Extension Of Fuzzy Set Theory Research Articles

Risk Assessment of Employing Digital Robots in Process Automation

Using digital technologies is essential to gain a competitive advantage in the global market by adapting to new business models. While digital technologies make business processes efficient, they enable companies to make faster and more accurate decisions by automating daily and routine process tasks. Robotic process automation (RPA) automates routine and repetitive business processes, allowing many jobs performed by humans to be performed faster. This way, advantages such as reduced error rates, reduced costs, increased production speed, and labor productivity are provided. For the successful implementation of RPA, potential risks need to be considered. In this study, failure mode and effect analysis (FMEA) based on decomposed fuzzy sets (DFSs), a new extension of intuitionistic fuzzy sets, has been used to evaluate subjectiveness in expert judgments. Differing from the other extensions of fuzzy set theory, the advantage of DFSs is to simultaneously consider decision-makers’ optimistic and pessimistic answers. Thus, the answer given by the decision-maker to the positive and negative questions on the same subject defines the indeterminacy of the decision-maker, and the method takes this indeterminacy into account in the evaluation. This study assesses and evaluates the potential risks of six digital robots in process automation. Thirteen risks were individually assessed for each automated process. This study found “Sustainability challenge” critical in three processes, “Absence of governance management” in two, and “Security“ in one. Variability in risk importance arose from process vulnerabilities.

Estimation of Reservoir Storage Capacity Using the Gould-Dincer Formula with the Aid of Possibility Theory

This paper presents a method for estimating reservoir storage capacity using the Gould–Dincer normal formula (G-DN), enhanced by the possibility theory. The G-DN equation is valuable for regional studies of reservoir reliability, particularly under climate change scenarios, using regional statistics. However, because the G-DN formula deals with measured data, it introduces a degree of uncertainty and fuzziness that traditional probability theory struggles to address. Possibility theory, an extension of fuzzy set theory, offers a suitable framework for managing this uncertainty and fuzziness. In this study, the G-DN formula is adapted to incorporate fuzzy logic, and the possibilistic nature of reservoir capacity is translated into a probabilistic framework using α-cuts from the possibility theory. These α-cuts approximate probability confidence intervals with high confidence. Applying the proposed methodology, in the present crisp case with the storage capacity D = 0.75, the value of the capacity C was found to be 1271×106 m3, and that for D = 0.5 was 634.5×106 m3. On the other hand, in the fuzzy case using the possibility theory, the value of the capacity for D = 0.75 is the internal [315,5679]×106 m3 and for D = 0.5 the value is interval [158,2839]×106 m3, with a probability of ≥95% and a risk level of α = 5% for both cases. The proposed approach could be used as a robust tool in the toolkit of engineers working on irrigation, drainage, and water resource projects, supporting informed and effective engineering decisions.

A Study on AG-Groups in Spherical Fuzzy Environment

An AG-group is an algebraic structure that satisfies the left invertive law and includes its left identity and inverse elements. This framework is naturally suited for representing and manipulating various real-life applications in civil engineering, information engineering, artificial intelligence, and more. In this paper, we present the structural application of AG-groups in data encryption and in the rotational transformation of water molecules. Additionally, numerous authors have explored fuzzy set theory over AG-group systems, yielding many valuable results. Spherical fuzzy set theory, an extension of fuzzy set theory, allows for the representation of uncertainty in decision-making, where there may be multiple possible choices or uncertainty about the degree of membership of an element in a set. However, no prior work has combined spherical fuzzy set theory with AG-groups, which motivates our study. In this paper, we apply spherical fuzzy set theory to AG-groups and introduce the concept of spherical fuzzy AG-subgroupoids. We provide the characterization of spherical fuzzy AG-subgroupoids over AG-groupoids and examine their related properties. As an application of spherical fuzzy sets over AG-groups, we develop the concept of normal spherical fuzzy groups over AG-groups and investigate their various properties.

