Fuzzy Set Operations Research Articles

Optimizing construction company selection using einstein weighted aggregation operators for q-rung orthopair fuzzy hypersoft set

Infrastructure development and the economy heavily rely on the construction industry. However, decision-making in construction projects can be intricate and difficult due to conflicting standards and requirements. To address this challenge, the q-rung orthopair fuzzy soft set (q-ROFSS) has emerged as a useful tool incorporating fuzzy and uncertain contractions. In many cases, further characterization of attributes is necessary as their values are not mutually exclusive. The prevalent q-ROFSS structures cannot resolve this state. The q-rung orthopair fuzzy hypersoft sets (q-ROFHSS) is a leeway of q-ROFSS that use multi-parameter approximation functions to scare the scarcities of predominant fuzzy sets structures. The fundamental objective of this research is to introduce the Einstein weighted aggregation operators (AOs) for q-rung orthopair fuzzy hypersoft sets (q-ROFHSS), such as q-rung orthopair fuzzy hypersoft Einstein weighted average and geometric operators, and discuss their fundamental properties. Mathematical explanations of decision-making (DM) contractions is present to approve the rationality of the developed approach. Einstein AOs, based on predictions, carried an animated multi-criteria group decision (MCGDM) method with the most substantial significance with the prominent MCGDM structures. Moreover, we utilize our proposed MCGDM model to select the most suitable construction company for a given construction project. The proposed method is evaluated through a statistical analysis, which helps ensure the DM process's efficiency. This analysis demonstrates that the proposed method is more realistic and reliable than other DM approaches. Overall, the research provides valuable insights for decision-makers in the construction industry who seek to optimize their DM processes and improve the outcomes of their projects.

Prioritization of thermal energy storage techniques based on Einstein-ordered aggregation operators of q-rung orthopair fuzzy hypersoft sets

The capability to stock energy and manage consumption in the future is one of the keys to retrieving huge quantities of renewable energy on the grid. There are numerous techniques to stock energy, such as mechanical, electrical, chemical, electrochemical, and thermal. The q-rung orthopair fuzzy soft set (q-ROFSS) is a precise parametrization tool with fuzzy and uncertain contractions. In several environments, the attributes need to be further categorized because the attribute values are not disjointed. The existing q-rung orthopair fuzzy soft set configurations cannot resolve this state. Hypersoft sets are a leeway of soft sets (SSs) that use multi-parameter approximation functions to overcome the inadequacies of prevailing SS structures. The significance of this investigation lies in anticipating Einstein-ordered weighted aggregation operators (AOs) for q-rung orthopair fuzzy hypersoft sets (q-ROFHSSs), such as the q-rung orthopair fuzzy hypersoft Einstein-ordered weighted average (q-ROFHSEOWA) and the q-rung orthopair fuzzy hypersoft Einstein-ordered weighted geometric (q-ROFHSEOWG) operators, using the Einstein operational laws, with their requisite properties. Mathematical interpretations of decision-making constrictions are considered able to ensure the symmetry of the utilized methodology. Einstein-ordered aggregation operators, based on prospects, enable a dynamic multi-criteria group decision-making (MCGDM) approach with the most significant consequences with the predominant multi-criteria group decision techniques. Furthermore, we present the solicitation of Einstein-ordered weighted aggregation operators for selecting thermal energy-storing technology. Moreover, a numerical example is described to determine the effective use of a decision-making pattern. The output of the suggested algorithm is more authentic than existing models and the most reliable to regulate the favorable features of the planned study.

New Arithmetic Operations of Non-Normal Fuzzy Sets Using Compatibility

The new arithmetic operations of non-normal fuzzy sets are studied in this paper by using the extension principle and considering the general aggregation function. Usually, the aggregation functions are taken to be the minimum function or t-norms. In this paper, we considered a general aggregation function to set up the arithmetic operations of non-normal fuzzy sets. In applications, the arithmetic operations of fuzzy sets are always transferred to the arithmetic operations of their corresponding α-level sets. When the aggregation function is taken to be the minimum function, this transformation is clearly realized. Since the general aggregation function was adopted in this paper, the concept of compatibility with α-level sets is needed and is proposed, which can cover the conventional case using minimum functions as the special case.

