Fuzzy number ifn seems to suitably describe an ill. The objective of this work is to present a novel multiattribute decision making madm method under interval valued intuitionistic fuzzy ivif set environment by integrating a technique for order preference by similarity to ideal solution topsis method. New operations over interval valued intuitionistic hesitant. The existing shortcomings are overcome by proposing a new possibility degree measure for ifns. Section 3 gives the simplified interval valued intuitionistic fuzzy set sivifs and the simplified interval valued intuitionistic fuzzy number sivifn, and the operations of sivifss. Intervalvalued intuitionistic fuzzy confidence intervals. A superior tool for the first task is linguistic interval valued intuitionistic fuzzy number livifn, and an effective tool for the second task is aggregation operator ao. It reports on cuttingedge research carried out by the founder of the intuitionistic fuzzy sets, prof. To satisfy much more demands from fuzzy decision making problems, we propose a method to solve the magdm problem in which all the information supplied by the decision makers is expressed as interval valued intuitionistic fuzzy decision matrices where each of the elements is characterized by an interval valued intuitionistic fuzzy number, and. A new multicriteria decisionmaking method for intervalvalued intuitionistic fuzzy number is proposed by the advantage of intuitionistic fuzzy set and electre method. Electre method based on intervalvalued intuitionistic.
Interval valued intuitionistic trapezoidal fuzzy number and its application junhong li1. To date, nearly ten aos of livifns have been presented. Thus, a new accuracy function of an intervalvalued intuitionistic fuzzy number was proposed as follows. The optimal ordered weighted intuitionistic fuzzy quasiaveraging oowifq operator and the continuous oowifq operator are presented to aggregate all the values in an interval intuitionistic fuzzy. Xu 2007h defined the concept of intervalvalued intuitionistic fuzzy number ivifn, and gave some basic operational laws of ivifns. Intuitionistic fuzzy number and its arithmetic operation. The judgment matrices between the clusters are constructed, and the interval valued intuitionistic fuzzy normalized weight vector is obtained, as shown in table 2. A study on ranking of trapezoidal intuitionistic fuzzy numbers.
Pdf interval intuitionistic fuzzy clustering algorithm. Intervalvalued intuitionistic fuzzy multiple attribute group. A new multicriteria decisionmaking method for interval valued intuitionistic fuzzy number is proposed by the advantage of intuitionistic fuzzy set and electre method. In recent decades, several types of sets, such as fuzzy sets 2, interval valued fuzzy sets 3, intuitionistic fuzzy sets 4, 5, interval valued intuitionistic fuzzy sets 6, type 2 fuzzy. Ranking of intuitionistic fuzzy numbers by new distance. Research article an intervalvalued intuitionistic fuzzy. Assignment problem is consider with intervalvalued intuitionistic fuzzy number on the basis of similarity measure and score function in. However in some cases the proposed techniques for ranking interval valued intuitionistic fuzzy numbers using a score function or an accuracy function.
Each intervalvalued intuitionistic fuzzy number represents the intervalvalued membership. Interval valued intuitionistic fuzzy number and its. In this paper, the intervalvalued intuitionistic fuzzy matrix ivifm is introduced. Simplified intervalvalued intuitionistic multiplicative. The hesitant fuzzy concept is merges with intervalvalued intuitionistic fuzzy number and find the arithmetic operation in. Interval valued intuitionistic fuzzy envelopment analysis and preference fusion journal preproofs interval valued intuitionistic fuzzy envelopment analysis and preference fusion wei zhou, jin chen, bingqing ding, sun meng pii. Intuitionistic fuzzy set explanation of a real number. Intervalvalued intuitionistic fuzzy envelopment analysis and. To expand its application, new possibility degree functions of interval valued intuitionistic fuzzy numbers were proposed. In addition, a ranking sensitivity analysis with respect to the risk attitude is provided. Highlightsoperations on interval valued intuitionistic fuzzy values.
