Alternatively, you can download the file locally and open with any standalone pdf reader. Decision making with uncertainty using hesitant fuzzy sets. Considering the hesitant situation, xu and liang14 introduced hfss into pfss. Di erent approaches have been proposed to deal with such an uncertainty. The probabilistic intervalvalued hesitant pythagorean fuzzy set and its application in selecting processes of project private partner. Under this environment, dual hesitant fuzzy soft set dhfss is one of the most successful extensions of a fuzzy soft set in which preferences are represented in terms of a set of possible. Letmi be the set of all fuzzy sets of type ion 0,1. Recently, a new extension of fuzzy sets socalled hesitant fuzzy sets has been. A notion for distance between hesitant fuzzy data is given. Modelling uncertainties in multicriteria decision making.
Torra and narukawa 1, 2 extended fuzzy sets 3 to hesitant fuzzy sets. All these new extensions aim at better defining membership functions together with experts hesitancy degrees. Combining the advantages of the two fuzzy sets, xu et al. It can be shown that these operators coincide with the crisp uni. For convenience, we call a hesitant fuzzy element hfe and the set of all hfes. The hesitant fuzzy sets are a new efficient mathematical approach to study imprecise, uncertain, or incomplete knowledge. That is, membership, instead of being a single value. Hesitant fuzzy sets torra 2010 international journal. How to fix blurry font when opening pdf files with adobe.
Request pdf on hesitant fuzzy sets and decision intuitionistic fuzzy sets ifs are a generalization of fuzzy sets where the membership is an interval. The notions of inclusion, union, intersection, complement, relation, convexity, etc. New operations over interval valued intuitionistic. 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. A large number of operations have been defined for this type of fuzzy sets, and several applications have been developed in the last years. As a novel extension of the fuzzy set zadeh, 1965, torra 2010 defined the hesitant fuzzy set by allowing the membership degree of an object to have a set of possible values. Such a set is characterized by a membership characteristic function which assigns to each object a grade of membership ranging between zero and one. Journal of information science and engineering 32, xxxxxxxx 2016 1249 a hesitant fuzzy set theory based approach for project portfolio selection with interactions under uncertainty maryam azari takami1, reza sheikh2 and shib sankar sana3 1department of management and industrial endineering, shahrood university, iran.
In this connection, many wellknown magdm methods have been extended to. Typically, we have found that the intuitionistic fuzzy. Hesitant fuzzy linguistic term sets for decision making. Hesitant fuzzy set theory is a suitable tool to deal with this kind of problems. Pdf hesitant fuzzy concept lattice and its application. A new distancebased decision model in intervalvalued. Hesitant fuzzy aggregation operators and their applications. In this paper, we propose two new basic operations over hfss, which are the. Weighted hesitant fuzzy sets and their application to multi.
Fuzzy set theoryand its applications, fourth edition. Hesitant probabilistic fuzzy information aggregation using. Dual hesitant fuzzy sets hindawi publishing corporation. Correlation coefficients of hesitant fuzzy sets and their.
As a generalization of a fuzzy set, torra and narukawa in 9 and torra in 10 proposed notion of a hesitant fuzzy set hfs and its application in decisionmaking. The hesitant fuzzy set hfs can reflect the hesitation and uncertainty of decisionmakers for the reason that it uses some possible values instead of a certain value. Citescore values are based on citation counts in a given year e. In this paper, we have introduced the dual hesitant fuzzy set dhfs, which is a comprehensive set encompassing several existing sets, and whose membership degrees and nonmembership degrees are represented by a set of possible values. Request pdf hesitant fuzzy sets several extensions and generalizations of fuzzy sets have been introduced in the literature, for example, atanassovs intuitionistic fuzzy sets. The proposed model measures the divergence between components a and b by the hesitant score i. In this paper, new entropy measures for hesitant fuzzy sets hfss are proposed. Enhancement of dronogram aid to visual interpretation of. Hesitant fuzzy sets theory studies in fuzziness and soft.
