Xindong Peng

Bio: Xindong Peng is an academic researcher from Shaoguan University. The author has contributed to research in topics: Fuzzy logic & Pythagorean theorem. The author has an hindex of 27, co-authored 59 publications receiving 3292 citations. Previous affiliations of Xindong Peng include Northwest Normal University.

Some Results for Pythagorean Fuzzy Sets

Abstract: Pythagorean fuzzy sets PFSs, originally proposed by Yager Yager, Abbasov. Int J Intell Syst 2013;28:436-452, are a new tool to deal with vagueness considering the membership grades are pairs µ,i¾? satisfying the condition µ2+i¾?2i¾?1. As a generalized set, PFSs have close relationship with intuitionistic fuzzy sets IFSs. PFSs can be reduced to IFSs satisfying the condition µ+i¾?i¾?1. However, the related operations of PFSs do not take different conditions into consideration. To better understand PFSs, we propose two operations: division and subtraction, and discuss their properties in detail. Then, based on Pythagorean fuzzy aggregation operators, their properties such as boundedness, idempotency, and monotonicity are investigated. Later, we develop a Pythagorean fuzzy superiority and inferiority ranking method to solve uncertainty multiple attribute group decision making problem. Finally, an illustrative example for evaluating the Internet stocks performance is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Fundamental Properties of Interval-Valued Pythagorean Fuzzy Aggregation Operators

Abstract: In this paper, we investigate the multiple attribute group decision making MAGDM problems with interval-valued Pythagorean fuzzy sets IVPFSs. First, the concept, operational laws, score function, and accuracy function of IVPFSs are defined. Then, based on the operational laws, two interval-valued Pythagorean fuzzy aggregation operators are developed for aggregating the interval-valued Pythagorean fuzzy information, such as interval-valued Pythagorean fuzzy weighted average IVPFWA operator and interval-valued Pythagorean fuzzy weighted geometric IVPFWG operator. A series of inequalities of aggregation operators are studied. Later, we develop some interval-valued Pythagorean fuzzy point operators. Moreover, combining the interval-valued Pythagorean fuzzy point operators with IVPFWA operator, we present some interval-valued Pythagorean fuzzy point weighted averaging IVPFPWA operators, which can adjust the degree of the aggregated arguments with some parameters. Then, we propose an interval-valued Pythagorean fuzzy ELECTRE method to solve uncertainty MAGDM problem. Finally, an illustrative example for evaluating the software developments is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Pythagorean Fuzzy Information Measures and Their Applications

Abstract: Pythagorean fuzzy set (PFS), originally proposed by Yager, is more capable than intuitionistic fuzzy set (IFS) to handle vagueness in the real world. The main purpose of this paper is to investigate the relationship between the distance measure, the similarity measure, the entropy, and the inclusion measure for PFSs. The primary goal of the study is to suggest the systematic transformation of information measures (distance measure, similarity measure, entropy, inclusion measure) for PFSs. For achieving this goal, some new formulae for information measures of PFSs are introduced. To show the efficiency of the proposed similarity measure, we apply it to pattern recognition, clustering analysis, and medical diagnosis. Some illustrative examples are given to support the findings and also demonstrate their practicality and effectiveness of similarity measure between PFSs.

Pythagorean Fuzzy Choquet Integral Based MABAC Method for Multiple Attribute Group Decision Making

Abstract: In this paper, we define the Choquet integral operator for Pythagorean fuzzy aggregation operators, such as Pythagorean fuzzy Choquet integral average PFCIA operator and Pythagorean fuzzy Choquet integral geometric PFCIG operator. The operators not only consider the importance of the elements or their ordered positions but also can reflect the correlations among the elements or their ordered positions. It is worth pointing out that most of the existing Pythagorean fuzzy aggregation operators are special cases of our operators. Meanwhile, some basic properties are discussed in detail. Later, we propose two approaches to multiple attribute group decision making with attributes involving dependent and independent by the PFCIA operator and multi-attributive border approximation area comparison MABAC in Pythagorean fuzzy environment. Finally, two illustrative examples have also been taken in the present study to verify the developed approaches and to demonstrate their practicality and effectiveness.

Pythagorean fuzzy set: state of the art and future directions

Abstract: Pythagorean fuzzy set, generalized by Yager, is a new tool to deal with vagueness considering the membership grade $$\mu $$ and non-membership $$ u $$ satisfying the condition $$\mu ^2+ u ^2\le 1$$ . It can be used to characterize the uncertain information more sufficiently and accurately than intuitionistic fuzzy set. Pythagorean fuzzy set has attracted great attention of many scholars that have been extended to new types and these extensions have been used in many areas such as decision making, aggregation operators, and information measures. Because of such a growth, we present an overview on Pythagorean fuzzy set with aim of offering a clear perspective on the different concepts, tools and trends related to their extension. In particular, we provide two novel algorithms in decision making problems under Pythagorean fuzzy environment. It may be served as a foundation for developing more algorithms in decision making.

Multiple criteria decision making

Abstract: In this Chapter, we imagine a decision maker (or a group of experts) trying to establish or examine fair procedures to combine opinions about alternatives related to different points of view.

