Picture Fuzzy Research Articles

New Operations on Interval-Valued Picture Fuzzy Set, Interval-Valued Picture Fuzzy Soft Set and Their Applications

An interval-valued picture fuzzy set (IVPFS) is one of the generalizations of an interval-valued fuzzy set to handle the uncertainties in the data during analysis. The aim of this paper is to introduce and study new operations of IVPFS, along with its properties, and examples. In addition, we present the notion of the interval-valued picture fuzzy soft set theory and investigated their properties. Several operations on such as subset, equal, complement, inf product, sup product, union, and intersection are defined over the interval-valued picture fuzzy soft set and discussed their basic properties. Furthermore, we construct an algorithm using an interval-valued picture fuzzy soft set to solve the decision-making problems and illustrate its applicability through a numerical example. From the study, we conclude that the proposed approach is viable in order to handle the uncertainties during the decision-making problems.

Integration Stages of Project Risk Management (PRM) into Enterprise Risk Management (ERM)

Enterprise risk management (ERM) is a relatively new concept for a project-based organization than for a functional organization. A project-based organization, in general, faces several difficulties in the implementation of ERM due to the diversity of risk associated with several projects. From a system thinking perspective, a project-based organization needs an integrated approach to interrelate the isolated processes of diverse projects. The issues are related to fuzzy picture of integration, such as, the difference between ERM and PRM processes, how to integrate the two concepts, what happens if integration process goes wrong, as well as issues with risk technologies and change in risk culture. The article provides informal and formal approaches to integration of ERM and PRM. Successful integration requires not only an understanding the value of integration, improvement in risk culture, but needs a learning-based approach to improve risk expertise, interaction, team building, and decision making.

Methods for MADM with Picture Fuzzy Muirhead Mean Operators and Their Application for Evaluating the Financial Investment Risk

In this article, we study multiple attribute decision-making (MADM) problems with picture fuzzy numbers (PFNs) information. Afterwards, we adopt a Muirhead mean (MM) operator, a weighted MM (WMM) operator, a dual MM (DMM) operator, and a weighted DMM (WDMM) operator to define some picture fuzzy aggregation operators, including the picture fuzzy MM (PFMM) operator, the picture fuzzy WMM (PFWMM) operator, the picture fuzzy DMM (PFDMM) operator, and the picture fuzzy WDMM (PFWDMM) operator. Of course, the precious merits of these defined operators are investigated. Moreover, we have adopted the PFWMM and PFWDMM operators to build a decision-making model to handle picture fuzzy MADM problems. In the end, we take a concrete instance of appraising a financial investment risk to demonstrate our defined model and to verify its accuracy and scientific merit.

NEW DISSIMILARITY MEASURES ON PICTURE FUZZY SETS AND APPLICATIONS

The dissimilarity measures between fuzzy sets/intuitionistic fuzzy sets/picture fuzzy sets are studied and applied in various matters. In this paper, we propose some new dissimilarity measures on picture fuzzy sets. This new dissimilarity measures overcome the restrictions of all existing dissimilarity measures on picture fuzzy sets. After that, we apply these new measures to the pattern recognition problems. Finally, we introduce a multi-criteria decision making (MCDM) method that used the new dissimilarity measures and apply them in the supplier selection problems.

Picture fuzzy heronian mean aggregation operators in multiple attribute decision making

The Heronian mean and generalized Heronian mean provide two aggregation operators that consider the inter-dependent phenomena among the aggregated arguments. In this paper, the Heronian mean and generalized Heronian mean under picture fuzzy environments is studied. First, the generalized picture fu zzy Heronian mean (GPFHM) operator and generalized picture fuzzy weighted Heronian mean (GPFWHM) operator are proposed and some of their desirable properties and special cases are investigated in detail. Then, an approach to multiple attribute decision making (MADM) based on GPFWHM operator is proposed. Finally, a practical example for enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Some Picture Fuzzy Dombi Heronian Mean Operators with Their Application to Multi-Attribute Decision-Making

