Some properties of phfrss are also given in this section. Intuitionistic fuzzy measures download ebook pdf, epub. 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. Real applications validate this model and decision making approaches of various forms permit to act in a flexible manner. The aim of this paper is to investigate weighted hesitant fuzzy sets and their application to multicriteria decision making. Approaches based on computing with words find good applicability in decision making systems. However, all the evaluation values under the same membership degree are endowed with similar importance. Hesitant fuzzy relation that is reflexive symmetric and transitive hesitant fuzzy set. Letmi be the set of all fuzzy sets of type ion 0,1. Hesitant fuzzy sets and hesitant fuzzy preference relations.
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. An extension of a classical notion of a set whose elements have degrees of membership hesitant fuzzy relation. An illustrative example is constructed to show the feasibility and practicality of the new method. 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. New operations over interval valued intuitionistic hesitant fuzzy set.
By abuse of language, following the habits of the literature, we will use the terms fuzzy sets instead of fuzzy. Modelling uncertainties in multicriteria decision making. Hesitant fuzzy sets and hesitant fuzzy preference relations author. 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.
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. Multiexperts evaluations are integrated by aggregation operators. Feb 26, 2020 approaches based on computing with words find good applicability in decision making systems. Hesitant fuzzy sets, international journal of intelligent.
The hesitant fuzzy set theory is a useful tool to deal with uncertainty in decisionmaking problems, which is proved by many scientific papers. We extend the concept of fuzzy biideals and fuzzy interior ideals to the context of hesitant fuzzy biideals and hesitant fuzzy interior ideals, respectively. Rough approximations on hesitant fuzzy sets igi global. By using type2 fuzzy sets and hesitant fuzzy sets, type2 hesitant fuzzy. 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. Dual hesitant fuzzy sets hindawi publishing corporation. Grey relational analysis for hesitant fuzzy sets and its applications to multiattribute decisionmaking.
In this paper, we propose dual hesitant fuzzy sets dhfss, which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant. A note on operations of hesitant fuzzy sets atlantis press. Fuzzy sets, hesitant fuzzy sets, proportional hesitant fuzzy sets, multiattribute group decision making. Pdf by using type2 fuzzy sets and hesitant fuzzy sets, type2 hesitant fuzzy sets are defined and their mathematical structure and characteristics.
Hesitant fuzzy multiattribute decision making based on. Decision making with uncertainty using hesitant fuzzy sets. 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. Applications of hesitant fuzzy sets to ternary semigroups.
Introduction of hesitant fuzzy rough sets would facilitate the use of rough set based techniques to hesitant fuzzy environment. Grey relational analysis for hesitant fuzzy sets and. 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. 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 sets torra 2010 international journal. 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. 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. Intuitionistic fuzzy sets ifs are a generalization of fuzzy sets where the membership is an interval. 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. Otherwise, a part of the special type2 hesitant fuzzy sets can be changed into discrete type2 fuzzy sets, but their operations have many differences. Obviously, the dhfs is an effective and convenient tool applied to group forecasting. 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. 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.
Farhadinia, information measures for hesitant fuzzy sets and intervalvalued hesitant fuzzy sets, information science 240 20 129144. In the process, the hesitant fuzzy positive ideal solution and hesitant fuzzy negative. Presently, group decisionmaking problems are solved for hesitant fuzzy sets and with aggregation operators in 3336. View enhanced pdf access article on wiley online library html view download pdf for offline viewing. A novel magdm approach with proportional hesitant fuzzy. Oct 25, 2018 type2 hesitant fuzzy sets may deal with the problem that hesitant fuzzy sets cant have repeated memberships. A hesitant fuzzy linguistic todim method based on a score. Zhang, hesitant fuzzy power aggregation operators and their application to multiple attribute group decision making, information science 234 20 150181. Symmetry free fulltext dual extended hesitant fuzzy sets. Group decisionmaking for hesitant fuzzy sets based on. It presents the most recent research results and advanced methods in the field. As uncertainty takes place almost everywhere in our daily life, many.
The hesitant fuzzy sets are a new efficient mathematical approach to study imprecise, uncertain, or incomplete knowledge. Intervalvalued probabilistic dual hesitant fuzzy sets for. A notion for distance between hesitant fuzzy data is given. This approach represents the situation in which different membership functions are considered possible in respect of decision situation. In this paper, we propose an extension of hesitant fuzzy sets, i.
Picture hesitant fuzzy rough sets are introduced using this relation, and an example is provided. Multiattribute decision making with hesitant fuzzy. Wei 2012 proposed prioritized aggregation operators for hesitant fuzzy information, in different priority levels, developed some models for hesitant fuzzy madm problems. In this paper, we propose dual hesitant fuzzy sets dhfss, which encompass.
