominance relationship and fuzzy algebras. The proposed method is able to handle incomplete and uncertain information and can generate consistent and accurate rankings.

M-Hazy Module and Its Homomorphism Theorem

Based on a completely distributive lattice M , we propose a new fuzzification approach to a module, which leads to the concept of an M -hazy module. Different from the traditional fuzzification approach that defines a fuzzy algebra as a fuzzy subset of a classical algebra, we introduce an M -hazy module by fuzzifications of algebraic operations. Then, we investigate the fundamental properties of M -hazy modules and M -hazy submodules. In particular, we present the M -hazy module homomorphism theorem.

Fuzzy Algebras of Concepts

Preconcepts are basic units of knowledge that form the basis of formal concepts in formal concept analysis (FCA). This paper investigates the relations among different kinds of preconcepts, such as protoconcepts, meet and join-semiconcepts and formal concepts. The first contribution of this paper, is to present a fuzzy powerset lattice gradation, that coincides with the preconcept lattice at its 1-cut. The second and more significant contribution, is to introduce a preconcept algebra gradation that yields different algebras for protoconcepts, semiconcepts, and concepts at different cuts. This result reveals new insights into the structure and properties of the different categories of preconcepts.

EFQM and business model relation effect on performance of manufacturing enterprises

In the changing business environment conditions, one of the primary management tasks is competitiveness enhancement. This goal can be achieved, among other things, by improving performance, which has the greatest impact on business success. This research paper aims to indicate that the alignment between the European Foundation for Quality Management (EFQM) model and the business model leads to an increase in enterprise performance. By applying the Fuzzy Simple Additive Weighting (FSAW) method and fuzzy algebra rules, the aggregated value of quality was calculated. Determining the value of the considered performance is set as a fuzzy decision-making problem. Aggregated performance value is given by fuzzy geometric mean with combined fuzzy algebra rules. By applying correlation analysis, the significance of the influence of business models and quality models on the value of performance was determined. The proposed model was tested on a sample of 20 SMEs that operate in the Republic of Serbia.

On conjunctive complex fuzzification of Lagrange's theorem of <i>ξ</i>−CFSG

<abstract><p>The application of a complex fuzzy logic system based on a linear conjunctive operator represents a significant advancement in the field of data analysis and modeling, particularly for studying physical scenarios with multiple options. This approach is highly effective in situations where the data involved is complex, imprecise and uncertain. The linear conjunctive operator is a key component of the fuzzy logic system used in this method. This operator allows for the combination of multiple input variables in a systematic way, generating a rule base that captures the behavior of the system being studied. The effectiveness of this method is particularly notable in the study of phenomena in the actual world that exhibit periodic behavior. The foremost aim of this paper is to contribute to the field of fuzzy algebra by introducing and exploring new concepts and their properties in the context of conjunctive complex fuzzy environment. In this paper, the conjunctive complex fuzzy order of an element belonging to a conjunctive complex fuzzy subgroup of a finite group is introduced. Several algebraic properties of this concept are established and a formula is developed to calculate the conjunctive complex fuzzy order of any of its powers in this study. Moreover, an important condition is investigated that determines the relationship between the membership values of any two elements and the membership value of the identity element in the conjunctive complex fuzzy subgroup of a group. In addition, the concepts of the conjunctive complex fuzzy order and index of a conjunctive complex fuzzy subgroup of a group are also presented in this article and their various fundamental algebraic attributes are explored structural. Finally, the conjunctive complex fuzzification of Lagrange's theorem for conjunctive complex fuzzy subgroups of a group is demonstrated.</p></abstract>

γ– algebra of Sets and Some of its Properties

The main objective of this work is to generalize the concept of fuzzy algebra by introducing the notion of fuzzy algebra. Characterization and examples of the proposed generalization are presented, as well as several different properties of fuzzy algebra are proven. Furthermore, the relationship between fuzzy algebra and fuzzy algebra is studied, where it is shown that the fuzzy algebra is a generalization of fuzzy algebra too. In addition, the notion of restriction, as an important property in the study of measure theory, is studied as well. Many properties of restriction of a nonempty family of fuzzy subsets of fuzzy power set are investigated and it is shown that the restriction of fuzzy algebra is fuzzy algebra too.