Khan,1 andkostaqhila 2 1departmentofmathematics,jamiamilliaislamia,newdelhi112234,india. A natural motivation for such objects is a mathematical model for an evaluation by a group of perhaps mutually dependent experts. I have both adobe reader x and adobe acrobat x pro. Some new similarity measures for hesitant fuzzy sets. New operations over interval valued intuitionistic hesitant. Hesitant fuzzy sets have been applied in some decision making problems and received some good practical effects 2932 now. Due to the superiority in expressing the uncertain and vague information, the hesitant fuzzy set hfs is regarded as an important tool to deal with multiattribute decisionmaking madm problems. Hesitant fuzzy set permits the membership having a set of one about the first four types of fuzzy sets, however, little has been done about sed the relationship between hesitant fuzzy set and other three kinds of fuzzyhesitant fuzzy information aggregation in decision making q meimei xia, zeshui xu. A novel magdm approach with proportional hesitant fuzzy sets. In fact, we can easily see that the hesitant fuzzy. For example, experts evaluate a houses comfort using an hfe 0.
Hesitant fuzzy sets theory this book provides the readers with a thorough and systematic introduction to hesitant fuzzy theory. Medical decision making our approach in medical data, considering hesitancy in every stage, can be. Sep 25, 2015 the union, the intersection and the composition of hesitant fuzzy approximation spaces are proposed, and some properties are also investigated. Hesitant fuzzy topsis based investment projects selection. Pdf by using type2 fuzzy sets and hesitant fuzzy sets, type2 hesitant fuzzy sets are defined and their mathematical structure and. Subtraction and division operations over hesitant fuzzy sets.
Hesitant fuzzy soft set and its applications in multicriteria. In this study, we introduce two different points of view to apply hesitant fuzzy sets in the data mining tasks, specially in the clustering algorithms. An axiomatic definition of entropy measure for hfss is. Ordinary fuzzy sets introduced by zadeh 1965 have been later extended to type2 fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and neutrosophic fuzzy sets. In this paper, we propose a variety of correlation coefficient measures for hesitant fuzzy sets hfss and investigate their properties. We then give a new approach of decision making in uncertainty environment using the hesitant fuzzy rough sets over two universes. The hesitant fuzzy set is a useful generalization of the fuzzy set that is designed for situations in which it is difficult to determine the membership of an element to a set owing to ambiguity between a few different values. Intervalvalued pythagorean hesitant fuzzy set and its. Dual hesitant qrung orthopair fuzzy hamacher aggregation. A hesitant fuzzy set theory based approach for project.
Grey relational analysis for hesitant fuzzy sets and its. Hesitancy is the most common problem in decision making, for which hesitant fuzzy set can be considered as a useful tool allowing several possible degrees of membership of an element to a set. Since these operators are useful for different operation on hesitant fuzzy sets, the various theorems are proved by using them. If, however, i opened adobe reader x first and then opened pdf files from there, the font was clear. Type2 fuzzy set based hesitant fuzzy linguistic term sets for.
A fuzzy set is a class of objects with a continuum of grades of membership. Pdf by using type2 fuzzy sets and hesitant fuzzy sets, type2 hesitant fuzzy sets are defined and their mathematical structure and characteristics. For example, if a is a fuzzy interval between 5 and 8 and b be a fuzzy number about 4 as shown in the figure below figure 3. Hausdorff metric is used to calculate a distance between an hfs and its complement which assists us to construct novel entropy of hfss. Using this new distance notion, we propose the technique for order preference by similarity to ideal solution for hesitant fuzzy sets and a new approach in modelling uncertainties. A new distance measure based on pythagorean hesitant fuzzy. Hesitant fuzzy power aggregation operators and their. Torra and narukawa 2009 established an extension principle which generalized the existing operations on fuzzy sets to hesitant fuzzy sets. Pdf as uncertainty takes place almost everywhere in our daily life, many.