In neutrosophic set every element has three membership degrees including a true membership degree t, an indeterminacy membership degree i and a falsity membership degree f independently, which are within the real. To normalize the supermatrix column vectors, the interval valued intuitionistic fuzzy weighted supermatrix must be constructed. The interval valued intuitionistic fuzzy sets have received great attention of researchers because they can comprehensively depict the characters of things. To solve this problem, the concepts of the interval valued multiplicative intuitionistic fuzzy set ivmifs and the interval valued multiplicative intuitionistic fuzzy number ivmifn were introduced by yu et al. However, this is too simple to deal with all interval valued intuitionistic fuzzy multi. Possibility degree and divergence degree based method for. Moreover, we intend to develop a new method to solve intervalvalued intuitionistic fuzzy mcdm problems. A new prospect projection multicriteria decisionmaking. Introduction hesitant fuzzy information under confidence levels, xia et al. The grade of membership of an element xi x in a fuzzy set is represented by real value in. Section 3 introduces the basic operations for imifns and formulates some aggregation operators for aggregating imifns, serials of properties are also investigated in detail. To overcome this drawback, in this paper, we have proposed a simplified interval valued intuitionistic fuzzy set sivifs and the corresponding simplified interval valued intuitionistic fuzzy number sivifn which are characterized by two ifns. The remaining of this paper is organized as follows.
Foundation of intervalvalued intuitionistic fuzzy limit. Two important tasks in multiattribute group decisionmaking magdm are to describe the attribute values and to generate a ranking of all alternatives. Request pdf simplified intervalvalued intuitionistic fuzzy sets with intuitionistic fuzzy numbers there has been a growing interest and activity in the field of interval valued intuitionistic. Fuzzy numbers intuitionistic fuzzy descriptor systems. The comparison between some intervalvalued intuitionistic fuzzy numbers can not be undertaken because of its limitation. Exponential operations of intervalvalued intuitionistic. Intervalvalued intuitionistic fuzzy analytic network process.
Intervalvalued intuitionistic trapezoidal fuzzy number and. Interval valued fuzzy sets, possibility theory and. An intervalvalued intuitionistic fuzzy topsis method. In the present paper, we define an improved possibility degree method to rank the different intuitionistic fuzzy numbers ifns. An intervalvalued intuitionistic fuzzy topsis method based. Firstly, based on the possibility degree of intuitionistic fuzzy values, the possibility degree and divergence degree of ivifvs are defined to provide a new order relation of ivifvs. The book offers a comprehensive survey of interval valued intuitionistic fuzzy sets. Dec 21, 2016 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. In this paper, we propose a new ranking method of intuitionistic fuzzy number based on distance measure. Intervalvalued intuitionistic fuzzy ideal extensions in semiring. The linguistic intervalvalued intuitionistic fuzzy. Intervalvalued intuitionistic fuzzy analytic network.
Pdf trapezoidaltriangular intuitionistic fuzzy numbers. Possibility degree of intervalvalued intuitionistic fuzzy. Especially, considering an interval valued pythagorean fuzzy element ivphfe is formed by several pairs of interval values, this paper proposes the concepts of score function and accuracy function in the form of two interval numbers which can retain interval valued pythagorean fuzzy information as. Multiattribute decisionmaking, intervalvalued intuitionistic sets. If the intervalvalued intuitionistic fuzzy ideal extension of by equal to intervalvalued intuitionistic fuzzy set for all then is a constant function which is proved in the following proposition. The novelty of these functions is that they allow the comparison of ivifns by taking into account of the decision makers attitudinal character. Under these environments, the various researchers pay more attention to aggregate the di. Linguistic intervalvalued intuitionistic fuzzy archimedean. Therefore, in this paper we proposed an improved score function and develop an interval valued intuitionistic fuzzy topsis method based on the improved score function to solve multicriteria decisionmaking problems in which the performance rating values are expressed by ivifss. Intervalvalued intuitionistic fuzzy information aggregation. A novel exponential distance and its based topsis method. This monograph offers a timely guide to the theory and applications of interval valued intuitionistic fuzzy sets.
Abstractthis work was motivated by the revealed limitations and drawbacks of the classical definition of interval valued intuitionistic fuzzy set ivifs. Pdf on feb 18, 2018, ezzatallah baloui jamkhaneh and others published new generalized interval valued intuitionistic fuzzy numbers find, read and cite all the research you need on researchgate. To overcome these shortcomings, this paper aims to develop a new risk evaluation in fmea method. Subsequently in interval valued intuitionistic fuzzy magdm, an intuitionistic fuzzy linear programming model is constructed to derive decision makers weights.
The intervalvalued intuitionistic fuzzy weight vectors are integrated into a weight vector matrix a. Simplified intervalvalued intuitionistic fuzzy integrals. In the following part, we utilize or to denote an intervalvalued intuitionistic fuzzy number ivifn or an intuitionistic fuzzy number ifn. First, this paper converts linguistic evaluation information into corresponding interval valued intuitionistic fuzzy numbers ivifns to effectively address the uncertainty and vagueness of the information. As a supplementation, the exponential operational law of intuitionistic fuzzy numbers has been defined. Intervalvalued multiplicative intuitionistic fuzzy.