Some q‐Rung Orthopair Fuzzy Aggregation Operators and their Applications to Multiple‐Attribute Decision Making

Abstract: The q-rung orthopair fuzzy sets (q-ROFs) are an important way to express uncertain information, and they are superior to the intuitionistic fuzzy sets and the Pythagorean fuzzy sets. Their eminent characteristic is that the sum of the qth power of the membership degree and the qth power of the degrees of non-membership is equal to or less than 1, so the space of uncertain information they can describe is broader. Under these environments, we propose the q-rung orthopair fuzzy weighted averaging operator and the q-rung orthopair fuzzy weighted geometric operator to deal with the decision information, and their some properties are well proved. Further, based on these operators, we presented two new methods to deal with the multi-attribute decision making problems under the fuzzy environment. Finally, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods.

A New Generalized Pythagorean Fuzzy Information Aggregation Using Einstein Operations and Its Application to Decision Making

Abstract: The objective of this article is to extend and present an idea related to weighted aggregated operators from fuzzy to Pythagorean fuzzy sets PFSs. The main feature of the PFS is to relax the condition that the sum of the degree of membership functions is less than one with the square sum of the degree of membership functions is less than one. Under these environments, aggregator operators, namely, Pythagorean fuzzy Einstein weighted averaging PFEWA, Pythagorean fuzzy Einstein ordered weighted averaging PFEOWA, generalized Pythagorean fuzzy Einstein weighted averaging GPFEWA, and generalized Pythagorean fuzzy Einstein ordered weighted averaging GPFEOWA, are proposed in this article. Some desirable properties corresponding to it have also been investigated. Furthermore, these operators are applied to decision-making problems in which experts provide their preferences in the Pythagorean fuzzy environment to show the validity, practicality, and effectiveness of the new approach. Finally, a systematic comparison between the existing work and the proposed work has been given.

An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets

Abstract: Human opinion cannot be restricted to yes or no as depicted by conventional fuzzy set (FS) and intuitionistic fuzzy set (IFS) but it can be yes, abstain, no and refusal as explained by picture fuzzy set (PFS). In this article, the concept of spherical fuzzy set (SFS) and T-spherical fuzzy set (T-SFS) is introduced as a generalization of FS, IFS and PFS. The novelty of SFS and T-SFS is shown by examples and graphical comparison with early established concepts. Some operations of SFSs and T-SFSs along with spherical fuzzy relations are defined, and related results are conferred. Medical diagnostics and decision-making problem are discussed in the environment of SFSs and T-SFSs as practical applications.

Multicriteria Pythagorean fuzzy decision analysis

Abstract: A new closeness index-based ranking method of PFNs is presented.A novel concept of interval-valued Pythagorean fuzzy set is proposed.A new interval-valued Pythagorean fuzzy distance measure is presented.A new hierarchical Pythagorean fuzzy QUALIFLEX method is developed.The proposed method is further extended to manage heterogeneous information. Pythagorean fuzzy set initially developed by Yager (2014) is a new tool to model imprecise and ambiguous information in multicriteria decision making problems. In this paper, we propose a novel closeness index for Pythagorean fuzzy number (PFN) and also introduce a closeness index-based ranking method for PFNs. Next, we extend the Pythagorean fuzzy set to present the concept of interval-valued Pythagorean fuzzy set (IVPFS) which is parallel to interval-valued intuitionistic fuzzy set. The elements in IVPFS are called interval-valued Pythagorean fuzzy numbers (IVPFNs). We further introduce the basic operations of IVPFNs and investigate their desirable properties. Meanwhile, we also explore the ranking method and the distance measure for IVPFNs. Afterwards, we develop a closeness index-based Pythagorean fuzzy QUALIFLEX method to address hierarchical multicriteria decision making problems within Pythagorean fuzzy environment based on PFNs and IVPFNs. This hierarchical decision problem includes the main-criteria layer and the sub-criteria layer in which the relationships among main-criteria are interdependent, the relationships among sub-criteria are independent and the weights of sub-criteria take the form of IVPFNs. Therefore, in the developed method we first define the concept of concordance/discordance index based on the closeness index-based ranking methods and compute the sub-weighted concordance/discordance indices by employing the weighted averaging aggregation operator based on the closeness indices of IVPFNs. In order to take main-criteria interactions into account, we further employ Choquet integral to calculate the main-weighted concordance/discordance indices. By investigating all possible permutations of alternatives with the level of concordance and discordance of the complete preference order, we finally obtain the optimal rankings of alternatives. The proposed method is implemented in a risk evaluation problem in order to demonstrate its applicability and superiority. The salient features of the proposed method, compared to the state-of-the-art QUALIFLEX-based methods, are: (1) it can take the interactive phenomena among criteria into account; (2) it can manage simultaneously the PFN and IVPFN decision data; (3) it can deal effectively with the hierarchal structure of criteria. The proposed method provides us with a useful way for hierarchical multicriteria decision making problems within Pythagorean fuzzy contexts. In addition, we also extend the proposed method to manage heterogeneous information which includes five different types of information such as real numbers, interval numbers, fuzzy numbers, PFNs and hesitant fuzzy elements.