As an extension of the intuitionistic fuzzy set (IFS), the recently proposed picture fuzzy set (PFS) is more suitable to describe decision-makers’ evaluation information in decision-making problems. Picture fuzzy aggregation operators are of high importance in multi-attribute decision-making (MADM) within a picture fuzzy decision-making environment. Hence, in this paper our main work is to introduce novel picture fuzzy aggregation operators. Firstly, we propose new picture fuzzy operational rules based on Dombi t-conorm and t-norm (DTT). Secondly, considering the existence of a broad and widespread correlation between attributes, we use Heronian mean (HM) information aggregation technology to fuse picture fuzzy numbers (PFNs) and propose new picture fuzzy aggregation operators. The proposed operators not only fuse individual attribute values, but also have a good ability to model the widespread correlation among attributes, making them more suitable for effectively solving increasingly complicated MADM problems. Hence, we introduce a new algorithm to handle MADM based on the proposed operators. Finally, we apply the newly developed method and algorithm in a supplier selection issue. The main novelties of this work are three-fold. Firstly, new operational laws for PFSs are proposed. Secondly, novel picture fuzzy aggregation operators are developed. Thirdly, a new approach for picture fuzzy MADM is proposed.

Medical Diagnosis Based on Distance Measures Between Picture Fuzzy Sets

This article describes how most frequently uncertainty arises due to vagueness, imprecision, partial information, etc., are encountered in medical diagnosis. To deal with this type of uncertainty, initially fuzzy set theory (FST) was explored and accordingly, medical decision making became one of the most important and interesting areas of applications of FST. Interval valued fuzzy sets (IVFSs) and intuitionistic fuzzy sets (IFS's) were developed and successfully applied in different areas including medical diagnosis. Although, IFS forms a membership degree and a non-membership degree separately in such a way that sum of the two degrees must not exceed one, but one of the important and integral part i.e., degree of neutrality is not taken into consideration in IFS, which is generally occurred in medical diagnosis. In such circumstances, picture fuzzy set (PFS) can be considered as a strong mathematical tool, which adequate in situations when human opinions involved more answers of type: yes, abstain, no. For this purpose, this article, proposes some distance measures on PFS and studies some of its properties. Also, an attempt has been made to carry out medical diagnosis via the proposed distance measures on PFSs and exhibit the technique with a suitable case study. It is found that the distance measures make it possible to introduce weights of all symptoms and consequently patient can be diagnosed directly.

Different Approaches to Multi-Criteria Group Decision Making Problems for Picture Fuzzy Environment

The main objective of proposed work is to introduce a series of picture fuzzy weighted geometric aggregation operators by using t-norm and t-conorm. In this paper, we discussed generalized form of weighted geometric aggregation operator for picture fuzzy information. Further, the proposed geometric aggregation operators of picture fuzzy number are applied to multi-attribute group decision making problems. Also, we propose the TOPSIS method to aggregate the picture fuzzy information. To implement the proposed models, we provide some numerical applications of group decision making problems. Also compared with previous model, we conclude that the proposed technique is more effective and reliable.

Some Measures of Picture Fuzzy Sets and Their Application in Multi-attribute Decision Making

Some Measures of Picture Fuzzy Sets and Their Application in Multi-attribute Decision Making

Medical Decision Making the Arithmetic of Generalized Triangular Fuzzy Numbers

Background: When patient(s) approach to a medical expert to explain their problems, they often explain their conditions through vague linguistic expression [1]. Medical expert needs to prepare a list of potential symptoms for the particular diseases of the patients based on their vague linguistic statements. Together with the vagueness in medical documents and imprecise information gathered for decision making makes the medical experts’ job more complex. Due to the occurrence of uncertainty in medical decision making exploitation of the Fuzzy Set (FST) is required. Generally in literature, type-I fuzzy set, Intuitionistic Fuzzy Sets (IFSs), Interval Valued Fuzzy Sets (IVFSs), and Picture Fuzzy Sets (PFSs) are extensively applied in medical decision making.

A DSP-based blind deconvolution algorithm for motion image restoration

In the process of image shooting, image stabilization is an inevitable problem. Therefore, this paper finds an efficient and simple image stabilization algorithm in image stabilization. Using a new image regularization method to reduce the cost of real and clear images, and apply it to the blind deconvolution model without any additional cost. Because of its rapidity and robustness, it matches the processing performance of DSP in image processing. In this article, after re-encoding, so that it can be applied to the DSP, and thus enhance the processing speed of the image processing. In addition, because of the portability of DSP, the DSP embedded with the algorithm can be transplanted to the UAV. The fuzzy picture produced after the shooting is processed in real time to reduce the workload of the later picture processing. Experiments show that the scheme proposed in this paper can achieve real-time performance under the precondition of guaranteeing the computing effect, so as to improve the operating efficiency of the whole system.

