Hamy Mean Operators Based on Complex q-Rung Orthopair Fuzzy Setting and Their Application in Multi-Attribute Decision Making

To determine the connection among any amounts of attributes, the Hamy mean (HM) operator is one of the more broad, flexible, and dominant principles used to operate problematic and inconsistent information in actual life dilemmas. Furthermore, for the option to viably portray more complicated fuzzy vulnerability data, the idea of complex q-rung orthopair fuzzy sets can powerfully change the scope of sign of choice data by changing a boundary q, dependent on the distinctive wavering degree from the leaders, where ζ ≥ 1, so they outperform the conventional complex intuitionistic and complex Pythagorean fuzzy sets. In genuine dynamic issues, there is frequently a communication problem between credits. The goal of this study is to initiate the HM operators based on the flexible complex q-rung orthopair fuzzy (Cq-ROF) setting, called the Cq-ROF Hamy mean (Cq-ROFHM) operator and the Cq-ROF weighted Hamy mean (Cq-ROFWHM) operator, and some of their desirable properties are investigated in detail. A multi-attribute decision-making (MADM) dilemma for investigating decision-making problems under the Cq-ROF setting is explored with certain examples. Finally, a down-to-earth model for big business asset-arranging framework determination is provided to check the created approach and to exhibit its reasonableness and adequacy. The exploratory outcomes show that the clever MADM strategy is better than the current MADM techniques for managing MADM issues.

(m, n)-Ideals in Semigoups Based on Int-Soft Sets

Algebraic structures play a prominent role in mathematics with wide ranging applications in many disciplines such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, and topological spaces. This provides sufficient motivation to researchers to review various concepts and results from the realm of abstract algebra in the broader framework of fuzzy setting. In this paper, we introduce the notions of int-soft m , n -ideals, int-soft m , 0 -ideals, and int-soft 0 , n -ideals of semigroups by generalizing the concept of int-soft bi-ideals, int-soft right ideals, and int-soft left ideals in semigroups. In addition, some of the properties of int-soft m , n -ideal, int-soft m , 0 -ideal, and int-soft 0 , n -ideal are studied. Also, characterizations of various types of semigroups such as m , n -regular semigroups, m , 0 -regular semigroups, and 0 , n -regular semigroups in terms of their int-soft m , n -ideals, int-soft m , 0 -ideals, and int-soft 0 , n -ideals are provided.

Einstein Geometric Aggregation Operators using a Novel Complex Interval-valued Pythagorean Fuzzy Setting with Application in Green Supplier Chain Management

The principle of a complex interval-valued Pythagorean fuzzy set (CIVPFS) is a valuable procedure to manage inconsistent and awkward information genuine life troubles. The principle of CIVPFS is a mixture of the two separated theories such as complex fuzzy set and interval-valued Pythagorean fuzzy set which covers the truth grade (TG) and falsity grade (FG) in the form of the complex number whose real and unreal parts are the sub-interval of the unit interval. The superiority of the CIVPFS is that the sum of the square of the upper grade of the real part (also for an unreal part) of the duplet is restricted to the unit interval. The goal of this article is to explore the new principle of CIVPFS and its algebraic operational laws. By using the CIVPFSs, certain Einstein operational laws by using the t-norm and t-conorm are also developed. Additionally, we explore the complex interval-valued Pythagorean fuzzy Einstein weighted geometric (CIVPFEWG), complex interval-valued Pythagorean fuzzy Einstein ordered weighted geometric (CIVPFEOWG) operators and utilized their special cases. Moreover, a multicriteria decision-making (MCDM) technique is explored based on the elaborated operators by using the complex interval-valued Pythagorean fuzzy (CIVPF) information. To determine the consistency and reliability of the elaborated operators, we illustrated certain examples by using the explored principles. Finally, to determine the supremacy and dominance of the explored theories, the comparative analysis and graphical expressions of the developed principles are also discussed.

