New operations over interval valued intuitionistic hesitant fuzzy set. As a result, the multimoora method was updated by using generalized interval valued trapezoidal fuzzy numbers orintuitionistic fuzzy numbers. Some entropy measures of intervalvalued intuitionistic. Intuitionistic fuzzy sets 1 and intervalvalued fuzzy sets 54,67 and more recently, 58 are two intuitively straightforward extensions of zadehs fuzzy sets 66, that were conceived independently to alleviate some of the drawbacks of the latter. Cubic intervalvalued intuitionistic fuzzy sets and their. Our intervalvalued intuitionistic fuzzy soft set theory is a combination of an interval valued intuitionistic fuzzy set theory and a soft set theory. Algorithms based on copras and aggregation operators with. New entropybased similarity measure between intervalvalued. We also introduce two decomposition theorems of the correlation of interval valued intuitionistic fuzzy sets, one in terms of the correlation of interval valued fuzzy sets and the entropy of the intuitionistic fuzzy sets, and the other theorem in terms of the correlation of intuitionistic fuzzy sets. As a new extension of a cubic set, the notion of a cubic intervalvalued intuitionistic fuzzy set is introduced, and its application in b c k b c ialgebra is considered. The confident weight is assigned to each of the experts based on their preferred attributes and opinions, which reduces the chances of biasness. This paper focusses on those fuzzy set extensions that address the difficulties that experts find in order to build the membership values. The confident weight is assigned to each of the experts based on their preferred attributes and.
Abstract remarksonhistory,theory,andapplications of intuitionistic fuzzy sets are given. Reliability analysis of a powerloom plant using interval. The definition of hesitant interval valued intuitionistic fuzzy sets hivifss is developed based on interval valued intuitionistic fuzzy sets ivifss and hesitant fuzzy sets hfss. Correlation for dual hesitant fuzzy sets and dual interval. Pdf new operations over interval valued intuitionistic. Presently, intuitionistic fuzzy sets are an object of intensive research by scholars and scientists from over ten countries. In this chapter, the basic definitions and properties of the interval valued intuitionistic fuzzy sets ivifss will be introduced. Aggregation operators permit to simplify the evaluation of ivif sets and the comparison of two interval valued intuitionistic fuzzy numbers ivifns using an accuracy function or a possibility measure. Download book pdf intuitionistic fuzzy sets pp 9177 cite as. In this paper one generalizes the intuitionistic fuzzy set ifs, paraconsistent set, and intuitionistic set to the neutrosophic set ns. Interval, doublevalued neutrosophic intuitionistic fuzzy graph.
Pdf the notion of the intervalvalued intuitionistic fuzzy set ivifs is a generalization of that of the atanassovs intuitionistic fuzzy set. It is generally useful to express the variations of the membership function and the nonmembership function in fuzzy circumstances. In some special cases, despite the fact of using ivfss and aifs, still remain problems that are similar to those encountered in. Covers cuttingedge theories concerning intervalvalued intuitionistic fuzzy. By a cubic intervalvalued intuitionistic fuzzy set brie. A novel weighted average index model of interval valued intuitionistic fuzzy sets ivifs is presented in this paper. As a new extension of a cubic set, the notion of a cubic intervalvalued intuitionistic fuzzy set is introduced, and its application in b c k b c i algebra is considered.
Entropy measure is an important topic in the fuzzy set theory and has been investigated by many researchers from different points of view. Many variants of these mathematical objects exist, under. The theory of interval valued intuitionistic fuzzy sets ivifss has been an impactful and convenient tool in the construction of advanced multiple attribute group decision making magdm models to counter the uncertainty in the developing complex decision support system. The aim of this manuscript to combine the decision support system based on interval valued intuitionistic fuzzy set and image encryption to analyze the different sbox transformation. Their concept is characterized by a membership function and a nonmembership function whose values are intervals rather than real number. By analyzing the degree of hesitancy, this paper introduces generalized intervalvalued intuitionistic fuzzy sets with parameters givifsp. Simplified intervalvalued intuitionistic fuzzy integrals. Here we present the basic preliminaries of ivifs theory. Under these environments, the various researchers pay more attention to aggregate the di.