Picture Fuzzy Hamacher Aggregation Operators and their Application to Multiple Attribute Decision Making

Picture Fuzzy Hamacher Aggregation Operators and their Application to Multiple Attribute Decision Making

Some New De Morgan Picture Operator Triples in Picture Fuzzy Logic

A new concept of picture fuzzy sets (PFS) were introduced in 2013, which are directextensions of the fuzzy sets and the intuitonistic fuzzy sets. Then some operations on PFS withsome properties are considered in [ 9,10 ]. Some basic operators of fuzzy logic as negation, tnorms, t-conorms for picture fuzzy sets firstly are defined and studied in [13,14]. This paper isdevoted to some classes of representable picture fuzzy t-norms and representable picture fuzzyt-conorms on PFS and a basic algebra structure of Picture Fuzzy Logic – De Morgan triples ofpicture operators.

Морфологическая оценка ультраструктурных изменений в органах и тканях линейных мышей Эллиса после введения Ивомека Ф

Представлены сведения о том, что после введения мышам линии Эллиса Ивомека Ф (Bayer, Германия) в рекомендованной фирмой терапевтической дозе (20 мг/кг массы тела) развиваются нарушения: серозный отек, частичная фрагментация поперечно-полосатых волокон в ткани на месте введения препарата, набухание митохондрий с нечетким рисунком крист в эпителиоцитах печени и почек, слабо выраженное накопление плазмобластов в селезенке и нечеткая лимфатизация почек. Применение Ивомека Ф в терапевтической дозе (20 мг/кг массы тела) не вызывало ультраструктурных изменений в поджелудочной железе мышей. Ультраструктурные изменения в организме мышей после введения Ивомека Ф в 2 раза увеличенной дозе (40 мг/кг массы тела) характеризируются деструкцией мышечных волокон и дермы с появлением некротического детрита, макрофагальной реакцией с последующей фибротизацией в тканях на месте введения, разрушением митохондрий в гепатоцитах и эпителии мочеобразующих канальцев почек. Введение Ивомека Ф в 3 раза увеличенной дозе (60 мг/кг массы тела) вызывало сильно выраженные ультраструктурные повреждения в тканях на месте введения, в селезенке, в печени, приводило к серьезным повреждениям митохондриального аппарата в эпителиоцитах, более выраженным разрушениям митохондрий в гепатоцитах и эпителия мочеобразующих канальцев, набуханиям подоцитов в сосудистых клубочках почек. В связи с этим категорически запрещается ветеринарным специалистам нарушать Инструкцию по применению препарата Ивомек Ф и назначать животным дозы, превышающие терапевтическую в 2 и 3 раза.

The Generalized Dice Similarity Measures for Picture Fuzzy Sets and Their Applications

As the extension of fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, and picture fuzzy set, the spherical fuzzy set is characterized by three functions expressing the positive-membership degree, the neutral-membership degree and the negative-membership degree which the sum squares of them is equal or less than 1. In this work, we shall present some novel Dice similarity measures of spherical fuzzy sets and the generalized Dice similarity measures of spherical fuzzy sets and indicates that the Dice similarity measures and asymmetric measures (projection measures) are the special cases of the generalized Dice similarity measures in some parameter values. Then, we propose the generalized Dice similarity measures-based multiple attribute group decision making models with spherical fuzzy information. Then, we apply the generalized Dice similarity measures between spherical fuzzy sets to multiple attribute group decision making. Finally, an illustrative example is given to demonstrate the efficiency of the similarity measures for selecting the desirable ERP system.

Some Measures of Picture Fuzzy Sets and Their Application

To measure the difference of two fuzzy sets (FSs) / intuitionistic sets (IFSs), we can use the distance measure and dissimilarity measure between fuzzy sets/intuitionistic fuzzy set. Characterization of distance/dissimilarity measure between fuzzy sets/intuitionistic fuzzy set is important as it has application in different areas: pattern recognition, image segmentation, and decision making. Picture fuzzy set (PFS) is a generalization of fuzzy set and intuitionistic set, so that it have many application. In this paper, we introduce concepts: difference between PFS-sets, distance measure and dissimilarity measure between picture fuzzy sets, and also provide the formulas for determining these values. We also present an application of dissimilarity measures in the sample recognition problems, can also be considered a decision-making problem.