Fuzzy approximation based on $ \tau- \mathfrak{K} $ fuzzy open (closed) sets

Rough set theory can be generalized by induced topology through equivalence relations. Motivated by the work of generalization of the rough set via topology, the concept and properties of $ \tau-\mathfrak{K} $-fuzzy open (closed) sets are proposed. Considering the $ \tau-\mathfrak{K} $-fuzzy open (closed) sets, we have obtained the $ \tau-\mathfrak{K} $-fuzzy lower and upper approximations and also proved their properties. $ \tau-\mathfrak{K} $-fuzzy open sets can be represented as $ \tau-\mathfrak{K} $-open sets by $ \alpha $ level sets. The properties of $ \tau-\mathfrak{K} $-fuzzy approximations and fuzzy rough approximations on the basis of binary fuzzy relation are compared. Finally, an example and the decision method's algorithm to illustrate the $ \tau-\mathfrak{K} $-fuzzy approximation-based approach to decision making are presented.

An Approach to MADM Based on Aczel-Alsina Power Bonferroni Aggregation Operators for q-Rung Orthopair Fuzzy Sets

The power Bonferroni mean (PBM) is a combined networking system that can benefit both the power average (PA) operator, which might attenuate the effects of irrational data provided by the prejudiced decision-makers (DMs), and the BM operator, which may incorporate the interconnections between any two attributes. In this paper, we defined the aggregation operators (AOs), such as the power average (PA) operator and the power Bonferroni mean (PBM) operator, based on the Aczel-Alsina (AA) operational rules under the environment of the q-Rung Orthopair fuzzy set (q-ROFS), and provided their specific characteristics for the solution of numerical problems. We extend the power Bonferroni mean (PBM) operator under the framework of q-ROFVs to establish the q-Rung Orthopair Fuzzy Aczel-Alsina power Bonferroni mean (q-ROFAAPBM) operator and the q-Rung Orthopair Fuzzy Aczel-Alsina weighted power Bonferroni mean (q-ROFAAWPBM) operator and discuss a few of the most useful properties of these AOs. After that, the q-ROFAAWPBM operator is used to solve the multi-attribute decision-making steps for q-ROFVs. The disease is diagnosed with the MADM method, which shows its usefulness and effectiveness. Finally, the comparison of our developed approach has been demonstrated to be superior and more effective than the existing literature, and we can conclude the result.

Picture fuzzy power Muirhead mean operators and their application to multi attribute decision making

<p style='text-indent:20px;'>The main objective of this paper is to develop some aggregating operators for Picture fuzzy sets (PFS) by integrating power average (PA) and Muirhead mean (MM) operators. This paper develops Picture fuzzy power Muirhead mean (PFPMM), Picture fuzzy weighted power Muirhead mean (PFWPMM), Picture fuzzy dual power Muirhead mean (PFDPMM) and Picture fuzzy weighted dual power Muirhead mean (PFWDPMM) operators along with some desirable properties and special cases. Some advantages of developed operators are that they define the interrelationship between all aggregated values and lead to a flexible aggregation process through a parameter vector. Further, a multi-attribute decision making (MADM) problem based on proposed operators has been presented. To exemplify the availability and practicability of the proposed study, a financial investment risk problem in an enterprise is solved numerically. A sensitivity analysis is conducted to examine the effect of different values of parameters on aggregated values, while a comparative analysis is carried out to compare the results with some other existing operators.</p>

Q-Rung orthopair fuzzy information aggregation and their application towards material selection

<abstract><p>Material selection is a complex process that involves selecting the best material for a given application. It is a critical process in engineering, and the importance of selecting the right material for the job cannot be overstated. Multi-criteria decision-making (MCDM) is an important tool that can be used to help engineers make informed decisions about material selection. The logistic function can be extended using the soft-max function, which is widely used in stochastic classification methods like neural nets, soft-max extrapolation, linear differential analysis, and Naïve Bayes detectors. This has inspired researchers to develop soft-max-based fuzzy aggregation operators (AOs) for q-rung orthopair fuzzy sets (q-ROPFS) and to propose an MCDM approach based on these AOs. To test the effectiveness of this approach, the researchers applied it to a practical problem using q-rung orthopair fuzzy data and conducted a numerical example to validate the suggested procedures.</p></abstract>

