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. Hesitant fuzzy aggregation operators and their applications. 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. A new distance measure based on pythagorean hesitant fuzzy. 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.
Fuzzy set theoryand its applications, fourth edition. That is, membership, instead of being a single value. Wei 2012 proposed prioritized aggregation operators for hesitant fuzzy information, in different priority levels, developed some models for hesitant fuzzy madm problems. New operations over interval valued intuitionistic hesitant. To address the situations where the elements in a set are correlative, several shapley weighted correlation coefficients are presented. An axiomatic definition of entropy measure for hfss is. 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. Hesitant fuzzy topsis based investment projects selection.
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. Such a set is characterized by a membership characteristic function which assigns to each object a grade of membership ranging between zero and one. However, dms for dealing with uncertain situations can define their opinions in linguistic variables based on fuzzy sets in industrial selection problems. Pdf by using type2 fuzzy sets and hesitant fuzzy sets, type2 hesitant fuzzy sets are defined and their mathematical structure and. 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. Subtraction and division operations over hesitant fuzzy sets. In section 3, the notion of hesitant multifuzzy soft topology and.
In this connection, many wellknown magdm methods have been extended to. An illustrative example is constructed to show the feasibility and practicality of the new method. In classical group decisionmaking gdm analysis, ratings of potential alternatives and weights of criteria or decision makers dms are known precisely. Multiset hesitant fuzzy sets mhfss can deal effectively with a case where some values are repeated more than once in an hfs. Especially, we will denote the set of all hesitant fuzzy sets in x as hsx. A large number of operations have been defined for this type of fuzzy sets, and several applications have been developed in the last years. Request pdf hesitant fuzzy sets several extensions and generalizations of fuzzy sets have been introduced in the literature, for example, atanassovs intuitionistic fuzzy sets. A novel magdm approach with proportional hesitant fuzzy sets. Hesitant fuzzy linguistic term sets for decision making. The hesitant fuzzy set theory is a useful tool to deal with uncertainty in decisionmaking problems, which is proved by many scientific papers. Medical decision making our approach in medical data, considering hesitancy in every stage, can be. 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. Correlation coefficients of hesitant fuzzy sets and their. Alternatively, you can download the file locally and open with any standalone pdf reader.
Khan,1 andkostaqhila 2 1departmentofmathematics,jamiamilliaislamia,newdelhi112234,india. For example, experts evaluate a houses comfort using an hfe 0. 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. 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. Based on the proposed similarity measures, a method of multiple attribute decision making under hesitant fuzzy environment is also introduced. Pdf hesitant fuzzy concept lattice and its application. Intuitionistic fuzzy sets ifs are a generalization of fuzzy sets where the membership is an interval. 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. A new distancebased decision model in intervalvalued.
Modelling uncertainties in multicriteria decision making. Hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making. A method for hesitant fuzzy multiple attribute decision. 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. All these new extensions aim at better defining membership functions together with experts hesitancy degrees. Sep 25, 2015 the union, the intersection and the composition of hesitant fuzzy approximation spaces are proposed, and some properties are also investigated. Type2 fuzzy set based hesitant fuzzy linguistic term sets for. Hesitant fuzzy sets theory studies in fuzziness and soft. The hesitant fuzzy sets are a new efficient mathematical approach to study imprecise, uncertain, or incomplete knowledge. In section 3, we propose the continuous hfowa operator. Pythagorean hesitant fuzzy sets are widely watched because of their excellent ability to deal with uncertainty, imprecise and vague information. A logic based on the two truth values, true and false, is sometimes inadequate when describing human reasoning.
Hesitant fuzzy sets theory this book provides the readers with a thorough and systematic introduction to hesitant fuzzy theory. In this paper, new entropy measures for hesitant fuzzy sets hfss are proposed. The distance of hesitant fuzzy set used in this method is put forward. Considering the hesitant situation, xu and liang14 introduced hfss into pfss. The notions of inclusion, union, intersection, complement, relation, convexity, etc. We then give a new approach of decision making in uncertainty environment using the hesitant fuzzy rough sets over two universes. Fuzzy sets were introduced independently by lotfi a. Some new similarity measures for hesitant fuzzy sets. 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. 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. Pdf by using type2 fuzzy sets and hesitant fuzzy sets, type2 hesitant fuzzy sets are defined and their mathematical structure and characteristics. Hesitant fuzzy power aggregation operators and their. How to fix blurry font when opening pdf files with adobe. Dual hesitant fuzzy sets hindawi publishing corporation.
Grey relational analysis for hesitant fuzzy sets and its. 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. Since the concept of the hesitant fuzzy set was established, it has gained. 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. Hesitant probabilistic fuzzy information aggregation using. In this paper, we propose a variety of correlation coefficient measures for hesitant fuzzy sets hfss and investigate their properties. Hesitant fuzzy sets soft computing and intelligent information.
A fuzzy set is a class of objects with a continuum of grades of membership. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Example fuzzy sets in this case, the fuzzy set between 5 and 8. This approach represents the situation in which different membership functions are considered possible in respect of decision situation.
