Pythagorean fuzzy sets, an extension of intuitionistic fuzzy sets, is developed for the purpose of providing more freedom to experts in expressing their opinions about the vagueness and impreciseness of the considered problem. In section 3, some operators on fuzzy sets will be discussed. Sep 19, 2017 in this paper, we propose a variety of distance measures for pythagorean fuzzy sets and pythagorean fuzzy numbers, which take into account the four parameters of pythagorean fuzzy sets. Different tools and approaches have been introduced to handle the imprecise environment of group decisionmaking. Pythagorean hesitant fuzzy sets and their application to. In this paper, we propose a variety of distance measures for pythagorean fuzzy sets and pythagorean fuzzy numbers, which take into account the four parameters of pythagorean fuzzy sets. Interval valued pythagorean fuzzy set ivpfs, originally proposed by peng and yang, is.
The pythagoreanfuzzy sets pfss proposed by yager in 20 can deal with more uncertain situations than intuitionistic fuzzy sets because of its larger range of describing the membership grades. Sc fuzzy set theory introduction fuzzy set theory fuzzy set theory is an extension of classical set theory where elements have varying degrees of membership. Pythagorean mpolar fuzzy soft sets with topsis method for. This paper extends pythagorean hesitant fuzzy environments to intervalvalued pythagorean hesitant fuzzy environments and proposes the concept of intervalvalued pythagorean hesitant fuzzy set ivphfs, which allows the membership of each object. Complex fuzzy sets and complex fuzzy logic an overview of.
The main purpose of this paper is to show that zhang and xus distance measure between pfss fails the conditions of distance measure. Since the space of membership grades of pfs is larger than that of ifs, so that the pfs has become an useful math tool to express the uncertain information in decision making problems 61, 62. The sets are represented by pairs of two values, which satisfies. We look at the basic set operations for the pythagorean fuzzy subsets. How to measure the distance of pythagorean fuzzy sets is still an open issue. Also, we give some operators and operators on the bipolar pythagorean fuzzy sets. This work introduces the notion of pythagorean fuzzy graphs pfgs. Then s and t are called similar sets if the following conditions hold. Pythagorean fuzzy sets pfss, originally proposed by yager yager, abbasov. Threeway group conflict analysis based on pythagorean fuzzy. New operations for intervalvalued pythagorean fuzzy set.
Introduction for multicriteria decisionmaking mcdm problem1, atanassov2 introduced a series of concepts of intuitionistic fuzzy set ifs. Keywords pythagorean fuzzy set intuitionistic fuzzy set decision making aggregation operators information measures. B, c p j s b, c, which is called as pfsjs distance measure. The concept of pythagorean fuzzy sets pfss was initially developed by yager in 20, which provides a novel way to model uncertainty and vagueness with high precision and accuracy compared to intuitionistic fuzzy sets ifss. Pythagorean fuzzy sets, which is based on intuitionistic fuzzy sets ifss, is an important tool to solve problems and has attached a large number of researchers. In this paper, the concept of pythagorean fuzzy compactness, pythagorean fuzzy almost compactness and pythagorean fuzzy near compactness are introduced and studied. Pythagorean fuzzy set theory guangming lang, duoqian miao and hamido fujita abstractin some realworld situations, pythagorean fuzzy sets are more powerful and e. Zhang and meng proposedanapproachtointervalvaluedhesitant fuzzy multiattribute group decision making based on the generalized shapleychoquet integral. Later on, yager extended the intuitionistic fuzzy sets into the pythagorean fuzzy sets pfss 4, 5 in 20. Jul 09, 2018 pythagorean fuzzy sets pfss are characterized by a membership degree and a nonmembership degree satisfying the condition that their square sum is equal to or less than 1. Pythagorean mpolar fuzzy soft sets with topsis method for mcgdm 23 pythagorean fuzzy sets pf sets as an extension of if sets.
To this end, the correlation coefficient is proposed for the relationship measurement. Pdf hesitant pythagorean fuzzy sets and their aggregation. Their definition is given firstly, and the stability of this kind of systems is studied, the relation of. As a generalized set, pfss have close relationship with intuitionistic fuzzy sets ifss. As a generalization of intuitionistic fuzzy set, the pythagorean fuzzy set is interesting and very useful in modeling uncertain information in realworld decisionmaking problems. Bipolar pythagorean fuzzy sets and their application based. The other extension of ifs is what is known as pythagorean fuzzy sets. Extension of topsis to multiple criteria decision making with pythagorean, fuzzy sets. Intervalvalued pythagorean hesitant fuzzy set and its. Traditional speculations like fuzzy sets 1, intuitionistic fuzzy sets 2, and pythagorean fuzzy sets 3 are notable and assume vital jobs in demonstrating uncertainty. In this section, we will give the principles and basic operations of pythagorean fuzzy sets and the steps of pythagorean fuzzy ahp method. A novel approach to decisionmaking with pythagorean fuzzy. The major advantages of pfss over the other existing sets are to consider the parameterized tool of the family of pfs. Pythagorean fuzzy sets achieve this purpose because experts do not have to assign membership and nonmember.