A Study of n-ary Groupoids Based on Hesitant Fuzzy Sets

Fuzzy set theory plays a vital role in solving many complicated problems dealing with uncertainty. An [Formula: see text]-ary algebraic system as a generalization of algebraic structures that allow for operations involving more than two elements. They provide a natural framework for representing and manipulating complex relationships and interactions among multiple elements, which is essential for solving many real-world problems. Many authors have studied fuzzy set theory over an [Formula: see text]-ary algebraic systems and have provided many fruitful results. Hesitant fuzzy set theory is a further extension of fuzzy set theory, which allows for the representation of uncertainty in decision making where decision makers may have multiple possible choices or may be uncertain about the degree of membership of an element in a given set. No authors have studied, by combining hesitant fuzzy set theory with an [Formula: see text]-ary algebraic systems. This motivates us to study hesitant fuzzy set over an [Formula: see text]-ary algebraic system. In this paper, we have applied hesitant fuzzy set theory in an [Formula: see text]-ary algebraic systems and introduced the notions of hesitant fuzzy subgroupoid. We provide the characterization of hesitant fuzzy [Formula: see text]-ary subgroupoid over an [Formula: see text]-ary groupoids and have studied their related properties. As an application of hesitant fuzzy set over an [Formula: see text]-ary groupoids, we have developed the concept of normal hesitant fuzzy subgroupoids over an [Formula: see text]-ary groupoids and have studied their various properties.

Assuming Photon as Extended Point Particle in the HyperSoft Topological Space and other Hypotheses: Issues and Trend Analysis

Following our preceding article, where we discussed alternative interpretations of the advanced perihelion of Mercury, the present article revisits the 1919 solar eclipse expedition led by Arthur Eddington, which famously provided the first observational confirmation of Einstein's theory of general relativity. We focus on the deflection of starlight data obtained during the eclipse, a cornerstone of this validation. Here, we explore three alternative explanations for the observed light bending that challenge the sole attribution to general relativity. Firstly, the paper begins by arguing based on criticisms raised by Tullio Levi-Civita, a contemporary mathematician, regarding Einstein's use of pseudo-tensors in his calculations. Levi-Civita argued that this approach introduced unnecessary complexity and obscured alternative interpretations of the data. Secondly, we delve into astrophysical phenomena that could mimic the observed light deflection, based on the varying speed of light, by assuming a photon has mass. (cf. ‘t Hooft et al., Light is Heavy). Moreover, in the literature, Molodtsov initiated soft set theory as an extension of fuzzy set theory to deal with uncertainties occurring in the natural and social sciences. It attracted the attention of mathematicians as well as social scientists due to its potential to unify certain mathematical aspects and applications in decision making processes; therefore, we shall discuss a bit how to model the photon as an extended massive particle of light, possibly related to such a soft set point [15, 16]. For further exploration, it is possible to assume the crystalline lattice of subvacuum structure (cf. Gremaud) as part of hypersoft topological spaces [16, 16a]. We strongly believe that the true strength of science lies in its continuous search for evidence and refinement of existing models. Therefore, it can be expected that new data can be helpful to reevaluate these matters, for instance, in the upcoming eclipse in the next month of 2024.

Multi – Fuzzy Ideals of Г - Near Ring

Multi – fuzzy set theory is an extension of fuzzy set theory. In this paper, we define the multi fuzzy ideals of Г - near ring. Also, the notion of anti multi fuzzy ideals of a Г - near ring is introduced and investigated some related properties. This concept of multi fuzzy ideals of a Г - near ring is a generalization of the concept of fuzzy ideals in Г - near rings. Also, we define the multi-level subsets and multi anti level subsets of a multi fuzzy sub Г - near ring of a Г- near ring. In this paper we define the multi level subset and multi anti level subset of AUB. The purpose of this study establishes the algebra of multi fuzzy Г- near ring.

An integrated MULTIMOORA method with 2-tuple linguistic Fermatean fuzzy sets: Urban quality of life selection application

<abstract><p>This article elaborates the enormous theory of MULTIMOORA (multi-objective optimization ratio analysis plus full multiplicative form) method to build up a new outranking approach for the innovative extension of fuzzy set theory, namely, 2-tuple linguistic Fermatean fuzzy sets (2TLFFSs). The main objective of the proposed work is to expand and present the components of MULTIMOORA method in 2-tuple linguistic Fermatean fuzzy framework. The resulted technique is named as 2-tuple linguistic Fermatean fuzzy MULTIMOORA method. This technique is designed to tackle the unclear information using 2-tuple linguistic Fermatean fuzzy numbers (2TLFFNs). The proposed model is intrinsically superior to deal with one-dimensional linguistic data. The 2TLFF-MULTIMOORA method takes into account standard relative correlations. Also, it handles the rank inversion problem when changing the rank of alternatives by adding one or more alternatives. The algorithm designed for the proposed methodology is elaborated with a numerical example (to opt for the most favorable city for the selection of quality of life). The accuracy and precision of the proposed strategy is determined by narrating a comparative study. Finally, the advantages of the developed technique over existing methods are discussed briefly.</p></abstract>