In this paper, we proposed an approach based on topsis and. A fuzzy algorithm is an ordered sequence of instructions which may contain fuzzy assignment and conditional statements, e. In section 3, the notion of hesitant multifuzzy soft topology and. Continuous hesitant fuzzy aggregation operators and their. Clustering within the framework of hesitant fuzzy sets. Multiset hesitant fuzzy sets mhfss can deal effectively with a case where some values are repeated more than once in an hfs. Several extensions and generalizations of fuzzy sets have been introduced in the literature, for example, atanassovs intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets. This book offers a comprehensive report on the stateoftheart in hesitant fuzzy sets theory and applications, aiming at becoming a reference guide for both researchers and practitioners in the area of fuzzy mathematics and other applied research fields e. In section 3, we propose the continuous hfowa operator. Hesitant fuzzy set hfs, which permits the membership having a set of possible values, has turned out to be a powerful structure in expressing uncertainty and vagueness. A logic based on the two truth values, true and false, is sometimes inadequate when describing human reasoning. A method for hesitant fuzzy multiple attribute decision making and its application to risk investment xiang gu, ying wang, bei yang journal of convergence information technology, volume 6, number 6, june 2011 step 3.
Hesitant fuzzy linguistic term sets for decision making rosa m. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Intuitionistic fuzzy sets ifs are a generalization of fuzzy sets where the membership is an interval. The hesitant fuzzy set theory is a useful tool to deal with uncertainty in decisionmaking problems, which is proved by many scientific papers. This approach represents the situation in which different membership functions are considered possible in respect of decision situation. In this paper, several new correlation coefficients of hesitant fuzzy sets are defined, not taking into account the length of hesitant fuzzy elements and the arrangement of their possible values.
It presents the most recent research results and advanced methods in the field. Documents in econstor may be saved and copied for your personal and scholarly. Rank all the alternatives a i mi 1,2,l and select the best ones in accordance with s h i m i 1,2,l. This paper focuses to extend this approach on a lattice and shows that two large application concepts of the fuzzy set theory namely resolution identity and representation theorem are true under this extended definition. Fuzzy sets, hesitant fuzzy sets, proportional hesitant fuzzy sets, multiattribute group decision making. Fuzzy sets were introduced independently by lotfi a. Recently upon opening pdf files, i noticed the font was no longer clear. A method for hesitant fuzzy multiple attribute decision. Study on hesitant fuzzy information measures and their clustering. Pythagorean hesitant fuzzy sets are widely watched because of their excellent ability to deal with uncertainty, imprecise and vague information.
However, most of the existing information measures for hfss are related to such fuzzy. How to fix blurry font when opening pdf files with adobe reader x. Hesitant fuzzy sets soft computing and intelligent information. The aim of this paper is to investigate weighted hesitant fuzzy sets and their application to multicriteria decision making. Measuring uncertainty for an hfs is computed by an amount of distinction between an hfs and its complement.
Hesitant fuzzy information aggregation in decision making. Additive consistency analysis and improvement for hesitant. Soft set theory acts as a fundamental tool for handling the uncertainty in the data by adding a parameterization factor during the process as compared to fuzzy and intuitionistic fuzzy set theories. Additionally, the hesitant multifuzzy soft set can more precisely re. On the basis of the combination of singlevalued neutrosophic sets and hesitant fuzzy sets, this article proposes a singlevalued neutrosophic hesitant fuzzy set svnhfs as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, singlevalued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set.
Inspired by this, torra19 proposed hesitant fuzzy sets hfss, which endorses the membership degree of an element to be a set of some feasible values between 0 and 1. Fuzzy conditional statements are expressions of the form if a then b, where aand bhave fuzzy meaning, e. To aggregate largescale group decisionmaking information under hesitant fuzzy environment, in this paper, we construct the multiple integrals for the hfes. This paper puts forward the concept of a weighted hesitant fuzzy set whfs, in which several possible membership degrees of each element have different weights. 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. Introduction to hesitant fuzzy set and its application in. The dhfss can reflect the disagreement and hesitancy of decision.
