Circular Pythagorean fuzzy sets and applications to multi-criteria decision making

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 center consists of non-negative real numbers $\mu$ and $\nu$ with the condition $\mu^2+\nu^2\leq 1$. 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 center 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 $t$-norms and $t$-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 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

(R1509) TOPSIS and VIKOR Methods for Spherical Fuzzy Soft Set Aggregating Operator Framework

The Spherical Fuzzy Soft (SFS) set is a generalization of the Pythagorean fuzzy soft set and the intuitionistic fuzzy soft set. We introduce the concept of aggregating SFS decision matrices based on aggregated operations. The techniques for order of preference by similarity to ideal solution (TOPSIS) and viekriterijumsko kompromisno rangiranje (VIKOR) for the SFS approaches are the strong points of multi criteria group decision making (MCGDM), which is various extensions of fuzzy soft sets. We define a score function based on aggregating TOPSIS and VIKOR methods to the SFS-positive and SFS-negative ideal solutions. The TOPSIS and VIKOR methods provide decision-making weights. To find the optimal alternative under this condition, closeness is introduced. Also, we obtain an algorithm that deals with the MCGDM problems based on an aggregating operator. Finally, a numerical example of the MCGDM problem is given to verify the practicality of the aggregating operators

A New Type of Neutrosophic Set in Pythagorean Fuzzy Environment and Applications to Multi-criteria Decision Making

In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and more sensitive evaluations are made by a decision maker in decision making problems compared to IFVNSs. In other words, such sets enable a decision maker to evaluate the degrees of the truth, the indeterminacy and the falsity as PFVs to model the uncertainty in the evaluations

Development of q-Rung Orthopair Trapezoidal Fuzzy Einstein Aggregation Operators and Their Application in MCGDM Problems

Compared to previous extensions, the q-rung orthopair fuzzy sets are superior to intuitionistic ones and Pythagorean ones because they allow decision-makers to use a more extensive domain to present judgment arguments. The purpose of this study is to explore the multicriteria group decision-making (MCGDM) problem with the q-rung orthopair trapezoidal fuzzy (q-ROTrF) context by employing Einstein t-conorms and t-norms. Firstly, some arithmetical operations for q-ROTrF numbers, such as Einstein-based sum, product, scalar multiplication, and exponentiation, are introduced based on Einstein t-conorms and t-norms. Then, Einstein operations-based averaging and geometric aggregation operators (AOs), viz., q-ROTrF Einstein weighted averaging and weighted geometric operators, are developed. Further, some prominent characteristics of the suggested operators are investigated. Then, based on defined AOs, a MCGDM model with q-ROTrF numbers is developed. In accordance with the proposed operators and the developed model, two numerical examples are illustrated. The impacts of the rung parameter on decision results are also analyzed in detail to reflect the suitability and supremacy of the developed approach

Characterization of approximate plane symmetries for 3D fuzzy objects

International audienceWe are interested in finding and characterizing the symmetry planes of fuzzy objects in 3D space. We introduce first a fuzzy symmetry measure which defines an object symmetry degree with respect to a given plane. It is computed by measuring the similarity between the original object and its reflection. The choice of an appropriate measure of comparison is based on the desired properties. In a second part, a method for finding the best symmetry planes of fuzzy objects is proposed. We then apply these results to the representation of directional relationships

NIDUS IDEARUM. Scilogs, V: joining the dots

My lab[oratory] is a virtual facility with noncontrolled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings ground , opinion , expectation ), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). * In this fifth book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, mostly referring to topics on NEUTROSOPHY – email messages to research colleagues, or replies, notes about authors, articles, or books, so on. Feel free to budge in or just use the scilogs as open source for your own ideas

The Interval-Valued Spherical Fuzzy Based Methodology and its Application to Electric Car Selection

