Informatica

In this paper, we introduce the concept of circular Pythagorean fuzzy set (value) (C-PFS(V)) as a new generalization of both circular intuitionistic fuzzy sets (C-IFSs) proposed by Atannassov and Pythagorean fuzzy sets (PFSs) proposed by Yager. A circular Pythagorean fuzzy set is represented by a circle that represents the membership degree and the non-membership degree and whose centre consists of non-negative real numbers μ and ν with the condition ${\mu ^{2}}+{\nu ^{2}}\leqslant 1$. A C-PFS models the fuzziness of the uncertain information more properly thanks to its structure that allows modelling the information with points of a circle of a certain centre and a radius. Therefore, a C-PFS lets decision makers to evaluate objects in a larger and more flexible region and thus more sensitive decisions can be made. After defining the concept of C-PFS we define some fundamental set operations between C-PFSs and propose some algebraic operations between C-PFVs via general triangular norms and triangular conorms. By utilizing these algebraic operations, we introduce some weighted aggregation operators to transform input values represented by C-PFVs to a single output value. Then to determine the degree of similarity between C-PFVs we define a cosine similarity measure based on radius. Furthermore, we develop a method to transform a collection of Pythagorean fuzzy values to a C-PFS. Finally, a method is given to solve multi-criteria decision making problems in circular Pythagorean fuzzy environment and the proposed method is practiced to a problem about selecting the best photovoltaic cell from the literature. We also study the comparison analysis and time complexity of the proposed method.

Today energy demand in the world cannot be met based on the growing population of the countries. Exhaustible resources are not enough to supply this energy requirement. Furthermore, the pollution created by these sources is one of the most important issues for all living things. In this context, clean and sustainable energy alternatives need to be considered. In this study, a novel interval-valued neutrosophic (IVN) ELECTRE I method is conducted to select renewable energy alternative for a municipality. A new division operation and deneutrosophication method for interval-valued neutrosophic sets is proposed. A sensitivity analysis is also implemented to check the validity of the proposed method. The obtained results and the sensitivity analysis demonstrate that the given decision in the application is robust. The results of the proposed method determine that the wind power plant is the best alternative and our proposed method’s decisions are consistent and reliable through the results of comparative and sensitivity analyses.

Using different operational laws on membership and non-membership information, various intuitionistic fuzzy aggregation operators based on Archimedean t-norm and t-conorm or their special cases have been extensively investigated for multi-criteria decision making. In spite of this, they are not suitable for some practical cases. In this paper, symmetric intuitionistic fuzzy weighted mean operators w.r.t. general weighted Archimedean t-norms and t-conorms are introduced to deal neutrally or fairly with membership and non-membership information to meet the need of decision makers in some cases. The relationship among the proposed operators and the existing ones is discussed. Particularly, using the parameters in the aggregation operators, the attitude whether the decision maker is optimistic, pessimistic or impartial is reflected. At last, an example is given to show the behaviour of the proposed operators for multi-criteria decision making under intuitionistic fuzzy environment.

A logistics system that involves a supplier who produces and delivers a single product and a buyer who receives and sells the product to the final customers was analyzed. A mathematical model was developed to describe the behavior of the system and to derive the optimal cycle length and order-up-to levels for the two parties. An analysis of the obtained results revealed that the methods were able to determine the optimal control parameters for each party in a short time frame. A coordination mechanism based on the optimal policies was ultimately proposed so that each party benefits more than if they use their own optimal control policy.

In some cases of using multi-criteria decision making methods for solving real-world problems ratings of alternatives cannot be determined precisely, and that is why they are expressed in the form of intervals. Therefore, the aim of this paper is to extend the MOORA method for solving decision making problems with interval data. By extending the ratio system part of MOORA method, an algorithm to determine the most preferable alternative among all possible alternatives, when performance ratings are given as intervals, is presented. Finally, an example is shown to highlight the proposed procedure, at the end of this paper.