For source image, we have separated the image area into components a and b, where component a be related to component b in the fuzzy membership plane. Dual hesitant fuzzy soft aggregation operators and their. A novel magdm approach with proportional hesitant fuzzy. The existing classical sets, including fss, ifss, hfss and pfss, can be. A multicriteria decisionmaking approach based on todim and. Rodrguez, luis mart nez, and francisco herrera, member, ieee abstractdealing with uncertainty is always a challenging problem, and different tools have been proposed to deal with it. In this paper, some new similarity measures for hfss are developed.
To address the situations where the elements in a set are correlative, several shapley weighted correlation coefficients are presented. In recent decades, several types of sets, such as fuzzy sets, intervalvalued fuzzy sets, intuitionistic fuzzy sets, intervalvalued intuitionistic fuzzy sets, type 2 fuzzy sets, type fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, four new operators o 1, o 2, o 3, o 4 are proposed, defined and considered to study the new properties and identities on hesitant fuzzy sets. Hesitant fuzzy multiattribute decision making based on. However, dms for dealing with uncertain situations can define their opinions in linguistic variables based on fuzzy sets in industrial selection problems. Hesitant fuzzy set theory, introduced by torra and. On hesitant fuzzy clustering and clustering of hesitant.
Especially, we will denote the set of all hesitant fuzzy sets in x as hsx. In order to widely use hesitant fuzzy sets, so it is. Wei 2012 proposed prioritized aggregation operators for hesitant fuzzy information, in different priority levels, developed some models for hesitant fuzzy madm problems. Group recommendations based on hesitant fuzzy sets 2059 rss,being themost popularones. The distance of hesitant fuzzy set used in this method is put forward. In classical group decisionmaking gdm analysis, ratings of potential alternatives and weights of criteria or decision makers dms are known precisely. Hesitant fuzzy sets are one of currently studied generalizations of fuzzy sets and in fact a special case of type2 fuzzy sets. In this paper, we propose dual hesitant fuzzy sets dhfss, which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant. An illustrative example is constructed to show the feasibility and practicality of the new method. Pdf hesitant fuzzy set and its extensions researchgate. A hesitant fuzzy set hfs on is in terms of a function that when applied to returns a subset of, which can be represented as the following mathematical symbol.
Fuzzy sets and significant figures one straightforward application of fuzzy sets is the reexamination of the idea of significant figures. That is, membership, instead of being a single value, is an interval. Example fuzzy sets in this case, the fuzzy set between 5 and 8. Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making. In this paper, the new comparison method and corresponding distance of multiset hesitant fuzzy elements mhfes are introduced. Since the concept of the hesitant fuzzy set was established, it has gained. Based on the proposed similarity measures, a method of multiple attribute decision making under hesitant fuzzy environment is also introduced. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a pdf plugin installed and enabled in your browser. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Quantitative and qualitative fuzzy measures have been proposed to solve such problems from different points. Hesitant fuzzy set hfs, which allows the membership degree of an element to be a set of several possible values, it has attracted more and more attention due to its powerfulness in representing uncertainty.
Zadeh and dieter klaua in 1965 as an extension of the classical notion of set. Moreover, we utilize the concepts of correlation relation matrix, composition matrix and equivalent correlation relation matrix to deal with the clustering problem under hesitant fuzzy environment. As a powerful extension to hesitant fuzzy sets hfss, dual hesitant fuzzy sets dhfss have been closely watched by many scholars. Recently, another suitable means were defined by zhiming zhang, called interval valued intuitionistic hesitant fuzzy sets, dealing with uncertainty and. On hesitant fuzzy sets and decision ieee conference publication. Section 2 introduces some preliminary concepts including hesitant fuzzy sets, intervalvalued hesitant fuzzy sets, and continuous ow cowa and cowg operators. Many scholars have focused on hesitant fuzzy sets and proposed diverse corresponding extensions, such as dual hesitant fuzzy sets 22, intervalvalued dual fuzzy sets 23,24, intuitionistic. Nov 17, 2012 torra 2010 proposed the notion of hesitant fuzzy sethfs, which is a generalization of the notion of zadeh fuzzy set.
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