Intervalvalued fuzzy sets, possibility theory and imprecise. Interval, doublevalued neutrosophic intuitionistic fuzzy. On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by k. To date, more than twenty different types of fuzzy sets have been presented with academia, where atanassovs intuitionistic fuzzy set ifs and interval valued ifs ivifs are two representative examples. We first defined intervalvalued neutrosophic soft rough sets ivnsoft rough sets for short which combine interval valued neutrosophic soft set and rough sets and studied some of its basic properties. Construction of admissible linear orders for intervalvalued atanassov intuitionistic fuzzy sets with an application to decision making l. Then, some operations on hivifss are introduced in detail, and their properties are further discussed. Proposed some aggregation operators, such as the intuitionistic fuzzy ordered weighted averaging ifowa. Atanassov, the notion of interval valued intuitionistic fuzzy subsemimodule of a semimodule with respect to tnorm t and snorm s is given and the characteristic properties are described. Furthermore, we 27 discussed the necessity and possibility operations on interval valued intuitionistic fuzzy soft sets, and zhang et al. Atanassov institute of microsytems, sofia, bulgaria g. Henceforth, for notational ease, we abbreviate intuitionistic. In 1989, atanassov and gargov 2 generalised the notion of intuitionistic fuzzy sets to interval valued intuitionistic fuzzy sets ivifss, in which the.
According to the features of the cosine function, the general forms of these two kinds of entropy. The organization of the remainder of the paper is as follows. By providing the readers with a thorough survey and important practical details, it is expected to support them in carrying out applied research and to encourage them to test the theory behind the sets for new advanced applications. Correlation of intervalvalued intuitionistic fuzzy sets. Pdf intervalvalued intuitionistic fuzzy aggregation operators. Entropy measures for intervalvalued intuitionistic fuzzy. The book offers a comprehensive survey of interval valued intuitionistic fuzzy sets. Intervalvalued intuitionistic fuzzy sets krassimir t.
Among those fuzzy sets, intervalvalued fuzzy sets ivfss 35 or, equivalently, atanassov intuitionistic fuzzy sets aifs 6 play indeed a crucial role. By using the concept of intuitionistic interval valued fuzzy sets, we introduce the notion of intuitionistic interval valued fuzzy topology. This paper puts forward an approach, which rates technical attributes in fuzzy qfd by integrating interval valued intuitionistic fuzzy sets and choquet integral under the case of considering the correlation among customer requirements. Section 3 introduces the basic operations for imifns and formulates some aggregation operators for aggregating imifns, serials of properties are also investigated in detail. Interval valued intuitionistic fuzzy sets are widely used in multiattribute decisionmaking problems to select the optimal alternative, but how to measure uncertainty is an open and significant problem. Abstract the notion of interval, double valued neutrosophic intuitionistic fuzzy sets is a generalization of fuzzy sets, intuitionistic fuzzy sets, interval valued intuitionistic fuzzy sets. Gargov lml, cictpas, sofia, bulgaria received august 1987 revised january 1988 abstract. By a cubic interval valued intuitionistic fuzzy set brie. In this paper, a novel generalized intervalvalued intuitionistic fuzzy sets givifs is presented, which is the generalization of conventional intuitionistic fuzzy sets ifs and interval valued. This concept is an extension of interval valued intuitionistic fuzzy soft rough sets ivifsoft rough sets. Research article algorithm for target recognition based on intervalvalued intuitionistic fuzzy sets with grey correlation xuanhuang, 1,2 lihongguo, 1 jiangli, 1 andyangyu 1 changchun institute of optics, fine mechanics and physics, chinese academy of sciences, changchun, china. In other words, our intervalvalued intuitionistic fuzzy soft set theory is an interval valued fuzzy extension of the intuitionistic fuzzy soft set theory or an intuitionistic fuzzy extension of.
By using the concept of intuitionistic intervalvalued fuzzy sets, we introduce the notion of intuitionistic intervalvalued fuzzy topology. To satisfy much more demands from fuzzy decision making problems, we propose a method to solve the magdm problem in which. Buhaescu has investigated interval valued real numbers. An intervalvalued intuitionistic fuzzy topsis method. The interval valued intuitionistic fuzzy sets have received great attention of researchers because they can comprehensively depict the characters of things. In this work we have joined the concept of interval valued intuitionistic fuzzy sets ivifs with secure communication. Research on ahp with intervalvalued intuitionistic fuzzy. Krassimir atanassov, giving a special emphasis to the practical applications of this extension. The book offers the first comprehensive guide on interval valued intuitionistic fuzzy sets. Strong interval valued neutrosophic intuitionistic fuzzy. Fuzzy sets md systems 31 1989 343349 northholland 343 interval valued intuitionstic fuzzy sets k. This chapter describes the definition and operations of fuzzy and intuitionistic fuzzy set ifs theory with examples. Moreover a new methodology has been developed to solve interval valued intuitionistic fuzzy soft set based real life decision making problems which may contain more than one decision maker and put an effort to apply it to a more relevant way in predicting election results in india by using the concept of choice matrix. Since atanassov 4 introduced the concept of intuitionistic fuzzy sets, fuzzy set theory has been utilized in many approaches to model the diagnostic process.
