Saleem Abdullah

Interval-valued Pythagorean fuzzy geometric aggregation operators and their application to group decision making problem

There are many aggregation operators have been defined up to date, but in this work, we define the interval valued Pythagorean fuzzy weighted geometric (IPFWG) operator, the interval-valued Pythagorean fuzzy ordered weighted geometric (IPFOWG) operator, and the interval-valued Pythagorean fuzzy hybrid geometric operator. We also discuss some properties and give some examples also to develop these operators. At the last we apply the interval-valued IPFWG operator and the interval-valued IPFOWG operator to multiple attribute decision-making problem under the interval-valued Pythagorean fuzzy information.

Interval-valued Pythagorean fuzzy GRA method for multiple-attribute decision making with incomplete weight information

In this paper, the concept of multiple‐attribute group decision‐making (MAGDM) problems with interval‐valued Pythagorean fuzzy information is developed, in which the attribute values are interval‐valued Pythagorean fuzzy numbers and the information about the attribute weight is incomplete. Since the concept of interval‐valued Pythagorean fuzzy sets is the generalization of interval‐valued intuitionistic fuzzy set. Thus, due the this motivation in this paper, the concept of interval‐valued Pythagorean fuzzy Choquet integral average (IVPFCIA) operator is introduced by generalizing the concept of interval‐valued intuitionistic fuzzy Choquet integral average operator. To illustrate the developed operator, a numerical example is also investigated. Extended the concept of traditional GRA method, a new extension of GRA method based on interval‐valued Pythagorean fuzzy information is introduced. First, utilize IVPFCIA operator to aggregate all the interval‐valued Pythagorean fuzzy decision matrices. Then, an optimization model based on the basic ideal of traditional grey relational analysis (GRA) method is established, to get the weight vector of the attributes. Based on the traditional GRA method, calculation steps for solving interval‐valued Pythagorean fuzzy MAGDM problems with incompletely known weight information are given. The degree of grey relation between every alternative and positive‐ideal solution and negative‐ideal solution is calculated. To determine the ranking order of all alternatives, a relative relational degree is defined by calculating the degree of grey relation to both the positive‐ideal solution and negative ideal solution simultaneously. Finally, to illustrate the developed approach a numerical example is to demonstrate its practicality and effectiveness.

Some Generalized Intuitionistic Fuzzy Einstein Hybrid Aggregation Operators and Their Application to Multiple Attribute Group Decision Making

AbstractnThe objective of the present work is divided into threefold. Firstly, we developed intuitionistic fuzzy Einstein hybrid averaging (IFEHA) aggregation operator and intuitionistic fuzzy Einstein hybrid geometric (IFEHG) aggregation operator along with their desirable properties. Secondly, we introduced two generalized aggregation operators along with their desirable properties, namely generalized intuitionistic fuzzy Einstein hybrid averaging (GIFEHA) aggregation operator and generalized intuitionistic fuzzy Einstein hybrid geometric (GIFEHG) aggregation operator. The main advantage of using the proposed methods is that these operators and methods give a more complete view of the problem to the decision makers. These methods provide more general, more accurate and precise results as compared to the existing methods. Therefore, these methods play a vital role in real-world problems. Finally the proposed operators have been applied to decision-making problems to show the validity, practicality and effectiveness of the new approach.

Analyses of S-boxes based on interval valued intuitionistic fuzzy sets and image encryption

Decision making implies selection of the best decision from a set of possible options. In some cases, this selection is based on past experience. Past experience is used to analyse the situations and the choice made in these situations. The aim of this work is to analyse the strength of the nonlinear component (S-box) of block cipher for image encryption applications based on Interval Valued Intuitionistic Fuzzy Sets (IVIFS). S-box is the only component in every block cipher which creates confusion in the data. First, we transform the three dimensional matrix corresponding to colour image with the help of nonlinear component and then use the algebraic structure of IVIFS to choose the best substitution box for image encryption based on entropy, contrast, homogeneity, correlation, energy and mean of absolute devotion. The analyses show that the readings of S8 S-box is very good for image data.

Cubic fuzzy Einstein aggregation operators and its application to decision-making

ABSTRACT In this paper, we define some Einstein operations on cubic fuzzy set (CFS) and develop three arithmetic averaging operators, which are cubic fuzzy Einstein weighted averaging (CFEWA) operator, cubic fuzzy Einstein ordered weighted averaging (CFEOWA) operator and cubic fuzzy Einstein hybrid weighted averaging (CFEHWA) operator, for aggregating cubic fuzzy data. The CFEHWA operator generalises both the CFEWA and CFEOWA operators. Furthermore, we develop various properties of these operators and derive the relationship between the proposed operators and the exiting aggregation operators. We apply CFEHWA operator to multiple attribute decision-making with cubic fuzzy data. Finally, a numerical example is constructed to demonstrate the established approach.