Imagining, thinking, producing, developing and changing what you produce are among the main traits that make human beings human. Human beings question their raison d’être, their life, the quality of their lives; in other words, they ask why and how. All these inquiries result in the production of information, a flow of the information produced, and sometimes a product. Today, in a world where production takes place at an unprecedented pace, one needs to possess the technology to keep up with developments. This is a dynamic capability and must be continuously developed to make it endure. Electric vehicles, a gift of technological developments of the world of today, are a combination of imagination, a needs assessment, and sustainable innovations. This study addressed the problem of electric car selection and included a case study involving six criteria and ten alternatives. The proposed decision model has integrated AHP and ELECTRE methods with interval-valued spherical fuzzy sets. The novelty of this study stems from evaluating the performance of electric cars using IVSF-AHP-ELECTRE and selecting accordingly for the first time. In this study, the level of importance of battery capacity, autonomous driving, charging network, price, efficiency and performance criteria were determined. A ranking was then made for the electric car alternatives based on these criteria

Approaches to multi-attribute group decision-making based on picture fuzzy prioritized Aczel–Alsina aggregation information

The Aczel-Alsina t-norm and t-conorm were derived by Aczel and Alsina in 1982. They are modified forms of the algebraic t-norm and t-conorm. Furthermore, the theory of picture fuzzy values is a very valuable and appropriate technique for describing awkward and unreliable information in a real-life scenario. In this research, we analyze the theory of averaging and geometric aggregation operators (AOs) in the presence of the Aczel-Alsina operational laws and prioritization degree based on picture fuzzy (PF) information, such as the prioritized PF Aczel-Alsina average operator and prioritized PF Aczel-Alsina geometric operator. Moreover, we examine properties such as idempotency, monotonicity and boundedness for the derived operators and also evaluated some important results. Furthermore, we use the derived operators to create a system for controlling the multi-attribute decision-making problem using PF information. To show the approach's effectiveness and the developed operators' validity, a numerical example is given. Also, a comparative analysis is presented

A strategy for hepatitis diagnosis by using spherical q-linear Diophantine fuzzy Dombi aggregation information and the VIKOR method

Hepatitis is an infectious disease typified by inflammation in internal organ tissues, and it is caused by infection or inflammation of the liver. Hepatitis is often feared as a fatal illness, especially in developing countries, mostly due to contaminated water, poor sanitation, and risky blood transfusion practices. Although viruses are typically blamed, other potential causes of this kind of liver infection include autoimmune disorders, toxins, medicines, opioids, and alcohol. Viral hepatitis may be diagnosed using a variety of methods, including a physical exam, liver surgery (biopsy), imaging investigations like an ultrasound or CT scan, blood tests, a viral serology panel, a DNA test, and viral antibody testing. Our study proposes a new decision-support system for hepatitis diagnosis based on spherical q-linear Diophantine fuzzy sets (Sq-LDFS). Sq-LDFS form the generalized structure of all existing notions of fuzzy sets. Furthermore, a list of novel Einstein aggregation operators is developed under Sq-LDF information. Also, an improved VIKOR method is presented to address the uncertainty in analyzing the viral hepatitis categories demonstration. Interesting and useful properties of the proposed operators are given. The core of this research is the proposed algorithm based on the proposed Einstein aggregation operators and improved VIKOR approach to address uncertain information in decision support problems. Finally, a hepatitis diagnosis case study is examined to show how the suggested approach works in practice. Additionally, a comparison is provided to demonstrate the superiority and efficacy of the suggested decision technique

Disaster decision-making with a mixing regret philosophy DDAS method in Fermatean fuzzy number

In this paper, the use of the Fermatean fuzzy number (FFN) in a significant research problem of disaster decision-making by defining operational laws and score function is demonstrated. Generally, decision control authorities need to brand suitable and sensible disaster decisions in the direct conceivable period as unfitting decisions may consequence in enormous financial dead and thoughtful communal costs. To certify that a disaster comeback can be made, professionally, we propose a new disaster decision-making (DDM) technique by the Fermatean fuzzy Schweizer-Sklar environment. First, the Fermatean fuzzy Schweizer-Sklar operators are employed by decision-makers to rapidly analyze their indefinite and vague assessment information on disaster choices. Then, the DDM technique based on the FFN is planned to identify highly devastating disaster choices and the best available choices. Finally, the proposed regret philosophy DDM technique is shown functional to choose the ideal retort explanation for a communal fitness disaster in Pakistan. The dominance and realism of the intended technique are further defensible through a relative study with additional DDM systems