A Study on Intuitionistic Fuzzy Critical Path Problems Through Centroid Based Ranking Method

In this study the intuitionistic fuzzy version of the critical path method has been proposed to solve networking problems with uncertain activity durations. Intuitionistic fuzzy set [1] is an extension of fuzzy set theory [2] unlike fuzzy set, it focuses on degree of belonging, the degree of nonbelonging or non-membership function and the degree of hesitancy which helps the decision maker to adopt the best among the worst cases. Trapezoidal and the triangular intuitionistic fuzzy numbers are utilized to describe the uncertain activity or task durations of the project network. Here trapezoidal and triangular intuitionistic fuzzy numbers are converted into their corresponding parametric form and applying the proposed intuitionistic fuzzy arithmetic operations and a new method of ranking based on the parametric form of intuitionistic fuzzy numbers, the intuitionistic fuzzy critical path with vagueness reduced intuitionistic fuzzy completion duration of the project has been obtained. The authentication of the proposed method can be checked by comparing the obtained results with the results available in pieces of literature.

A new ELECTRE-based method for group decision-making with complex spherical fuzzy information

This study exploits the tremendous theory of ELimination and Choice Expressing REality (ELECTRE) method to enhance the number of outranking approaches for the ground-breaking and recent extension of fuzzy set theory, namely, complex spherical fuzzy set. The noticeable edge of this striking model is its wider and flexible structure that empowers it to encompass the abstinence part of vague information in addition to satisfaction and dissatisfaction in two dimensional scenarios. In short, this article delivers the compact procedure of the widely applicable, high skilled and multi-purpose complex spherical fuzzy ELECTRE II approach. The designed algorithm of the presented methodology cumulates the worthy opinions of the decision-making experts in the light of complex spherical fuzzy weighted averaging operator. Furthermore, proposed method is privileged with the remarkable notions of concordance and discordance sets in order to unfold the pairwise relation between the alternatives regarding any criterion. The proposed approach predicts the final ranking of alternatives with the aid of crisp strong and weak outranking relations to filter the strict and weak precedence between any pair of alternatives. The practical application of the proposed approach is demonstrated via a case study to opt the most efficient technology to treat cadmium-contaminated water. A comparative study with complex spherical fuzzy ELECTRE I (CSF-ELECTRE I) and spherical fuzzy TOPSIS (SF-TOPSIS) methods is conducted to collect the enough evidence to foreground the authenticity and aptitude of proposed technique.

A study on some relations on multi-fuzzy (left-right)ideals of rings

multi fuzzy set theory is an extension of fuzzy set theory, which deals with the multi dimensional fuzziness. In this paper, we introduce the concepts of multi-fuzzy rings, multi fuzzy ideal, image of multi- fuzzy ideal of a ring under homomorphism, Cartesian product of multi-fuzzy set, and some related properties and theorems are investigated. The purpose of this study is to implement the fuzzy set theory and rings theory in multi-fuzzy rings.

(2012-6338) Design and Analysis of Acceptance Sampling Plans Based on Intuitionistic Fuzzy Linguistic Terms

Acceptance sampling plans (ASPs) offer inspection of a small set of items from a lot within a predefined plan to procure a certain output quality level with minimum cost in terms of time, effort, and damage to the inspected items. Although traditional ASPs use crisp plan parameters, quality characteristics of the incoming items or human evaluations about inspection process may contain uncertainties and may not always be defined as crisp values in real life problems. The fuzzy set theory (FST) is one of the most popular techniques to model these uncertainties by defining plan parameters as fuzzy numbers. Despite the advantages, traditional fuzzy sets are not flexible enough to model all kinds of uncertainties. For example, it has some disadvantages because of defining the status of any item based on defectiveness or non-defectiveness conditions and presuming the parts as non-defective whose defectiveness is not indeed determined. New extensions of FST can improve the quality of uncertainty modeling of ASPs. Intuitionistic Fuzzy Sets (IFSs) allow slackness for non-determination about the membership and give more sensitive modeling opportunity in human-related evaluations by the help of this ability. Since the inspection procedure of the ASPs depends on human-related judgements, IFSs have been used to define the defectiveness degree of the items in this study. ASPs based on interval-valued IFSs (IVIFSs) have also been designed and some characteristic functions of ASPs, such as acceptance probability ($P_a$), average sample number ($ASN$) and average total inspection ($ATI$) have been reformulated. Intuitionistic binomial and Poisson distributions have been defined to be able to formulate the ASPs. Additionally, the defectiveness of the items has been represented by using linguistic terms to overcome the difficulty of quantifying the verbal evaluation results as numerical measures. The $alpha$-cut technique has been combined with the linguistic approach to allow defining with multiple $alpha$ values for different product segments. Finally, some numerical examples have been presented to analyze the effectiveness of proposed ASPs and discuss the obtained results.

