Hesitant fuzzy aggregation operators and their applications. The dice measure of cubic hesitant fuzzy sets and its initial evaluation method of benign prostatic hyperplasia symptoms. In the present study, we introduce notion of occurring probability of possible values into hesitant fuzzy linguistic element hfle and define hesitant probabilistic fuzzy linguistic set hpfls for ill structured and complex decision making problem. Introduction the hesitant fuzzy problems are common in daily life, which have been initially interpreted by torra1 as. As uncertainty takes place almost everywhere in our daily life, many. As a powerful extension to hesitant fuzzy sets hfss, dual hesitant fuzzy sets dhfss have been closely watched by many scholars. 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. Picture hesitant fuzzy rough sets are introduced using this relation, and an example is provided. Introduction of hesitant fuzzy rough sets would facilitate the use of rough set based techniques to hesitant fuzzy environment. Uncertainties due to randomness and fuzziness comprehensively exist in control and decision support system.
The relations of the structures of type2 hesitant fuzzy sets and hesitant fuzzy sets are further studied. Letmi be the set of all fuzzy sets of type ion 0,1. We propose a new method to aggregate the opinion of experts or decision makers on different criteria, regarding a set of alternatives, where the opinion of the experts is represented by hesitant fuzzy linguistic term sets. Fuzzy sets, hesitant fuzzy sets, proportional hesitant fuzzy sets, multiattribute group decision making abstract in this paper, we propose an extension of hesitant fuzzy sets, i. 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. Additionally, the hesitant multifuzzy soft set can more precisely re. Correspondingly, lots of the extensions of these aforementioned distance measures have been. In this paper, we propose dual hesitant fuzzy sets dhfss, which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant. Further, based on level soft sets of the dual hesitant fuzzy soft set, a characterization theorem for the dual hesitant fuzzy soft ring is established. Intuitionistic fuzzy sets ifs are a generalization of fuzzy sets where the membership is an interval. 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. Symmetry free fulltext dual extended hesitant fuzzy sets. Obviously, the dhfs is an effective and convenient tool applied to group forecasting. Multiattribute decision making with hesitant fuzzy.
Pdf hesitant fuzzy set and its extensions researchgate. The hesitant fuzzy set theory is a useful tool to deal with uncertainty in decisionmaking problems, which is proved by many scientific papers. Information measures for hesitant fuzzy sets and their. Some multicriteria decisionmaking mcdm methods have been developed to deal with hfltss. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. 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. Ideal solutions for hesitant fuzzy soft sets ios press.
The aim of this paper is to introduce a new concept of hesitant fuzzy biideals and hesitant fuzzy interior ideals on ternary semigroups. With the growing complexity and uncertainty of the reallife problems, many different extensions of fuzzy sets, such as intuitionistic fuzzy sets ifss, intervalvalued ifss, linguistic variables, type2 fuzzy sets, etc. The dhfss can reflect the disagreement and hesitancy of decisionmakers dms flexibly and conveniently. Novel distance and similarity measures on hesitant fuzzy. Hesitant fuzzy subset of the cartesian product of several crisp sets equivalence hesitant fuzzy relation. On hesitant fuzzy sets and decision ieee conference publication. This book aims to be a comprehensive and accurate survey of stateofart research on intuitionistic fuzzy sets theory and could be considered a continuation and extension of the author. Some properties of phfrss are also given in this section. Intuitionistic fuzzy measures download ebook pdf, epub. That is, membership, instead of being a single value. 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. Type2 fuzzy set based hesitant fuzzy linguistic term sets. Dual hesitant fuzzy sets hindawi publishing corporation. Recently, another suitable means were defined by zhiming zhang, called interval valued intuitionistic hesitant fuzzy sets, dealing with uncertainty and.
Modelling uncertainties in multicriteria decision making. It can also be used as a textbook for postgraduate and senioryear undergraduate students of the relevant professional institutions of higher learning. For convenience, we call a hesitant fuzzy element hfe and the set of all hfes. An extension of a classical notion of a set whose elements have degrees of membership hesitant fuzzy relation. Rough approximations on hesitant fuzzy sets igi global. Multiexperts evaluations are integrated by aggregation operators. In the process, the hesitant fuzzy positive ideal solution and hesitant fuzzy negative. That is, membership, instead of being a single value, is an interval. However, type2 fuzzy sets have been proven to be scientifically more appropriate to represent linguistic information in practical systems. Jan 11, 2019 the dice measure of cubic hesitant fuzzy sets and its initial evaluation method of benign prostatic hyperplasia symptoms.
Hesitant fuzzy sets and hesitant fuzzy preference relations. Hesitant fuzzy sets are very useful to deal with group decision making problems when experts have a hesitation among several. A large number of operations have been defined for this type of fuzzy sets, and several applications have been developed in the last years. The hesitant fuzzy sets are a new efficient mathematical approach to study imprecise, uncertain, or incomplete knowledge. Hesitant fuzzy sets and hesitant fuzzy preference relations author. We extend the concept of fuzzy biideals and fuzzy interior ideals to the context of hesitant fuzzy biideals and hesitant fuzzy interior ideals, respectively. Intervalvalued probabilistic dual hesitant fuzzy sets for. A hesitant fuzzy linguistic todim method based on a score. Generalized hesitant fuzzy sets and their application in decision. Then we investigate the basic operations and properties of dhfss.
A note on operations of hesitant fuzzy sets atlantis press. Novel multicriteria decisionmaking approaches based on. The dice measure of cubic hesitant fuzzy sets and its. Hesitant fuzzy multiattribute decision making based on. The aim of this paper is to investigate weighted hesitant fuzzy sets and their application to multicriteria decision making. Grey relational analysis for hesitant fuzzy sets and. Group decisionmaking for hesitant fuzzy sets based on. However, all the evaluation values under the same membership degree are endowed with similar importance.