β-PREREGULAR SPACE IN FUZZY SETTING

In this paper a new type of fuzzy regular space is introduced and studied by introducing fuzzy β-preopen set, the class of which is strictly larger than that of fuzzy open set as well as fuzzy preopen set. Here we also introduce two new types of functions, viz., fuzzy β-precontinuous and fuzzy β-preirresolute functions. Lastly, the application of fuzzy β-precontinuous function on fuzzy β- preregular space is shown here.

Power partitioned neutral aggregation operators for T-spherical fuzzy sets: An application to [formula omitted] refuelling site selection

T-spherical fuzzy set (T-SFS) is emerged as one of the effective tools for dealing uncertainty in decision-making process. Whereas, power aggregation operators help us in normalizing the impact of extreme values and capture the interconnectedness of the arguments. Meantime, one of the most prominent factors in multi-attribute decision-making (MADM) problems is the lack of awareness of biasness. Neutral operations highlight fair and unbiased character of decision makers. Thus, aiming these advantages and heterogeneity of arguments, a hybrid form of operators, weighted power partitioned neutral average operator and weighted power partitioned neutral geometric operator are developed under T-SFS environment for the first time. Beside these, power weighted neutral average, power ordered weighted neutral average, power hybrid neutral average operators, and their dual forms are initiated too. A new modified score function for T-SFS is formulated. Based on the developed operators and score function, an MADM algorithm is constituted and utilized in solving a hypothetical case study problem on hydrogen (H2) refuelling station site selection. Finally, comparative study of the developed operators with other operators is carried out to explore the applicability and supremacy of the designed MADM algorithm.

Decision Support System Based on Complex q -Rung Orthopair Fuzzy Rough Hamacher Aggregation Operator through Modified EDAS Method

The best mathematical tools for combining numerous inputs into a single result are aggregation operators. The aggregation operators work to combine all of the individual evaluation values provided in a uniform form, and they are very useful for evaluating the options provided in the decision-making process. To provide a larger space for decision makers, complex q -rung orthopair fuzzy rough sets can express their uncertain information. As a generalization of the algebraic operations, the Einstein t -norm and t -conorm, Hamacher operations have become significant in aggregation theory. The Hamacher aggregation operator’s major characteristic is that it can capture the interrelationship between several input arguments. In this article, some Hamacher aggregation operators for complex q -rung orthopair fuzzy rough sets are presented. We define a complex q -rung orthopair fuzzy rough Hamacher operation laws and a new score function. In addition, we propose a serious of averaging aggregation operators for complex q -rung orthopair fuzzy rough set. We present the essential properties of these operators. We use the defined operators and modified EDAS (evaluation based on distance from average solution) method to propose an approach for solving a multicriteria decision making problem. To demonstrate the practicality and effectiveness of our propose model, we consider a numerical example of area selection for an arboretum. Finally, a comparison between the suggested approach with existing operators has been presented for authenticity and reliability.

Extension operators for type-2 fuzzy sets derived from overlap functions

Overlap and grouping functions, as two novel continuous binary aggregation functions, have been discussed in the literature for applications in image processing, decision making, classification and so on. Since Walker et al. proved that the algebraic structure of fuzzy truth values has the same property as the algebraic structure of type-2 fuzzy sets, the study of extension operators for fuzzy truth values has become a hot research topic. This article considers this research topic and discusses mainly the so-called O-extension operators based on overlap functions. Firstly, the O-extension operators of general binary operators for fuzzy truth values on a linearly ordered set are introduced, and some of their basic properties are discussed. Secondly, the properties of O-extended maximum operators, O-extended minimum operators, O-extended overlap functions and O-extended grouping functions are studied. Thirdly, O-extension operators on normal fuzzy sets and O-convex fuzzy sets are investigated. Fourthly, the O-extension operators for fuzzy truth values are extended to type-2 fuzzy sets. Finally, we provide a brief comparison of O-extension operators with other common operators for fuzzy truth values.