Complex multi–fuzzy subgroups

There has been an increased recognition that more attention needs to be paid to the area of fuzzy algebra. A closer look at the literature, reveals several gaps and shortcomings such as the concept of complex multi-fuzzy subgroups. This article introduces the concept as well as investigates the nexus between complex multi-fuzzy subgroups and multi-fuzzy subgroups. Further, this article discovers that each complex multi-fuzzy subgroup produces two multi-fuzzy subgroups. Furthermore, there is additional discussion of the nexus between complex multi-fuzzy subgroups and classical subgroups. Finally, characterizes and illustrates the back-and-forth images carried by such a group homomorphism.

Special Issue on Symmetry in Classical and Fuzzy Algebraic Hypercompositional Structures

Symmetry plays a fundamental role in our daily lives and in the study of the structure of different objects in physics, chemistry, biology, mathematics, architecture, arts, sociology, linguistics, etc [...]

Computational Technique for Solving Imprecisely Defined Non-negative Fully Fuzzy Algebraic System of Linear Equations

Computational Technique for Solving Imprecisely Defined Non-negative Fully Fuzzy Algebraic System of Linear Equations

Evaluation and ranking of failures in manufacturing process by combining best‐worst method and VIKOR under type‐2 fuzzy environment

AbstractOne of the important and persistent problems that engineers face in the automotive industry is the reliability of production equipment. This research promotes a new fuzzy multicriteria model for determining the priority of failures in an exact manner. In this way, the decision makers can determine the management activities whose application should result in enhanced manufacturing process reliability, promptly. The analysis of failures is based on Failure mode and effects analysis that is extended with added risk factors, which represents the incremental improvement compared to the current literature sources. The relative importance of risk factors and their values are presented by pre‐defined linguistic expressions modelled by the interval type‐2 fuzzy numbers. The assessment of risk factors' relative importance is set as a fuzzy group decision‐making problem. The weights vector is determined by using the extended Best‐Worst Method. The rank of failures is obtained by employing the modified VIseKriterijumska Optimizacija i kompromisno Resenje (Eng. Multi‐criteria optimization and compromise solution) which reflects the scientific contribution of the research, and simultaneously, the second incremental improvement of the proposed model compared to the existing state of the art. These incremental improvements are: (i) The fuzzy algebra rules have been used for determining the group utility value and (ii) and individual regret value is determined by comparing the two interval type‐2 fuzzy numbers. The model testing and verification are performed on real data in an automotive supply chain.

Analysis of Risks and Security of E-Commerce by Using the Novel Concepts of Complex Cubic Picture Fuzzy Information

Digital technology is so broad today as to encompass almost everything. It eases the difficulties of day-to day life with internet. E-commerce plays an important role in digital age of technology. Instead of many benefits of online system, it faces many types of threats. Sometime, choosing the best e-commerce security has a lot of uncertainties and ambiguities to reduce the effect of threats. To reduce these uncertainties, this article developed a new concept of complex cubic picture fuzzy set (CoCPFS) of fuzzy algebra that explains the positive effect, neutral effect, and negative effect of any object and additionally discussed the Cartesian product between two CoCPFSs, CoCPF relations, and their types. The relationship among the e-commerce securities and threats is investigated for the first time in the history of fuzzy algebra. These relations show the ways of disabling the effects of a threat by an effective security technique. Furthermore, the advantages and benefits of CoCPFS are explained through comparison tests with preexisting frameworks of fuzzy sets.

On a new kind of ordered fuzzy group

This paper aims to further study the new kind of ordered fuzzy group named ordered L-group, which is put forward in literature [20]. Some algebraic properties of ordered L-groups, such as the relationship between elements, the equivalent characterizations and the products of these groups are discussed. Following that, the properties of substructures including characterization theorems, the convexity, the products of (normal) subgroups maintain the original substructure, along with the properties of ordered L-group homomorphisms are explored. The discussion of ordered fuzzy groups in this paper is from the perspective of fuzzy binary operation, which is different from the commonly method that just discuss the fuzzification of substructures in the research of fuzzy algebra. It can better reflect the essence of fuzzy groups logically just like that of classical groups.