Donsker’s fuzzy invariance principle under the Lindeberg condition

We prove an analogue of the Donsker theorem under the Lindeberg condition in a fuzzy setting. Specifically, we consider a certain triangular system of d-dimensional fuzzy random variables { X n , i ∗ } , $\begin{array}{} \{X_{n,i}^*\}, \end{array}$ n ∈ ℕ and i = 1, 2, …, kn , which take as their values fuzzy vectors of compact and convex α-cuts. We show that an appropriately normalized and interpolated sequence of partial sums of the system may be associated with a time-continuous process defined on the unit interval t ∈ [0, 1] which, under the assumption of the Lindeberg condition, tends in distribution to a standard Brownian motion in the space of support functions.

Induced L-bornological vector spaces and L-Mackey convergence1

Motivated by the concept of lattice-bornological vector spaces of J. Paseka, S. Solovyov and M. Stehlík, which extends bornological vector spaces to the fuzzy setting over a complete lattice, this paper continues to study the theory of L-bornological vector spaces. The specific description of L-bornological vector spaces is presented, some properties of Lowen functors between the category of bornological vector spaces and the category of L-bornological vector spaces are discussed. In addition, the notions and some properties of L-Mackey convergence and separation in L-bornological vector spaces are showed. The equivalent characterization of separation in L-bornological vector spaces in terms of L-Mackey convergence is obtained in particular.

PROCEDURES FOR INVESTMENT IN CYBER SECURITY, TAKING INTO ACCOUNT MULTIFACTORITY AND FUZZY STATEMENT

It is shown that the application of multi-step quality games theory allows financing of various information technologies considering various factors. In particular, there are lots of approaches to building effective information security systems in the enterprise. Using such model will make it possible to develop, based on game models, decision support systems (DSS), for example, software products (PP). Which, in turn, will allow making rational decisions on investing in the development of such technologies. This circumstance makes it necessary and relevant to develop new models and software products that can implement decision support procedures in the process of finding rational investment strategies, including in information security field of enterprises, and obtaining forecast assessment for feasibility of a specific strategy. The model proposed by us is based on analysis of financing process by investors in information technology for protecting information tasks for the case of their multi-factoring in fuzzy setting. The investment process management model is proposed, using the example of investing in the information security of informatization objects taking into account multi-factoring and in fuzzy setting for DSS computational core. The difference between the model and previously developed ones is that it considers the investment process as complex structure, for which it is not enough to model it as a single-factor category. Computational experiments were performed for the developed model. The simulation results are visualized in the Python programming language, which allows you to optimize the procedures for investment process managing.

m-Polar Generalization of Fuzzy T-Ordering Relations: An Approach to Group Decision Making

Recently, T-orderings, defined based on a t-norm T and infimum operator (for infinite case) or minimum operator (for finite case), have been applied as a generalization of the notion of crisp orderings to fuzzy setting. When this concept is extending to m-polar fuzzy data, it is questioned whether the generalized definition can be expanded for any aggregation function, not necessarily the minimum operator, or not. To answer this question, the present study focuses on constructing m-polar T-orderings based on aggregation functions A, in particular, m-polar T-preorderings (which are reflexive and transitive m-polar fuzzy relations w.r.t T and A) and m-polar T-equivalences (which are symmetric m-polar T-preorderings). Moreover, the construction results for generating crisp preference relations based on m-polar T-orderings are obtained. Two algorithms for solving ranking problem in decision-making are proposed and validated by an illustrative example.

Convex structures in a new kind of ordered fuzzy group1

By means of a fuzzy binary operation defined on partially ordered sets, a new kind of ordered fuzzy group is proposed in this paper. Some properties of this ordered fuzzy group are studied. Following that, its substructures, such as subgroup and convex subgroup, as well as its homomorphisms, along with their properties are explored. It is shown that each family of these substructures forms a convex structure, where the convex hull of a subset is exactly the (convex) subgroup generated by itself, and the homomorphisms between two ordered fuzzy groups are convexity-preserving mappings between the corresponding convex spaces. In addition, when these substructures are extended to fuzzy setting, several L-convex structures are constructed and investigated.