By abuse of language, following the habits of the literature, we will use the terms fuzzy sets instead of fuzzy. 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 vagueness, and which is more powerful than the hesitant fuzzy sets. Farhadinia, information measures for hesitant fuzzy sets and intervalvalued hesitant fuzzy sets, information science 240 20 129144. An illustrative example is constructed to show the feasibility and practicality of the new method. This paper develops the fuzzy present worth analysis.
Otherwise, a part of the special type2 hesitant fuzzy sets can be changed into discrete type2 fuzzy sets, but their operations have many differences. In this article, the concept of dual hesitant fuzzy soft sets is applied to the subring and ideal structures of the classical rings. Hesitant fuzzy sets theory this book provides the readers with a thorough and systematic introduction to hesitant fuzzy theory. Decision making with uncertainty using hesitant fuzzy sets. Fuzzy sets, hesitant fuzzy sets, proportional hesitant fuzzy sets, multiattribute group decision making. Since its introduction by torra and narukawa in 2009, hesitant fuzzy sets have become more and more popular and have been used for a. Archimedean tconorm and tnorm provide a generalization of a variety of other tconorms. Grey relational analysis for hesitant fuzzy sets and its applications to multiattribute decisionmaking. Hesitant fuzzy sets theory studies in fuzziness and soft. Jun 19, 2018 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.
Alcantud 2, 1 department of mathematics, national institute of technology calicut, calicut 673 601, india. Hesitant fuzzy sets torra 2010 international journal of. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. If we can avail ourselves of hesitant information on nonmembership degrees too, then dual hesitant fuzzy sets provide a natural extension of both hesitant fuzzy sets and. Feb 26, 2020 approaches based on computing with words find good applicability in decision making systems. Although from a formal point of view, they can be seen as fuzzy multisets, we will show that their interpretation differs from the two existing approaches for fuzzy. Consequently, we prove that type2 hesitant fuzzy sets are the generalization of hesitant fuzzy sets. 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. Based on hesitant fuzzy sets and the topsis method, an extended topsis method is proposed to rank the preference of alternatives and determined the weights through entropyweighted. The classical set theory is a subset of the theory of fuzzy sets fuzzy logic is based on fuzzy set theory, which is a generalization of the classical set theory zadeh, 1965. A notion for distance between hesitant fuzzy data is given.
Predominantly finding their basis in type1 fuzzy sets, computing with words approaches employ type1 fuzzy sets as semantics of the linguistic terms. Weighted hesitant fuzzy sets and their application to. Here we propose a new way for the description of hesitant fuzzy soft set. Jun 01, 2010 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. 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. Approaches based on computing with words find good applicability in decision making systems. In this paper, we propose dual hesitant fuzzy sets dhfss, which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as special cases. Hesitant fuzzy sets extend fuzzy sets by considering manyvalued sets of membership degrees. In this paper, we propose an extension of hesitant fuzzy sets, i. It presents the most recent research results and advanced methods in the field. Hesitant fuzzy sets torra 2010 international journal.
Since these operators are useful for different operation on hesitant fuzzy sets, the various theorems are proved by using them. Request pdf hesitant fuzzy sets several extensions and generalizations of fuzzy sets have been introduced in the literature, for example, atanassovs intuitionistic fuzzy sets. This book gives a thorough and systematic introduction to the latest research results on hesitant fuzzy and its extensions decision making theory. Real applications validate this model and decision making approaches of various forms permit to act in a flexible manner. Taoadditive consistency of hesitant fuzzy linguistic preference relation with a new expansion principle for hesitant fuzzy linguistic term sets ieee transactions on fuzzy systems, 27 4 2018, pp. Hesitant fuzzy sets, international journal of intelligent. Pdf by using type2 fuzzy sets and hesitant fuzzy sets, type2 hesitant fuzzy sets are defined and their mathematical structure and characteristics. An illustrative example is provided to elaborate the proposed method for selection of the best alternative. The components of phfss, which are referred to as proportional hesitant fuzzy elements phfes, contain two aspects of information provided by a decisionmaking team. View enhanced pdf access article on wiley online library html view download pdf for offline viewing. 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 values.
By using type2 fuzzy sets and hesitant fuzzy sets, type2 hesitant fuzzy. Hesitant fuzzy linguistic term sets hfltss are very useful for dealing with the situations in which the decision makers hesitate among several linguistic terms to assess an alternative. Mar 12, 2010 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. In section 3, the notion of hesitant multifuzzy soft topology and. Hesitant fuzzy relation that is reflexive symmetric and transitive hesitant fuzzy set. Applications of hesitant fuzzy sets to ternary semigroups. This approach represents the situation in which different membership functions are considered possible in respect of decision situation. A novel magdm approach with proportional hesitant fuzzy sets. A novel magdm approach with proportional hesitant fuzzy. In this paper, we propose dual hesitant fuzzy sets dhfss, which encompass.
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 n fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. 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. 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. Oct 25, 2018 type2 hesitant fuzzy sets may deal with the problem that hesitant fuzzy sets cant have repeated memberships. Zhang, hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making, information science 234 20 150181. Hesitant fuzzy soft set and its applications in multicriteria. Present worth analysis using hesitant fuzzy sets atlantis press. New operations over interval valued intuitionistic hesitant.
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. Dual hesitant fuzzy soft aggregation operators and their. Presently, group decisionmaking problems are solved for hesitant fuzzy sets and with aggregation operators in 3336. The dice measure of cubic hesitant fuzzy sets and its initial.
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