SEMIGROUPS IN TERMS OF INTUITIONISTIC FUZZY BI-IDEALS

Since Zadeh introduced fuzzy sets in 1965, a lot of new theories treating imprecision and uncertainty have been introduced. Some of these theories are extensions of fuzzy set theory. The concept of 'intuitionistic fuzzy set' (IFS) was introduced by Atanassov as a generalization of the concept fuzzy set by gives both a degree of membership and the degree of non-membership. As for fuzzy sets, the degree of membership is a real number between 0 and 1. This is also the case for the degree of non-membership, and further the sum of these two degrees is not greater than 1. Since fuzzy bi-ideal play an important role in the study of semigroup structures. The purpose of this paper is to initiate and study the intuitionistic fuzzification on the concept of several ideals in a semigroups S and investigate the basic theorem of intuitionistic fuzzy bi-ideals and discuss the relationships of left (resp. right and completely regular) semigroups in terms of intuitionistic fuzzy biideals. For any homomorphisim f from a semigroup S to semigroup T if B= (μB , VB) is an intuitionistic fuzzy bi-ideal of T, then the preimage f-1(B) = (f-1(μB),f-1(VB)) of B under f is an intuitionistic fuzzy bi-ideal of semigroup S.

Entropy measure and TOPSIS method based on correlation coefficient using complex q-rung orthopair fuzzy information and its application to multi-attribute decision making

Entropy measure (EM) and similarity measure (SM) are important techniques in the environment of fuzzy set (FS) theory to resolve the similarity between two objects. The q-rung orthopair FS (q-ROFS) and complex FS are new extensions of FS theory and have been widely used in various fields. In this article, the EM, Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) based on the correlation coefficient is investigated. It is very important to study the SM of Cq-ROFS. Then, the established approaches and the existing drawbacks are compared by an example, and it is verified that the explored work can distinguish highly similar but inconsistent Cq-ROFS. Finally, to examine the reliability and feasibility of the new approaches, we illustrate an example using the TOPSIS method based on Cq-ROFS to manage a case related to the selection of firewall productions, and then, a situation concerning the security evaluation of computer systems is given to conduct the comparative analysis between the established TOPSIS method based on Cq-ROFS and previous decision-making methods for validating the advantages of the established work by comparing them with the other existing drawbacks.

An extension of the WASPAS method for decision-making problems with intuitionistic fuzzy numbers: a case of website evaluation

The use of fuzzy sets in classical multiple criteria decision-making methods has led to forming fuzzy multiple criteria decision-making that enabled solving of a significantly larger number of decision-making problems. However, the membership function introduced in the fuzzy set theory has some limitations. Unlike the fuzzy set theory, intuitionistic fuzzy set theory also introduces the non-membership function. Therefore, intuitionistic fuzzy set theory, as an extension of fuzzy set theory, could provides some advantages in solving complex decision-making problems. WASPAS method is newly proposed, but widely used, multiple criteria decision-making method, for which numerous extensions have already been proposed. A new extension of WASPAS method, based on the use of single valued intuitionistic fuzzy sets and the Hamming distance proposed in this article. The efficiency and usability of the proposed approach are considered on the example website evaluation.

Index Number of Multi Fuzzy Sets

Multi fuzzy set theory is an extension of fuzzy set theory. In this paper we developing the theory of Index number of multi fuzzy sets. This theory is applied to medical diagnosis system and will help doctors to select the effective symptoms and could make diagnosis of diseases concern. This theory also helps in selecting right political leaders.

Index Number of Multi Fuzzy Sets

Multi fuzzy set theory is an extension of fuzzy set theory. In this paper we developing the theory of Index number of multi fuzzy sets. This theory is applied to medical diagnosis system and will help doctors to select the effective symptoms and could make diagnosis of diseases concern. This theory also helps in selecting right political leaders.