Interval valued intuitionistic fuzzy sets sciencedirect. Fuzzy sets fs, intuitionistic fuzzy sets ifs, intuitionistic fuzzy sets of second type ifsst, interval valued fuzzy sets ivfs. Construction of admissible linear orders for intervalvalued. In the past few years, some scholars have investigated the calculus of intuitionistic fuzzy information, but yet there is no research on the integrals in interval valued intuitionistic fuzzy circumstance. Interval valued intuitionistic fuzzy sets springerlink. Multicriteria decisionmaking approach with hesitant interval. Some aspects of interval valued and intuitionistic fuzzy mathematical morphology. Some entropy measures of intervalvalued intuitionistic fuzzy sets and their applications entropy measures is an important topic in the fuzzy set theory, and has been investigated by many researchers. Analyses of sboxes based on interval valued intuitionistic.
The novel generalized exponential entropy for intuitionistic. The main feature of ifs is it has two functions to express the uncertainty simultaneously. Intervalvalued multiplicative intuitionistic fuzzy. New extensions of the concepts of intuitionistic fuzzy generalized nets of type 1 ifgn1 and of type 3 ifgn3, namely intervalvalued intuitionistic fuzzy generalized nets ivifgn of first type and ivifgn of third type are introduced in the present paper. An intervalvalued intuitionistic fuzzy topsis method based. This book is the first attempt for a more comprehensive and complete report on the intuitionistic fuzzy set theory and its more relevant applications in a variety of diverse fields. We apply the concept of interval, double valued neutrosophic intuitionistic fuzzy sets an instance of neutrosophic intuitionistic fuzzy sets, to graphs. Pdf some aspects of intervalvalued and intuitionistic. Ever since fuzzy set has been introduced, several extensions have been established, such as interval. A generalization of the notion of intuitionistic fuzzy ct is given in the spirit of ordinary interval valued fuzzy sets.
Interval valued multiplicative intuitionistic fuzzy set atanassov 1 first introduce the intuitionistic fuzzy set ifs and have attracted much attention for many researchers. The novel generalized exponential entropy for intuitionistic fuzzy sets and interval valued intuitionistic fuzzy sets article in international journal of fuzzy systems 2 october 2019 with. An ivifs of an ivifts x, is said to be an i interval valued intuitionistic fuzzy regular closed set ivifrcs for short if. It reports on cuttingedge research carried out by the founder of the intuitionistic fuzzy sets, prof. Intuitionstic fuzzy graph, interval valued intuitionstic fuzzy graph. In this paper we, introduce the interval valued intuitionistic fuzzy sets of second type ivifsst and its basic operations. It describes in details relations and operations over interval valued fuzzy sets and pairs, and presents original authors findings upon their applications for different purposes. This paper proposes an improved score function for the effective ranking order of intervalvalued intuitionistic fuzzy sets ivifss and an intervalvalued intuitionistic fuzzy topsis method based on the score function to solve multicriteria decisionmaking problems in which all the preference information provided by decisionmakers is expressed as intervalvalued intuitionistic fuzzy decision. New operations over interval valued intuitionistic hesitant.
The homomorphic image and inverse image are investigated. The prominent characteristics of the pifss are that it considers the membership and nonmembership degrees of each object during evaluation and their corresponding possibility degree. Neutrosophic set a generalization of the intuitionistic fuzzy set florentin smarandache, university of new mexico, gallup, nm 87301, usa, email. A study on interval valued intuitionistic fuzzy generalized semipreclosed sets 49 is an ivifcs in x and.
Interval valued intuitionistic fuzzy sets an ivifs 16 18 is an extension of both, the ifs and ivfs. We will omit the majority of the proofs below, which are, in general, analogous to the proofs from chapter 1. Interval valued intuitionistic fuzzy sets of second type. Group decision making using intervalvalued intuitionistic. Intuitionistic fuzzy set explanation of a real number.