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. Documents in econstor may be saved and copied for your personal and scholarly. Fuzzy sets, hesitant fuzzy sets, proportional hesitant fuzzy sets, multiattribute group decision making. Hesitant fuzzy linguistic term sets for decision making rosa m. Additionally, the hesitant multifuzzy soft set can more precisely re. Since these operators are useful for different operation on hesitant fuzzy sets, the various theorems are proved by using them. Dual hesitant fuzzy soft aggregation operators and their. Hesitant fuzzy set theory is a suitable tool to deal with this kind of problems. I have both adobe reader x and adobe acrobat x pro.
Intervalvalued pythagorean hesitant fuzzy set and its. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. A novel magdm approach with proportional hesitant fuzzy. It presents the most recent research results and advanced methods in the field.
A multicriteria decisionmaking approach based on todim and. 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. Introduction to hesitant fuzzy set and its application in. On hesitant fuzzy clustering and clustering of hesitant. The aim of this paper is to investigate weighted hesitant fuzzy sets and their application to multicriteria decision making. For convenience, we call a hesitant fuzzy element hfe and the set of all hfes. Fuzzy conditional statements are expressions of the form if a then b, where aand bhave fuzzy meaning, e. Weighted hesitant fuzzy sets and their application to multi.
Torra and narukawa 2009 established an extension principle which generalized the existing operations on fuzzy sets to hesitant fuzzy sets. A fuzzy algorithm is an ordered sequence of instructions which may contain fuzzy assignment and conditional statements, e. Measuring uncertainty for an hfs is computed by an amount of distinction between an hfs and its complement. In this paper, we proposed an approach based on topsis and. 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. 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. Pdf hesitant fuzzy set and its extensions researchgate.
In this paper, the new comparison method and corresponding distance of multiset hesitant fuzzy elements mhfes are introduced. 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. Hesitant fuzzy sets torra 2010 international journal. The dhfss can reflect the disagreement and hesitancy of decision.
Hesitant fuzzy set theory, introduced by torra and. 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. To aggregate largescale group decisionmaking information under hesitant fuzzy environment, in this paper, we construct the multiple integrals for the hfes. Hesitant fuzzy soft set and its applications in multicriteria. Pdf as uncertainty takes place almost everywhere in our daily life, many. Hesitant fuzzy sets have been applied in some decision making problems and received some good practical effects 2932 now. Additive consistency analysis and improvement for hesitant.
Section 2 introduces some preliminary concepts including hesitant fuzzy sets, intervalvalued hesitant fuzzy sets, and continuous ow cowa and cowg operators. 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. 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. Decision making with uncertainty using hesitant fuzzy sets. Introduction the hesitant fuzzy problems are common in daily life, which have been initially interpreted by torra1 as. 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. 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. Combining the advantages of the two fuzzy sets, xu et al. Request pdf on hesitant fuzzy sets and decision intuitionistic fuzzy sets ifs are a generalization of fuzzy sets where the membership is an interval. Citescore values are based on citation counts in a given year e. 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 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. Letmi be the set of all fuzzy sets of type ion 0,1.
In this paper, we propose dual hesitant fuzzy sets dhfss, which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant. Fuzzy sets and significant figures one straightforward application of fuzzy sets is the reexamination of the idea of significant figures. In this paper, we propose two new basic operations over hfss, which are the. Hesitant fuzzy sets are one of currently studied generalizations of fuzzy sets and in fact a special case of type2 fuzzy sets. Study on hesitant fuzzy information measures and their clustering. Clustering within the framework of hesitant fuzzy sets. How to fix blurry font when opening pdf files with adobe reader x. If, however, i opened adobe reader x first and then opened pdf files from there, the font was clear. New operations over interval valued intuitionistic. Recently, another suitable means were defined by zhiming zhang, called interval valued intuitionistic hesitant fuzzy sets, dealing with uncertainty and. The proposed model measures the divergence between components a and b by the hesitant score i. Recently, a new extension of fuzzy sets socalled hesitant fuzzy sets has been.
On hesitant fuzzy sets and decision ieee conference publication. 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. 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. However, most of the existing information measures for hfss are related to such fuzzy. The existing classical sets, including fss, ifss, hfss and pfss, can be. 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. 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. It can be shown that these operators coincide with the crisp uni. That is, membership, instead of being a single value, is an interval. Torra and narukawa 1, 2 extended fuzzy sets 3 to hesitant fuzzy sets. Quantitative and qualitative fuzzy measures have been proposed to solve such problems from different points. The probabilistic intervalvalued hesitant pythagorean fuzzy set and its application in selecting processes of project private partner. Dual hesitant qrung orthopair fuzzy hamacher aggregation. 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.
Hesitant fuzzy element hfe, membership degree of which consists of a set of crisp values, is used as an expression form when the decision makers encounter hesitance in providing their judgements. A natural motivation for such objects is a mathematical model for an evaluation by a group of perhaps mutually dependent experts. 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 information aggregation in decision making. Hesitant fuzzy multiattribute decision making based on. Enhancement of dronogram aid to visual interpretation of. In order to widely use hesitant fuzzy sets, so it is. Hausdorff metric is used to calculate a distance between an hfs and its complement which assists us to construct novel entropy of hfss. 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. Recently upon opening pdf files, i noticed the font was no longer clear. 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. As a powerful extension to hesitant fuzzy sets hfss, dual hesitant fuzzy sets dhfss have been closely watched by many scholars.
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