Fuzzy Ideals and Fuzzy Filters on Topologies Generated by Fuzzy Relations

Recently, Mishra and Srivastava have introduced and studied the notion of fuzzy topology generated by fuzzy relation and several properties were proved. In this paper, we mainly investigate the lattice structure of fuzzy open sets in this topology, and show its various properties and characteristics. Additionally, we extend to this lattice the notions of fuzzy ideal and fuzzy filter. For each of these notions, we fully characterize them in terms of this lattice meet and join operations.

Fuzzy Distribution Sets

We introduce a new type of fuzzy set called Fuzzy Distribution Set (FDS). Fuzzy distribution sets are fuzzy sets defined on a finite domain subject to a sum of membership values equal to 1. Such fuzzy sets can serve as models of subjective probability distributions and subjective weight distributions. Considering these distributions as fuzzy sets gives a possibility to extend on such distributions the operations of fuzzy sets and, more generally, the calculus of fuzzy restrictions developed during the last decades. Recently Yager introduced the concept of negation of probability distributions. In our works, we studied several classes of such negations. Here we consider an involutive negation of probability distributions as a complement of FDS. We introduce the operations of union and intersection of fuzzy distribution sets. These basic operations on FDS can serve as a basis for the application of fuzzy logic methods to subjective probability and weight distributions. These operations can be used for the development of reasoning models with subjective probability distributions and subjective weighting functions. Weight distributions can be used in multi-criteria, multi-person, and multi-attribute decision-making models.

Similarity measurement of fuzzy entropies of respiratory sounds and risk measurement according to credibility distributions

In this paper, we have provided some definitions and theorems about fuzzy set, fuzzy set operations, the uncertainty theory used in fuzzy environments, and the credibility theory which exists on the base of the mathematical knowledge. Then, the definition and applications of fuzzy set operations, fuzzification, defuzzification, similarity, credibility distribution were included in diagnostic medicine. Sounds of respiratory patients were transferred to computer by recording and converted into numerical data. In particular, the entropies, similarities, credibility.distributions., expected values of sounds were analyzed using fuzzification and defuzzification methods to analyze respiratory sound data via fuzzy operations and to make sense of uncertain sound data. As the uncertainty of respiratory sounds increased, changes in fuzzy entropy similarity measures and expected credibility values were observed. In addition, a model for uncertain respiratory sounds was created and numerical numbers supported the diagnosis of the physician. Sound data were analyzed and interpreted using fuzzy multipurpose decision methods. Respiratory sounds were shown to be an indicator in diagnosing with the created model.

A Ship Fire Escape Speed Correction Method Considering the Influence of Crowd Interaction

The aim of this study is to explore the effect of different personnel attributes and the relationship between different people on evacuation efficiency in the case of a passenger ship fire. As such, this study proposes a speed correction method that considers human attributes and interactions between different populations. Firstly, a hesitant fuzzy set and hesitant fuzzy average operator are adopted to quantify four kinds of personnel attributes. Secondly, considering the influence of different people, this study extracts the formula for acceleration under the interactive influence of different groups of people. At the same time, based on the first-order linear relationship between velocity and acceleration, an interactive velocity correction method is presented in the evacuation of ship personnel. Finally, this study uses the personnel evacuation simulation software Pathfinder to conduct experiments, and introduces the corrected speed and the uncorrected speed into the evacuation simulation process, respectively. The results show that the simulation results of the revised speed plan are more consistent with reality.