Firstly, the possibilitydegree and deviationdegree of interval number are used to establish the preference relation of intervalvalued intuitionistic fuzzy number. Section 4 puts forward a series of operational laws of sivifns, including addition, subtraction, multiplication and division operations, etc. Intervalvalued pythagorean hesitant fuzzy set and its. Intervalvalued intuitionistic fuzzy multiple attribute group decision.
Ranking of intervalvalued intuitionistic fuzzy ivif numbers is a most popular and elegant work in the area of decisionmaking of several realworld problems. It is worth mentioning the score degree and accuracy degree functions recently developed by xu and chen in 38 to propose an order relation on the set of interval valued intuitionistic fuzzy numbers ivifns. Intervalvalued fuzzy sets, possibility theory and imprecise. By using interval type2 fuzzy systems and fuzzy numbers intuitionistic fuzzy sets, fuzzy numbers intuitionistic fuzzy descriptor systems are proposed in this paper. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers ivifns to solve the interval valued intuitionistic fuzzy multiobjective linear programming problem with pentagonal intuitionistic fuzzy numbers pifns by assuming different. The operations on intervalvalued intuitionistic fuzzy. A comparative study on interval arithmetic operations with. Trapezoidaltriangular intuitionistic fuzzy numbers versus.
First, the extended hamacher tnorm and snorm, which are applicable to linguistic information environment, are applied to define the linguistic interval valued intuitionistic fuzzy hamacher operational laws. Intervalvalued intuitionistic fuzzy sets krassimir t. Interval valued intuitionistic fuzzy sets an ivifs 16 18 is an extension of both, the ifs and ivfs. Set pair analysis spa theory is the modern uncertainty theory which is composed by the three components, namely identity.
Qiansheng, a generalized interval valued intuitionistic fuzzy sets theory, advanced in control engineering and information science, vol. The operations on interval valued intuitionistic fuzzy values in the framework of dempstershafer theory. 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. 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. A simple method is to put equal weights on each attribute. Garg and kumar 2019 proposed linguistic interval valued atanassov intuitionistic fuzzy sets and their application in group decision making problems. 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. When using the proposed algorithm to recognize an unknown target, one should rst establish a target recognition matrix composed of intervalvalued intuitionistic fuzzy numbers. From a geometric viewpoint, the expectation and expectant score of an. Here we have presented a chart of ifn with transformation rule to fuzzy numbers and interval and real number. In the present paper, two new extensions of the gns, called interval valued ifgn2 and interval valued ifgn4 ifgn2s and ifgn4s will be introduced. As a generalization of fuzzy numbers 20, an intuitionistic. Assignment problem is consider with interval valued intuitionistic fuzzy number on the basis of similarity measure and score function in. This paper addresses the modified arithmetic operations on interval valued intuitionistic fuzzy numbers ivifns for solving interval.
In case of incomplete and vague data, fuzzy confidence intervals can be used for decision making under uncertainty. Intervalvalued intuitionistic fuzzy todim sciencedirect. Then, we have given the operational laws and investigated their desirable properties. In this paper, we develop interval valued intuitionistic fuzzy ivif confidence intervals for population mean, population proportion, differences in means of two populations, and differences in proportions of two populations. Another key issue for the interval valued intuitionistic fuzzy multiattribute decision making is how to reasonably distribute attributes weights. Interval valued intuitionistic fuzzy generalized nets of.
This article investigates new score and accuracy functions for ranking interval valued intuitionistic fuzzy numbers ivifns. Ye26 also proposed a novel accuracy function to rank interval valued intuitionistic fuzzy numbers. To some extent, interval values can better reveal the characteristics of things. Intervalvalued trapezoidal intuitionistic fuzzy generalized. 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. Ranking of intuitionistic fuzzy numbers by new distance measure. Pdf new generalized interval valued intuitionistic fuzzy.
An optimization model based on the negative ideal solution and maxmin operator, by which the attribute. In the present paper we give a bijection between the set of trapezoidal intuitionistic fuzzy numbers and a subset of interval valued trapezoidal fuzzy numbers and a bijection between. Complete ranking on the class of intuitionistic fuzzy interval number was done by geetha et al. Interval valued trapezoidal intuitionistic fuzzy number. Technical attributes ratings in fuzzy qfd by integrating. New operations over interval valued intuitionistic. Research article algorithm for target recognition based on. Electre method based on intervalvalued intuitionistic fuzzy. Intervalvalued intuitionistic fuzzy envelopment analysis.