Picture fuzzy normalized projection-based VIKOR method for the risk evaluation of construction project

Identifying the priority of risk factors through risk evaluation is a significant decision-making problem for construction project management team. In this study, a multi-criteria decision-making framework is constructed for risk evaluation of construction project with picture fuzzy information. First, several limitations of the extant picture fuzzy projection model are identified. Second, a picture fuzzy normalized projection (PFNP) model is proposed to overcome the limitations of the extant picture fuzzy projection model. Third, an entropy weight method of picture fuzzy sets is established to calculate the objective weight vector of the criteria. Furthermore, an integrated picture fuzzy normalized projection-based VIKOR method is constructed by integrate the PFNP model and VIKOR method under picture fuzzy environment. The proposed method not only considers the difference between two picture fuzzy numbers (PFNs), including distance and included angle, but also considers the compromise among the criteria. Finally, a case study, sensitivity analysis, and comparative analysis are conducted to interpret the practicality and validity of the proposed method.

Model for evaluating the enterprise marketing capability with picture fuzzy information

In this paper, we investigate the multiple attribute decision making problems with picture fuzzy information. Then, we utilize induced OWA (IOWA) operator to develop picture fuzzy induced OWA (PFIOWA) operators. The prominent characteristic of this proposed operator are studied. Then, we have utili zed the PFIOWA to develop an approach to solve the picture fuzzy multiple attribute decision making problems. Finally, a practical example for evaluating the enterprise marketing capability is given to verify the developed approach and to demonstrate its practicality and effectiveness.

A Novel Picture Fuzzy Linguistic Aggregation Operator and Its Application to Group Decision-making

The intuitionistic fuzzy set (IFS) is an effective tool to express uncertain and incomplete cognitive information with the membership, non-membership, and hesitance degrees. The picture fuzzy set (PFS) is an extension of IFS, and it can contain more information than IFS. Linguistic variables (LVs) can easily describe the complex cognitive information provided by the decision makers. So it is necessary to combine the PFS with the linguistic term and define the picture fuzzy linguistic set (PFLS), then extend Archimedean triangular norms (t-norms) and triangular conorms (s-norms), which are the generalizations of a number of other t-norms and s-norms, such as Einstein, Hamacher, and Frank s-norms and t-norms, to process PFLS. By combining the PFS and the linguistic term, we define the picture fuzzy linguistic set (PFLS) and the operations of the picture fuzzy linguistic numbers (PFLNs). Further, we develop the Archimedean picture fuzzy linguistic weighted arithmetic averaging (A-PFLWAA) operator and discuss a number of properties and special cases of this operator. Besides, we propose an approach to deal with multiple attributes group decision-making (MAGDM) problem on the basis of the developed A-PFLWAA operator. An approach to solve MAGDM problem is proposed on the basis of the A-PFLWAA operator, and the validity and reliability of the proposed method are proven by an illustrative example. The PFLNs are the generalizations of the intuitionistic linguistic numbers (ILNs), and they contain more information than ILNs. In addition, our method cannot only be utilized to solve the problems with ILNs but also be used to deal with the problems with PFLNs, and it is a generalization of a number of the existing methods.

New Operations of Picture Fuzzy Relations and Fuzzy Comprehensive Evaluation

In this paper, some new operations and basic properties of picture fuzzy relations are intensively studied. First, a new inclusion relation (called type-2 inclusion relation) of picture fuzzy relations is introduced, as well as the corresponding type-2 union, type-2 intersection and type-2 complement operations. Second, the notions of anti-reflexive kernel, symmetric kernel, reflexive closure and symmetric closure of a picture fuzzy relation are introduced and their properties are explored. Moreover, a new method to solve picture fuzzy comprehensive evaluation problems is proposed by defining the new composition operation of picture fuzzy relations, and the picture fuzzy comprehensive evaluation model is built. Finally, an application example (about investment risk) of picture fuzzy comprehensive evaluation is given, and the effective experiment results are obtained.