This paper develops the fuzzy present worth analysis. Since its introduction by torra and narukawa in 2009, hesitant fuzzy sets have become more and more popular and have been used for a. 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. Present worth analysis using hesitant fuzzy sets atlantis press.
The dice measure of cubic hesitant fuzzy sets and its initial evaluation method of benign prostatic hyperplasia symptoms. Recently, another suitable means were defined by zhiming zhang, called interval valued intuitionistic hesitant fuzzy sets, dealing with uncertainty and. The components of phfss, which are referred to as proportional hesitant fuzzy elements phfes, contain two aspects of information provided by a decisionmaking team. The dice measure of cubic hesitant fuzzy sets and its initial. 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. Hesitant fuzzy soft set and its applications in multicriteria.
Alcantud 2, 1 department of mathematics, national institute of technology calicut, calicut 673 601, india. The relations of the structures of type2 hesitant fuzzy sets and hesitant fuzzy sets are further studied. 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. It can also be used as a textbook for postgraduate and senioryear undergraduate students of the relevant professional institutions of higher learning. Some multicriteria decisionmaking mcdm methods have been developed to deal with hfltss. 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. An illustrative example is provided to elaborate the proposed method for selection of the best alternative. Uncertainties due to randomness and fuzziness comprehensively exist in control and decision support system. 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. Pdf hesitant fuzzy set and its extensions researchgate. 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. For convenience, we call a hesitant fuzzy element hfe and the set of all hfes. The aim of this paper is to introduce a new concept of hesitant fuzzy biideals and hesitant fuzzy interior ideals on ternary semigroups. Introduction the hesitant fuzzy problems are common in daily life, which have been initially interpreted by torra1 as.
Hesitant fuzzy aggregation operators and their applications. Jan 11, 2019 the dice measure of cubic hesitant fuzzy sets and its initial evaluation method of benign prostatic hyperplasia symptoms. Hesitant fuzzy sets theory studies in fuzziness and soft. New operations over interval valued intuitionistic. This book gives a thorough and systematic introduction to the latest research results on hesitant fuzzy and its extensions decision making theory. Information measures for hesitant fuzzy sets and their. Hesitant fuzzy sets extend fuzzy sets by considering manyvalued sets of membership degrees. Novel distance and similarity measures on hesitant fuzzy. 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. 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. Hesitant fuzzy sets are very useful to deal with group decision making problems when experts have a hesitation among several.
Type2 fuzzy set based hesitant fuzzy linguistic term sets. Predominantly finding their basis in type1 fuzzy sets, computing with words approaches employ type1 fuzzy sets as semantics of the linguistic terms. 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. Novel multicriteria decisionmaking approaches based on. Generalized hesitant fuzzy sets and their application in decision. The dhfss can reflect the disagreement and hesitancy of decisionmakers dms flexibly and conveniently. A novel magdm approach with proportional hesitant fuzzy sets. That is, membership, instead of being a single value.
In section 3, the notion of hesitant multifuzzy soft topology and. Then we investigate the basic operations and properties of dhfss. However, type2 fuzzy sets have been proven to be scientifically more appropriate to represent linguistic information in practical systems. 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. Hesitant fuzzy sets theory this book provides the readers with a thorough and systematic introduction to hesitant fuzzy theory. In this article, the concept of dual hesitant fuzzy soft sets is applied to the subring and ideal structures of the classical rings. That is, membership, instead of being a single value, is an interval. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Additionally, the hesitant multifuzzy soft set can more precisely re.
Archimedean tconorm and tnorm provide a generalization of a variety of other tconorms. Since these operators are useful for different operation on hesitant fuzzy sets, the various theorems are proved by using them. 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. Weighted hesitant fuzzy sets and their application to.
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. Consequently, we prove that type2 hesitant fuzzy sets are the generalization of hesitant fuzzy sets. Here we propose a new way for the description of hesitant fuzzy soft set. Request pdf hesitant fuzzy sets several extensions and generalizations of fuzzy sets have been introduced in the literature, for example, atanassovs intuitionistic fuzzy sets. Hesitant fuzzy subset of the cartesian product of several crisp sets equivalence hesitant fuzzy relation. Hesitant fuzzy sets torra 2010 international journal of. New operations over interval valued intuitionistic hesitant. The dice measure of cubic hesitant fuzzy sets and its. As a powerful extension to hesitant fuzzy sets hfss, dual hesitant fuzzy sets dhfss have been closely watched by many scholars. Ideal solutions for hesitant fuzzy soft sets ios press. 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.
Correspondingly, lots of the extensions of these aforementioned distance measures have been. On hesitant fuzzy sets and decision ieee conference publication. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Dual hesitant fuzzy soft aggregation operators and their. A large number of operations have been defined for this type of fuzzy sets, and several applications have been developed in the last years. 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. Type2 hesitant fuzzy sets may deal with the problem that hesitant fuzzy sets cant have repeated memberships. 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. 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.