Pythagorean mpolar fuzzy soft sets with topsis method for mcgdm 23 pythagorean fuzzy sets pfsets as an extension of ifsets. The purpose of this paper is to develop the pythagorean fuzzy extension of codas method. A novel approach to decisionmaking with pythagorean fuzzy. Zadeh computer science division, department of electrical engineering and computer sciences and the electronics research laboratory, university of california, berkeley, ca 94720, usa. Pdf some basic operations on pythagorean fuzzy sets. 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. 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. A hybrid method for pythagorean fuzzy multiplecriteria. A novel approach to risk assessment for occupational. Pythagorean fuzzy weighted averaging aggregation operator and its application to decision making theory. 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. Pdf a novel entropy measure of pythagorean fuzzy soft sets. Pythagorean mpolar fuzzy soft sets with topsis method for. 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.
To improve the modeling capability, pythagorean fuzzy set pfs 16, 17 was put forward by yager et al. Pythagorean mpolar fuzzy soft sets with topsis method for mcgdm. The larger value the pfsjs distance measure has, the bigger difference the pythagorean. Implication operator on pythagorean fuzzy set international. Topsis method based on correlation coefficient and entropy. Keywords pythagorean fuzzy set intuitionistic fuzzy set decision making aggregation operators information measures. Pf sets outperform if sets and can deal with more ambiguous and uncertain information in mcdm practice. Finally, a numerical example is provided to illustrate the validity and applicability of the presented distance measures. It is well known that a lot of distance measures have been. Pythagorean fuzzy soft rough set, and investigate some important properties of soft rough pythagorean fuzzy set and pythagorean fuzzy soft rough set in detail. As a generalized set, pfss have close relationship with intuitionistic fuzzy sets ifss. Pythagorean fuzzy set and its application in career. 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. A new distance measure based on pythagorean hesitant fuzzy.
Generalized point operators for pythagorean fuzzy information and their application in multicriteria decision making lei zhu 2, xuefei liang 2. Then s and t are called similar sets if the following conditions hold. Zhang and meng proposedanapproachtointervalvaluedhesitant fuzzy multiattribute group decision making based on the generalized shapleychoquet integral. Abstract by using pythagorean fuzzy sets and ts fuzzy descriptor systems, the new.
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. Extension of topsis to multiple criteria decision making with pythagorean, fuzzy sets. Modified zhang and xus distance measure for pythagorean. 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. In this paper, the concept of pythagorean fuzzy compactness, pythagorean fuzzy almost compactness and pythagorean fuzzy near compactness are introduced and studied. Different tools and approaches have been introduced to handle the imprecise environment of group decisionmaking. Also, we investigate the behavior of pythagorean fuzzy. Pythagorean fuzzy set theory guangming lang, duoqian miao and hamido fujita abstractin some realworld situations, pythagorean fuzzy sets are more powerful and e. 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. Central to the use of fuzzy sets is the provision of membership grades. The linguistic pythagorean fuzzy set lpfs is an important implement for modeling the uncertain and imprecise information.
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. Reformat and yager 50 proposed a novel collaborativebased. In the next section, we give some basic results associated to the fuzzy sets. These sets generalize intuitionistic fuzzy sets with a wider scope of applications, and, thus, the motivation for investigating into its. Let x be a finite universe of discourse, and b and c be two pythagorean fuzzy sets.
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. A pythagorean fuzzy set pfs is a powerful tool for depicting fuzziness and uncertainty. Pythagorean fuzzy codas and its application to supplier. Ever since the introduction of pythagorean fuzzy pf sets, many scholars have focused on solving multicriteria decisionmaking mcdm problems with pf information. Imprecision is an important factor in any decisionmaking process. In section 3, some operators on fuzzy sets will be discussed. Neutrosophic set is a generalization of intuitionistic. Pythagorean fuzzy number, intervalvalued pythagorean fuzzy number, distance measure, closeness index, aggregation. By using pythagorean fuzzy sets and ts fuzzy descriptor systems, the new. As a generalization of intuitionistic fuzzy set, the pythagorean fuzzy set is interesting and very useful in modeling uncertain information in realworld decisionmaking problems. The sets are represented by pairs of two values, which satisfies. Pythagorean fuzzy sets achieve this purpose because experts do not have to assign membership and nonmember. 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. Divergence measure of pythagorean fuzzy sets and its.
Pythagorean fuzzy set and its application in career placements. Pythagorean fuzzy operators multicriteria decision making. 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. Pythagorean fuzzy weighted averaging aggregation operator. Intervalvalued pythagorean fuzzy set ivpfs, originally proposed by peng and yang, is. 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. Keeping this advantage, in this paper we define some new entropy measures for pfss to compute the degree of fuzziness. Pdf topsis method based on correlation coefficient and. Some results for pythagorean fuzzy sets request pdf. Pythagorean hesitant fuzzy sets are widely watched because of their excellent ability to deal with uncertainty, imprecise and vague information.
These theories have been applied to decisionmaking 30, 31, clustering analysis 32, and so on. One of the latest tools in dealing with imprecision is pythagorean fuzzy sets. Bipolar pythagorean fuzzy sets and their application based. Distance measure of pythagorean fuzzy sets li 2018. A novel approach to risk assessment for occupational health. 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. Pfss extend the concept of intuitionistic fuzzy sets ifss. This is why yager proposed the concept of pythagorean fuzzy sets. The objective of this study is to extend the topsis. How to measure the distance of pythagorean fuzzy sets is still an open issue. The concept was concretely designed to represent uncertainty and vagueness in mathematical way and to furnish a formalized tool for tackling imprecision to real.