A novel distance measure for pythagorean fuzzy sets and. This paper extends pythagorean hesitant fuzzy environments to intervalvalued pythagorean hesitant fuzzy environments and proposes the concept of intervalvalued pythagorean hesitant fuzzy set ivphfs, which allows the membership of each object to be. Pythagorean fuzzy dombi aggregation operators and their. The linguistic pythagorean fuzzy set lpfs is an important implement for modeling the uncertain and imprecise information. Furthermore, classical representations of pythagorean fuzzy soft rough approximation operators are presented. Fuzzy entropy for pythagorean fuzzy sets with application to. Merigo1, manoj sahni3 1department of management control and information systems, university of chile, av. These sets generalize intuitionistic fuzzy sets with a wider scope of applications, and, thus, the motivation for investigating into its. As another extension of fuzzy set theory, yager 33, 34 proposed another class of nonstandard fuzzy sets, called pythagorean fuzzy sets. The objective of this paper is to apply the concept of pythagorean fuzzy sets to graph theory. Pythagorean fuzzy soft rough sets and their applications.
Fuzzy sets fuzzy sets, fuzzy logic, and fuzzy systems. Recently, pythagorean fuzzy linmap method based on the entropy for railway project investment decision making was proposed by xue et al. Pf sets outperform if sets and can deal with more ambiguous and uncertain information in mcdm practice. Pythagorean fuzzy soft rough sets and their applications in. Central to the use of fuzzy sets is the provision of membership grades. Let x be a finite universe of discourse, and b and c be two pythagorean fuzzy sets. Finally, a numerical example is provided to illustrate the validity and applicability of the presented distance measures. Reformat and yager 50 proposed a novel collaborativebased.
Bipolar pythagorean fuzzy sets and their application based on. The concept was concretely designed to represent uncertainty and vagueness in mathematical way and to furnish a formalized tool for tackling imprecision to real. Neutrosophic set is a generalization of intuitionistic. Pythagorean hesitant fuzzy sets, distance measure, multicriteria decision making, mcdm 1. A logic based on the two truth values, true and false, is sometimes inadequate when describing human reasoning. Pythagorean fuzzy soft rough sets and their applications in decisionmaking azmat hussain department of mathematics and statistics, faculty of basic and applied sciences, international islamic university islamabad, islamabad, pakistan correspondence azmat. Notion of fuzzy sets introduced by zadeh 1 revolutionized not only mathematics and logic but also science and technology. In the next section, we give some basic results associated to the fuzzy sets. The technique for order preference by similarity to ideal solutions topsis is a wellknown and effective method for mcdm problems. To overcome this restriction, yager 3,4 introduced the pythagorean fuzzy pf sets, with the condition that the sum of the squares of the membership degree and the nonmembership degree is equal to or less than one. We give some characterizations of pythagorean fuzzy almost compactness in terms of pythagorean fuzzy regular open or pythagorean fuzzy regular closed. The larger value the pfsjs distance measure has, the bigger difference the pythagorean. Ever since the introduction of pythagorean fuzzy pf sets, many scholars have focused on solving multicriteria decisionmaking mcdm problems with pf information. Pythagorean fuzzy number, intervalvalued pythagorean fuzzy number, distance measure, closeness index, aggregation.
Divergence measure of pythagorean fuzzy sets and its. Complex fuzzy sets and complex fuzzy logic an overview of theory and applications dan e. Keeping this advantage, in this paper we define some new entropy measures for pfss to compute the degree of fuzziness. Also, we investigate the behavior of pythagorean fuzzy. In this study, we work on pythagorean fuzzy sets to reduce vagueness and handle the impreciseness of the system environment. Imprecision is an important factor in any decisionmaking process.
A suitable multi criteria decision making mcdm method that could consider vagueness and impreciseness in the assessments should be used for this kind of. P fuzzy sets p fuzzy information systems tay decision d rough sets 1 introduction pythagorean fuzzy sets pfss, as generalizations of intuitionistic fuzzy sets ifss, are characterized by a membership degree and a nonmembership degree satisfying the condition that the square sum of its membership degree and non. Then the proposed operators are applied on decisionmaking problem in which. Pfss extend the concept of intuitionistic fuzzy sets ifss. A new divergence measure of pythagorean fuzzy sets based. Rishe and abraham kandel abstract fuzzy logic, introduced by zadeh along with his introduction of fuzzy sets, is a continuous multivalued logic system.