In this paper, two new operator defined over ivifss were introduced, which will be multiplication of an ivifs with and multiplication of an ivifs with the natural number are proved. Construction of admissible linear orders for interval. There has been a growing interest and activity in the field of interval valued intuitionistic fuzzy sets ivifss. A study on matrices using interval valued intuitionistic. In this way, we resolve the controversy surrounding the formal equivalence of these two models, and open up the path for a new tradition for representing positive and negative information in fuzzy set theory. As a new extension of a cubic set, the notion of a cubic interval valued intuitionistic fuzzy set is introduced, and its application in b c k b c i algebra is considered. In section 4, we study the interval valued multiplicative intuitionistic fuzzy group. Furthermore, we 27 discussed the necessity and possibility operations on intervalvalued intuitionistic fuzzy soft sets, and zhang et al. Interval valued intuitionistic fuzzy sets krassimir t. In this paper, a new distance measure of interval valued intuitionistic fuzzy sets is proposed based on the distance of interval numbers. Neutrosophic set, a generalization of intuitionistic fuzzy set.
In this chapter, we define four separations of generalized interval valued intuitionistic fuzzy sets givifss. Technical attributes ratings in fuzzy qfd by integrating. Implication in intuitionistic fuzzy and intervalvalued fuzzy. Pdf in this paper, the intervalvalued intuitionistic fuzzy matrix ivifm is introduced. In this work we have joined the concept of interval valued intuitionistic fuzzy sets. On the most extended modal operator of first type over. The objective of this paper is to present novel algorithms for solving the multiple attribute decisionmaking problems under the possibility intuitionistic fuzzy soft set pifss information. In a fuzzy set, the degree of membership of an element signifies the extent to which the element belongs to a fuzzy set, i. The theory of intervalvalued intuitionistic fuzzy sets ivifss has been an impactful and convenient tool in the construction of advanced multiple. 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. Atanassov 1 introduced intuitionistic fuzzy sets ifss which are characterized by both a membership function and a nonmembership function. A generalized interval valued intuitionistic fuzzy sets theory. New operations over interval valued intuitionistic.
In this paper, the application of intuitionistic fuzzy sets in medical diagnosis using the distance measure by normalized hamming and. The new notion is called interval valued intuitionistic fuzzy set ivifs. Intervalvalued intuitionistic fuzzy multiple attribute group. In the proposed framework, we utilize interval valued intuitionistic fuzzy sets to calculate the weights of criteria and subcriteria, and then apply topsis approach based on ivifss to conduct the final assessment of the alternatives. In particular, we analyze type2 fuzzy sets, interval valued fuzzy sets, atanassovs intuitionistic fuzzy sets, or bipolar sets of type2 and atanassovs interval valued fuzzy sets. Ifs and ivifs are powerful extensions of zadehs fuzzy set for dealing with vagueness. In interval valued intuitionistic fuzzy ahp, intuitionistic fuzzy ratio scales are used to indicate the relative strength of the factors in the corresponding criteria. In fact, all interval valued intuitionistic fuzzy sets ivifss are givifss but all givifss are not ivifss. But, when the relations between nodes or vertices in problems are indeterminate, the fuzzy graphs and their extensions fail. For this purpose, we developed an interview chart with interval fuzzy degrees based on the relation between symptoms and diseases three types of headache, and utilized the interval valued intuitionistic fuzzy weighted arithmetic average operator to aggregate fuzzy information from the. A study on interval valued intuitionistic fuzzy generalized. By analyzing the interval of membership degree, the interval of nonmembership. This monograph offers a timely guide to the theory and applications of interval valued intuitionistic fuzzy sets. Intervalvalued intuitionistic fuzzy soft sets and their.
A generalization of the notion of intuitionistic fuzzy set is given in the spirit of ordinary interval valued fuzzy sets. A new ranking method for topsis and vikor under interval. Intervalvalued intuitionistic fuzzy multiple attribute group decision. Intervalvalued intuitionistic fuzzy sets springerlink. Intervalvalued intuitionistic fuzzy generalized nets. A new distance measure of intervalvalued intuitionistic. In this paper, the problem of measuring the degree of inclusion and similarity measure for two intervalvalued intuitionistic fuzzy sets is considered. Also, we studied some properties of the four separated subsets of givifss. Pdf in this paper, a generalized interval value intuitionistic fuzzy set givifsb is. Fuzzyintuitionistic fuzzy set theory fuzzy set and its. Implication in intuitionistic fuzzy and intervalvalued fuzzy set theory. We propose a novel concept for assigning confident weights to the experts based on cardinals of interval valued intuitionistic fuzzy soft sets ivifsss. Simplified intervalvalued intuitionistic fuzzy sets with. Intervalvalued intuitionistic fuzzy multiple attribute.
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