Optimum Approximation for ς–Lie Homomorphisms and Jordan ς–Lie Homomorphisms in ς–Lie Algebras by Aggregation Control Functions

In this work, by considering a class of matrix valued fuzzy controllers and using a (κ,ς)-Cauchy–Jensen additive functional equation ((κ,ς)-CJAFE), we apply the Radu–Mihet method (RMM), which is derived from an alternative fixed point theorem, and obtain the existence of a unique solution and the H–U–R stability (Hyers–Ulam–Rassias) for the homomorphisms and Jordan homomorphisms on Lie matrix valued fuzzy algebras with ς members (ς-LMVFA). With regards to each theorem, we consider the aggregation function as a matrix value fuzzy control function and investigate the results obtained.

The assessment and selection of suppliers using AHP and MABAC with type-2 fuzzy numbers in automotive industry

The selection of appropriate suppliers in an uncertain environment influences the sustainability and the competitive advantage of the automotive industry and hence presents one of the significant management problems. In the literature, it is suggested that an acceptable supplier may be determined concerning many criteria. In this manuscript, criteria selection is based on the relevant literature. Handling of different uncertainties is performed by using the type-2 fuzzy sets that have the capability of handling more considered impreciseness and uncertainties. In the presented research, the two-state model is proposed. In the first stage, the relative importance of criteria and sub-criteria are described by pre-defined linguistic expressions which are modeled by the interval type-2 triangular fuzzy numbers (IT2TFNs). The fuzzy weights vectors are given by using the fuzzy Analytic Hierarchical Process with IT2TFNs (IT2FAHP). After that, the ranking of suppliers is based on the modified Multi-Attributive Border Approximation area Comparison method (MABAC) with IT2TFNs (IT2FMABAC). The extension of the conventional MABAC includes: (a) modeling of sub-criteria values of IT2TFNs, (b) the fuzzy criteria values are calculated by using fuzzy algebra rules, (c) belonging of each supplier to border approximation areas (BAAs) is given by using procedure, and (d) the distance of suppliers to BAAs is determined by using the normalized Euclidean distance formulas. The proposed model is tested on the real-life data from the automotive supply chain. Through the presented research, it is shown that the proposed IT2FMABAC is a useful and reliable tool for the rational purchasing decision-making process.

Study of Fuzzy σ-Ring and Some Related Concepts

This paper introduces the concept of fuzzy σ-ring as a generalization of fuzzy σ-algebra and basic properties; examples of this concept have been given. As the first result, it has been proved that every σ-algebra over a fuzzy set x* is a fuzzy σ-ring-over a fuzzy set x* and construct their converse by example. Furthermore, the fuzzy ring concept has been studied to generalize fuzzy algebra and its relation. Investigating that the concept of fuzzy σ-Ring is a stronger form of a fuzzy ring that is every fuzzy σ-Ring over a fuzzy set x* is a fuzzy ring over a fuzzy set x* and construct their converse by example. In addition, the idea of the smallest, as an important property in the study of real analysis, is studied as well. Finally, the main goal of this paper is to study these concepts and give basic properties, examples, characterizations and relationships between them.

Characterization on fuzzy soft ordered Banach algebra

In this paper, we define fuzzy soft ordered Banach algebra with fuzzy soft algebra cone, and introduce the character on fuzzy soft ordered Banach algebra in both cases real and complex. Also, we deduce some of its basic properties and we define a new concept which is a maximal fuzzy soft algebra cone and showing that the set of all fuzzy soft character is isomorphism to the set of all maximal fuzzy soft algebra cone. we prove that the set of all real characters is convex and extreme point, we applied Gelfand- Mazur theorem on fuzzy soft Banach algebra, we showed that character (the set of all complex continuous character) is fuzzy soft ordered Banach algebra. with inverse –closed algebra cone ̆ and a non-zero element in ̆ has inverse we have is an isomorphism to Banach space ( ̆)