Pdf a novel entropy measure of pythagorean fuzzy soft sets. Sfss are a generalization of pythagorean fuzzy sets pfs and neutrosophic sets. Distance measure of pythagorean fuzzy sets li 2018. The pfs concept is an extension of the intuitionistic fuzzy set concept. Pdf in this article, a new hesitant pythagorean fuzzy set hpfs has been presented by combining the concepts of pythagorean fuzzy set. Intervalvalued pythagorean fuzzy set ivpfs, originally proposed by peng and yang, is. A novel distance measure for pythagorean fuzzy sets and its. Pythagorean fuzzy set and its application in career placements. Pdf on jan 16, 2020, t m athira and others published a novel entropy measure of pythagorean fuzzy soft sets find, read and cite all the research you need on researchgate. Pythagorean mpolar fuzzy soft sets with topsis method for mcgdm. Pythagorean hesitant fuzzy sets are widely watched because of their excellent ability to deal with uncertainty, imprecise and vague information. A pythagorean fuzzy set pfs is a powerful tool for depicting fuzziness and uncertainty. To improve the modeling capability, pythagorean fuzzy set pfs 16, 17 was put forward by yager et al. While it is true that the spherical fuzzy set is a generalizations of pythagorean fuzzy set and of intuitionistic fuzzy set, it is false that spherical fuzzy set is a generalization of neutrosophic set.
Conflict analysis for pythagorean fuzzy information. Pdf topsis method based on correlation coefficient and. Modified zhang and xus distance measure for pythagorean. Moreover, as a generalization of intuitionistic fuzzy sets, pythagorean fuzzy sets are powerful for describing imprecise information in practice.
Pythagorean fuzzy soft rough set, and investigate some important properties of soft rough pythagorean fuzzy set and pythagorean fuzzy soft rough set in detail. Pdf in this paper we present a short but important summary of pythagorean fuzzy sets. A new distance measure based on pythagorean hesitant fuzzy sets and its application to multicriteria decision making yanru azhong, xiuyan guo a, hong gao, meifa huangb, yuchu qinc, and xiaonan luo a guangxi key laboratory of intelligent processing of computer images and graphic, guilin university of electronic technology, guilin, pr china. A new distance measure based on pythagorean hesitant. Pythagorean mpolar fuzzy soft sets with topsis method for mcgdm 23 pythagorean fuzzy sets pfsets as an extension of ifsets. A new divergence measure of pythagorean fuzzy sets based on. Some results for pythagorean fuzzy sets request pdf. Topsis method based on correlation coefficient and entropy. Later on, yager extended the intuitionistic fuzzy sets into the pythagorean fuzzy sets pfss in 20. Neutrosophic set is a generalization of intuitionistic fuzzy. Fuzzy entropy for pythagorean fuzzy sets with application. It is well known that a lot of distance measures have been. Implication operator on pythagorean fuzzy set international.
The objective of this study is to extend the topsis. Threeway group conflict analysis based on pythagorean. Pythagorean fuzzy weighted averaging aggregation operator. Abstract pythagorean fuzzy sets,involvoing membership, non membership and hesitancy considerations present mathematically a very general structure. The purpose of this paper is to develop the pythagorean fuzzy extension of codas method. In this paper, we develop a new method for pythagorean fuzzy multiplecriteria decisionmaking mcdm problems with aggregation operators and distance measures. A new fuzzy entropy on pythagorean fuzzy sets ios press. Pythagorean fuzzy operators multicriteria decision making. Pythagorean fuzzy weighted averaging aggregation operator and its application to decision making theory.
Wed like to understand how you use our websites in order to improve them. Pythagorean fuzzy set and its application in career. In this paper, a novel topsis technique for order of preference by similarity to ideal solution method is proposed for lpfss based on correlation coefficient and entropy measure. The concept of distance between pythagorean fuzzy sets pfss has been proven to be relevant in the applications of pfss as seen in the literature. Pythagorean fuzzy soft set pfss is one of the useful extension of the pythagorean fuzzy set pfs to deal with the vagueness and uncertainties in the data. One of the latest tools in dealing with imprecision is pythagorean fuzzy sets. By using pythagorean fuzzy sets and ts fuzzy descriptor systems, the new. Pythagorean fuzzy codas and its application to supplier. Atanassovs intuitionistic fuzzy set of second type, also called pythagorean fuzzy set singlevalued atanassovs intuitionistic fuzzy sets of second type ifs2 23, also called singlevalued pythagorean fuzzy set pyfs 24, is defined as follows using t, i, f notations for the components. It is well known that a lot of distance measures have been proposed for the fuzzy sets and ifss in the last few decades 6. A hybrid method for pythagorean fuzzy multiplecriteria. A novel approach to risk assessment for occupational. Abstract by using pythagorean fuzzy sets and ts fuzzy descriptor systems, the new.
Some operations on pythagorean fuzzy sets in this section we discuss some operations and relations on pythagorean fuzzy sets. In this paper, we introduce the concept of bipolar pythagorean fuzzy sets which is an extension of the fuzzy sets,bipolar fuzzy sets,intuitionistic fuzzy sets and pythagorean fuzzy sets. Generalized point operators for pythagorean fuzzy information and their application in multicriteria decision making lei zhu 2, xuefei liang 2. A novel approach to risk assessment for occupational health.
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