A note on “Pythagorean uncertain linguistic hesitant fuzzy weighted averaging operator and its application in financial group decision making”

Shakeel et al. (Soft Comput 24: 1585–1597, 2020) proposed the concept of a Pythagorean uncertain linguistic hesitant fuzzy set (PULHFS), some arithmetic operations of Pythagorean uncertain linguistic hesitant fuzzy sets (PULHFSs), an approach for comparing PULHFSs and a Pythagorean uncertain linguistic hesitant fuzzy weighted averaging (PULHFWA) operator as well as it extensions. Also, using the proposed comparing approach and the proposed aggregation operators, Shakeel et al. proposed a method for solving multi-attribute group decision making (MAGDM) problems. In future other researchers may use Shakeel et al.’s work in their research work. However, it is observed that the approach for comparing PULHFSs and aggregation operators, proposed by Shakeel et al. (Soft Comput 24: 1585–1597, 2020), are not appropriate. Hence, the method for solving MAGDM problems, proposed by Shakeel et al., is also not appropriate. The aim of this note is to make the researchers aware of the inappropriateness of Shakeel et al. work. Furthermore, point out that to resolve the inappropriateness of Shakeel et al. work (Soft Comput 24: 1585–1597, 2020) is a challenging open research problem.

Another View on Picture Fuzzy Soft Sets and Their Product Operations with Soft Decision-Making

Cuong [Picture Fuzzy Sets, Journal of Computer Science and Cybernetics 30 (4) (2014) 409–420] has introduced the concept of picture fuzzy soft sets (pfs-sets) relying on his definition and operations of picture fuzzy sets (pf -sets), in which there exist some inconsistencies. Yang et al. [Adjustable Soft Discernibility Matrix Based on Picture Fuzzy Soft Sets and Its Applications in Decision Making, Journal of Intelligent & Fuzzy Systems 29 (4) (2015) 1711–1722] have claimed that they have introduced the concept of pfs-sets with the inconsistencies in Cuong’s definition of pf -sets. Therefore, this study redefines the concept of pfs-sets to deal with the inconsistencies therein. Moreover, it investigates some of the properties of pfs-sets and their product operations and proposes a soft decision-making method via pfs-sets. Finally, pfs-sets, their product operations, and the proposed method are discussed for further research.

Aggregation operators on shadowed sets

In this article, we study aggregation operators on shadowed sets. In particular, since shadowed sets can be obtained as approximations of fuzzy sets, we explore the relationships between aggregation operators on fuzzy sets and corresponding operators on shadowed sets. We focus on studying conditions under which the approximations of fuzzy sets into shadowed sets represent an homomorphism with respect to the corresponding aggregation operators, and we propose classes of fuzzy set operators that correspond to (and satisfy the same properties as) specific shadowed set operators.

Integrating fuzzy set function into floating catchment area measures: a determination of spatial accessibility of service points

ABSTRACT The use of discrete (binary or zonal/step-wise) instead of continuous travel impedance functions in floating catchment area (FCA) measures generates inconsistent and less reliable accessibility indices that might be overestimating or underestimating actual accessibility. Thus, this study illustrates the limitations of discrete travel impedance function in the enhanced two-step (E2S) FCA method; and develops a fuzzy-based continuous travel impedance function by combining the degree to which travel distances belong to different sub-zones of catchment areas and their respective E2SFCA zonal weights using the weighted mean fuzzy-set operation. With the developed fuzzy-based travel impedance function, a new accessibility measure, fuzzy-based two-step (F2S) FCA is defined. The E2SFCA and F2SFCA measures were implemented in the hypothetical set up and Rural Wards of Dodoma Urban District in Tanzania to determine spatial accessibility of service points and water points, respectively. The resulting E2SFCA and F2SFCA accessibility indices portrayed a slightly similar pattern. However, F2SFCA accessibility indices varied among households within and across sub-zones, while E2SFCA accessibility indices were identical within but changed abruptly across sub-zones. The variations in F2SFCA accessibility indices reflect the reality and to a greater extent Tobler’s first law of Geography. Thus, the developed F2SFCA measure could be used to measure spatial accessibility of other services or commodities as it properly models travel impedance. The F2SFCA measure could further be improved to generate much more realistic accessibility indices by capturing local instead of total potential demand, commonly modelled in FCA measures.

A modified VIKOR method for group decision-making based on aggregation operators for hesitant intuitionistic fuzzy linguistic term sets

A modified VIKOR method for group decision-making based on aggregation operators for hesitant intuitionistic fuzzy linguistic term sets