AN Application of Neutrosophic Vague Max-Min Composition Technique

The theory of fuzzy set was introduced by Zadeh, has a wider scope in terms of applications than the classical set theory in solving various problems. Extensive applications of the fuzzy set theory have been found in various fields such as Computer Sciences, Artificial Intelligence, Medical Sciences, Economics, Statistics, Neural Networks, etc. In fuzzy set each element had a degree of membership. Smarandache defined the neutrosophic set theory, which was one of the most important new mathematical tools for handling problems involving imprecise, indeterminacy, and inconsistent data. The theory of vague sets was first proposed by Gau and Buehrer as an extension of fuzzy set theory and vague sets are regarded as a special case of context-dependent fuzzy sets. Shawkat Alkhazaleh introduced the concept of neutrosophic vague set as a combination of neutrosophic set and vague set. Neutrosophic vague theory is an effective tool to process incomplete, indeterminate and inconsistent information. This paper attempts to develop a new model known as neutrosophic vague max-min composition technique to examine the daily life problems. One of the major problems that everyone comes across is their children’s studies. Education is a very important aspect of the lives of all people all over the world. What we learn, not just in the classroom, shapes who we are. We take our education everywhere we go. Student life is not as easier as it seems. Now a days the studies of the student is deviated due to various reasons. Here we identify those problems of students and by using neutrosophic vague max-min composition technique we analyze the problem faced by the students that affect their lack of concentration in studies.

Exponential, Logarithmic and Compensative Generalized Aggregation Operators Under Complex Intuitionistic Fuzzy Environment

This manuscript presents some new exponential, logarithmic and compensative exponential of logarithmic operational laws based on t-norm and co-norm for complex intuitionistic fuzzy (CIF) numbers. The prevailing extensions of fuzzy set theory handle the uncertain data by representing the satisfaction and dissatisfaction degrees as real values and can deal with only one-dimensional problems due to which some important information may be lost in some situations. A modification to these, CIF sets are characterized by complex-valued degrees of satisfaction and dissatisfaction and handle two dimensional data simultaneously in one set using additional terms, called phase terms, which generally give information related with periodicity. Motivated by the characteristics of CIF model, we present some new operational laws and compensative operators namely generalized CIF compensative weighted averaging and generalized CIF compensative weighted geometric. Some properties related to proposed operators are discussed. In light of the developed operators, a group decision-making method is put forward in which weights are determined objectively and is illustrated with the aid of an example. The reliability of the presented decision-making method is explored by comparing it with several prevailing studies. The influence of the parameters used in exponential and logarithmic operations on CIF numbers is also discussed.

New generalised Bonferroni mean aggregation operators of complex intuitionistic fuzzy information based on Archimedean t-norm and t-conorm

ABSTRACTThis manuscript presents aggregation operators which encapsulate the interaction among the criteria and preferences under complex intuitionistic fuzzy (CIF) conditions. The current extensions of fuzzy set theory handle the uncertain data by representing the satisfaction and dissatisfaction degrees as real values and can trade with only one-dimensional problems due to which some important knowledge may be lost in some situations. A modification to these, CIF sets are portrayed by complex-valued degrees of satisfaction and dissatisfaction and handle two-dimensional data concurrently in one set using additional terms, called phase terms, which usually give knowledge related with periodicity. Motivated by the features of the CIF model, we present some aggregation operators, namely, generalised CIF Bonferroni mean and generalised CIF weighted Bonferroni mean. Some features related to proposed operators are addressed. In light of the developed operators, a decision-making method is put forward and is drawn with the aid of an example. The reliability of the presented decision-making method is examined with the help of a validity test and by comparing the results of the example with several predominating studies.

Robust Averaging–Geometric Aggregation Operators for Complex Intuitionistic Fuzzy Sets and Their Applications to MCDM Process

This paper presents aggregation operators which encapsulate the interaction among the criteria and preferences under complex intuitionistic fuzzy (CIF) conditions. The current extensions of fuzzy set theory handle only the uncertain data by representing the satisfaction and dissatisfaction degrees as real values and hence lose some information. A modification to these, CIF sets are portrayed by complex-valued membership degrees and can handle the data concurrently using additional terms, called phase terms, which usually give knowledge related to periodicity. Motivated by the features of the CIF model, this paper studies some aggregation operators, weighted averaging and geometric, for CIF sets and investigates their properties. To ease with the possible application, we explore the decision-making (DM) process in the CIF set environment and present an algorithm to solve the multiple criteria DM problems. Finally, a practical example is presented to demonstrate the DM process based on the proposed operators and compared their performance with some similar approaches.