The power Bonferroni mean (PBM) operator can relieve the influence of unreasonable aggregation values and also capture the interrelationship among the input arguments, which is an important generalization of power average operator and Bonferroni mean operator, and Pythagorean fuzzy set is an effective mathematical method to handle imprecise and uncertain information. In this paper, we extend PBM operator to integrate Pythagorean fuzzy numbers (PFNs) based on the interaction operational laws of PFNs, and propose Pythagorean fuzzy interaction PBM operator and weighted Pythagorean fuzzy interaction PBM operator. These new Pythagorean fuzzy interaction PBM operators can capture the interactions between the membership and nonmembership function of PFNs and retain the main merits of the PBM operator. Then, we analyze some desirable properties and particular cases of the presented operators. Further, a new multiple attribute decision making method based on the proposed method has been presented. Finally, a numerical example concerning the evaluation of online payment service providers is provided to illustrate the validity and merits of the new method by comparing it with the existing methods.

https://onlinelibrary.wiley.com/doi/epdf/10.1002/int.22204

Pythagorean fuzzy interaction power Bonferroni mean aggregation operators in multiple attribute decision making

Fuzzy set theory, rough set theory and soft set theory are all generic mathematical tools for dealing with uncertainties. There has been some progress concerning practical applications of these theories, especially, the use of these theories in decision making problems. In the present article, we review some decision making methods based on (fuzzy) soft sets, rough soft sets and soft rough sets. In particular, we provide several novel algorithms in decision making problems by combining these kinds of hybrid models. It may be served as a foundation for developing more complicated soft set models in decision making.

A survey of decision making methods based on certain hybrid soft set models

Graphical abstractDisplay Omitted In this paper, we investigate the relationships among rough sets, soft sets and hemirings. The concept of soft rough hemirings is introduced, which is an extended notion of a rough hemiring. It is pointed out that in this paper, we first apply soft rough sets to algebraic structure-hemirings. Further, we first put forward the concepts of C-soft sets and CC-soft sets, which provide a new research idea for soft rough algebraic research. Moreover, we study roughness in hemirings with respect to MSR-approximation spaces. Some new soft rough operations over hemirings are explored. In particular, lower and upper MSR-hemirings (k-ideal and h-ideal) are investigated. Finally, we put forth an approach for multicriteria group decision making problem based on modified soft rough sets and offer an actual example.

A novel soft rough set

In this paper, we contribute to a recent and successful modelization of uncertainty, which the practitioner often encounters in the formulation of multicriteria group decision making problems. To be precise, in order to approach the uncertainty issue we introduce a novel type of soft rough covering by means of soft neighborhoods, and then we use it to improve decision making in a multicriteria group environment. Our research method is as follows. Firstly we introduce the soft covering upper and lower approximation operators of soft rough coverings. Then its relationships with well-established types of soft rough coverings are analyzed. Secondly, we define and investigate the measure degree of our novel soft rough covering. With this tool we produce a new class of soft rough sets. Finally, we propose an application of such soft rough covering model to multicriteria group decision making by means of an algorithmic solution. A fully developed example supports the implementability of this decision making method.

A novel type of soft rough covering and its application to multicriteria group decision making

By means of @?-soft sets and q-soft sets, some characterizations of (implicative, positive implicative and fantastic) filteristic soft BL-algebras are investigated. Finally, we prove that a soft set is an implicative filteristic soft BL-algebra if and only if it is both a positive implicative filteristic soft BL-algebra and a fantastic filteristic soft BL-algebra.

https://scientificbulletin.upb.ro/rev_docs_arhiva/fullafb_777899.pdf

Soft BL-algebras based on fuzzy sets

To the best of our knowledge, the tool of soft set theory is a new efficacious technique to dispose uncertainties and it focuses on the parameterization, while fuzzy set theory emphasizes the truth degree and rough set theory as another tool to handle uncertainties, it places emphasis on granular. However, the real-world problems that under considerations are usual very complicated. Consequently, it is very difficult to solve them by a single mathematical tool. It is worth noting that decision making (briefly, DM) in an imprecise environment has been showing more and more role in real-world applications. Researches on the idiographic applications of the above three uncertain theories as well as their hybrid models in DM have attracted many researchers’ widespread interest. DM methods are not yet proposed based on fusions of the above three uncertain theories. In view of the reason, by compromising the above three uncertain theories, we elaborate some reviews to DM methods based on two classes of hybrid soft models: SRF-sets and SFR-sets. We test all algorithms for DM and computation time on data sets produced by soft sets and FS-sets. The numerical experimentation programs are written for given pseudo codes in MATLAB. At the same time, the comparisons of all algorithms are given. Finally, we expatiate on an overview of techniques based on the involved hybrid soft set models.

A survey of decision making methods based on two classes of hybrid soft set models

Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings

This paper contributes to the expanding literature on VIKOR, a well-known multi-criteria decision-making technique. It is abundantly used to find the compromise solution regarding some significant criteria under different models. The general VIKOR methodology implements the principle that a recommended response must be a feasible solution which is nearest to positive ideal solution having maximum group utility and minimum individual regret. In this article, we propose a new strategy to address multi-criteria group decision-making problems named complex Pythagorean fuzzy VIKOR (CPF-VIKOR) method. It is designed to handle a great deal of vagueness and hesitation which are often present in human decisions. The CPF-VIKOR method allows the linguistic terms to express individual opinions of experts about the performance of alternatives and the weights of the criteria. We combine the individual judgments of experts with the help of complex Pythagorean fuzzy weighted averaging operator. Further, we compute the ranking measure with the help of group utility and regret measures by adjusting the weight of strategy of maximum group utility within the unit interval. We sort the alternatives in an ascending order relative to group utility measure and individual regret measure. Moreover, we demonstrate our proposed method with the help of a flow chart and two numerical examples: one for the selection of the most beneficial renewable energy project in Spain and another for the selection of the most suitable logistic village location in Turkey. Finally, we present the comparative analysis of our proposed method with the CPF-TOPSIS method to prove its validity.

Xueling Ma

Papers

A survey of decision making methods based on certain hybrid soft set models

A survey of decision making methods based on two classes of hybrid soft set models

Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings

Group decision-making framework using complex Pythagorean fuzzy information

Some kinds of (C,CCq)-interval-valued fuzzy ideals of BCI-algebras