In this paper, we develop a new method for pythagorean fuzzy multiplecriteria decisionmaking mcdm problems with aggregation operators and distance measures. Fuzzy entropy for pythagorean fuzzy sets with application to. A new divergence measure of pythagorean fuzzy sets based on. Also, we give some operators and operators on the bipolar pythagorean fuzzy sets. 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. Pdf hesitant pythagorean fuzzy sets and their aggregation. Sfss are a generalization of pythagorean fuzzy sets pfs and neutrosophic sets.
Rishe and abraham kandel abstract fuzzy logic, introduced by zadeh along with his introduction of fuzzy sets, is a continuous multivalued logic system. A new distance measure based on pythagorean hesitant. Moreover, as a generalization of intuitionistic fuzzy sets, pythagorean fuzzy sets are powerful for describing imprecise information in practice. 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. A novel distance measure for pythagorean fuzzy sets and. We look at the basic set operations for the pythagorean fuzzy subsets. The major advantages of pfss over the other existing sets are to consider the parameterized tool of the family of pfs. Wed like to understand how you use our websites in order to improve them. Furthermore, classical representations of pythagorean fuzzy soft rough approximation operators are presented.
Some operations on pythagorean fuzzy sets in this section we discuss some operations and relations on pythagorean fuzzy sets. 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. Threeway group conflict analysis based on pythagorean. A logic based on the two truth values, true and false, is sometimes inadequate when describing human reasoning. Fuzzy entropy for pythagorean fuzzy sets with application. Complex fuzzy sets and complex fuzzy logic an overview of theory and applications dan e. Fuzzy sets fuzzy sets, fuzzy logic, and fuzzy systems. In this study, we work on pythagorean fuzzy sets to reduce vagueness and handle the impreciseness of the system environment. Pdf in this article, a new hesitant pythagorean fuzzy set hpfs has been presented by combining the concepts of pythagorean fuzzy set. 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. 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 fuzzy dombi aggregation operators and their.
Pdf in this paper we present a short but important summary of pythagorean fuzzy sets. The technique for order preference by similarity to ideal solutions topsis is a wellknown and effective method for mcdm problems. A suitable multi criteria decision making mcdm method that could consider vagueness and impreciseness in the assessments should be used for this kind of. A new divergence measure of pythagorean fuzzy sets based. Notion of fuzzy sets introduced by zadeh 1 revolutionized not only mathematics and logic but also science and technology. Recently, pythagorean fuzzy linmap method based on the entropy for railway project investment decision making was proposed by xue et al. Abstract pythagorean fuzzy sets,involvoing membership, non membership and hesitancy considerations present mathematically a very general structure. A new fuzzy entropy on pythagorean fuzzy sets ios press. Conflict analysis for pythagorean fuzzy information. Pythagorean hesitant fuzzy sets and their application to. New operations for intervalvalued pythagorean fuzzy set. Pythagorean fuzzy soft rough sets and their applications in. Their definition is given firstly, and the stability of this kind of systems is studied, the relation of.
Merigo1, manoj sahni3 1department of management control and information systems, university of chile, av. Later on, yager extended the intuitionistic fuzzy sets into the pythagorean fuzzy sets pfss 4, 5 in 20. Introduction for multicriteria decisionmaking mcdm problem1, atanassov2 introduced a series of concepts of intuitionistic fuzzy set ifs. Afterwards, yager4 proposed the concept of pythagorean fuzzy set pfs characterized by the membership. The other extension of ifs is what is known as pythagorean fuzzy sets. 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. The objective of this paper is to apply the concept of pythagorean fuzzy sets to graph theory.
A novel distance measure for pythagorean fuzzy sets and its. Pythagorean fuzzy sets pfss, originally proposed by yager yager, abbasov. The main purpose of this paper is to show that zhang and xus distance measure between pfss fails the conditions of distance measure. Complex fuzzy sets and complex fuzzy logic an overview of. Ccis 442 suggesting recommendations using pythagorean. B, c p j s b, c, which is called as pfsjs distance measure. Neutrosophic set is a generalization of intuitionistic fuzzy. We give some characterizations of pythagorean fuzzy almost compactness in terms of pythagorean fuzzy regular open or pythagorean fuzzy regular closed. This work introduces the notion of pythagorean fuzzy graphs pfgs. Pythagorean fuzzy soft rough sets and their applications. Pythagorean mpolar fuzzy soft sets with topsis method for mcgdm 23 pythagorean fuzzy sets pf sets as an extension of if sets. Threeway group conflict analysis based on pythagorean fuzzy. Pythagorean hesitant fuzzy sets, distance measure, multicriteria decision making, mcdm 1. Later on, yager extended the intuitionistic fuzzy sets into the pythagorean fuzzy sets pfss in 20.
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. Intervalvalued pythagorean hesitant fuzzy set and its. As a generalized set, pfss have close relationship with. Bipolar pythagorean fuzzy sets and their application based on. 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. Intervalvalued pythagorean fuzzy set ivpfs, originally proposed by peng and yang, is a novel tool to deal with vagueness and incertitude. Then the proposed operators are applied on decisionmaking problem in which. Interval valued pythagorean fuzzy set ivpfs, originally proposed by peng and yang, is. In this section, we will give the principles and basic operations of pythagorean fuzzy sets and the steps of pythagorean fuzzy ahp method. To this end, the correlation coefficient is proposed for the relationship measurement.
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