Valued ifgn3 ifgn1s and ifgn3s were introduced in 14. Pdf in a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers ifns, interval valued intuitionistic. Then, we exposit the decision theory and the steps of this. In this paper we define triangular, trapezoidal, pentagonal, hexagonal and octagonal interval valued fuzzy numbers and develop new ranking technique on those fuzzy numbers which are more efficient. Intuitionisticfuzzysetspast,presentandfuture krassimirt. On the basis of the concept of the interval valued intuitionistic fuzzy sets. In the present paper, we generalize the intuitionistic fuzzy if number to interval valued intuitionistic fuzzy number by defining interval membership and nonmembership functions instead of fixed valued function and hence it will present uncertain situation better than if numbers. Formation of an interval valued intuitionistic fuzzy weighted supermatrix. Reliability analysis of a powerloom plant using interval. With respect to multiple attribute decisionmaking problems with interval valued intuitionistic fuzzy information, some operational laws of interval valued intuitionistic fuzzy numbers, correlation and correlation coefficient of interval valued intuitionistic fuzzy sets are introduced. New generalized interval valued intuitionistic fuzzy numbers. Intervalvalued intuitionistic fuzzy number uses membership degree and nonmember ship degree to express a decisionmakers hesitation, which make decisionmaker express hisher opinion in uncertainty decisionmaking environment easily. Later on wang and zhang 2009a, b developed the definition of intuitionistic.
Firstly, interval valued intuitionistic fuzzy generalized einstein weighted averaging ivifgewa operator, interval valued intuitionistic fuzzy. Some generalized einstein aggregation operators based on. Simplified intervalvalued intuitionistic fuzzy sets with. A study on interval valued intuitionistic fuzzy generalized. The hesitant fuzzy concept is merges with interval valued intuitionistic fuzzy number and find the arithmetic operation in. The intervalvalued intuitionistic fuzzy determinant is also defined. Extension of weighted aggregated sum product assessment with interval valued intuitionistic fuzzy numbers waspasivif. Intervalvalued intuitionistic fuzzy multiple attribute.
Abirami and stephen8 developed a new approach on ranking lr type interval valued fuzzy numbers. An ivifs of an ivifts x, is said to be an i interval valued intuitionistic fuzzy regular closed set ivifrcs for short if. Their definition is given firstly, and the stability of this kind of systems is studied, the relations of interval type2 fuzzy systems and ts fuzzy descriptor systems and fuzzy. Application of correlation coefficient to intervalvalued. The relationship between interval valued fuzzy sets and intuitionistic fuzzy sets is well known see 10.
Intervalvalued intuitionistic trapezoidal fuzzy number. A novel arithmetic technique for generalized intervalvalued. The main aim of this paper is to give a novel method to extend a similarity measure of generalized trapezoidal fuzzy numbers gtfns to similarity measures of generalized trapezoidal intuitionistic fuzzy numbers gtifns and generalized interval valued trapezoidal fuzzy numbers givtfns such that the initial properties to be preserved. Pdf in this paper, a generalized interval value intuitionistic fuzzy set givifsb is. The ivif todim method has been investigated on tw o.
To achieve it, we first present some shortcomings of the existing possibility degree method and score function of ifns. Some limited methods have been presented concerning the ranking of ivif sets in literature. Hedayati department of mathematics babol university of technology babol iran email. Krassimir atanassov, giving a special emphasis to the practical applications of this extension. Ranking of interval valued intuitionistic fuzzy ivif numbers is a most popular and elegant work in the area of decisionmaking of several realworld problems. Calculation of global priority vectors and weights. This paper addresses the modified arithmetic operations on interval valued intuitionistic fuzzy numbers ivifns for solving interval valued intuitionistic fuzzy linear programming problem iviflpp with hexagonal intuitionistic fuzzy numbers by. Due to the advantages of the ivifs, it has been investigated. A risk attitudinal ranking method for intervalvalued. Ye 49 also proposed a novel accuracy function to rank interval valued intuitionistic fuzzy numbers.
Adrian and delia 2014 developed the idea of trapezoidal fuzzy numbers and interval valued trapezoidal fuzzy numbers. A study on interval valued intuitionistic fuzzy generalized semipreclosed sets 49 is an ivifcs in x and. Complete ranking of intuitionistic fuzzy numbers sciencedirect. The ivifgns are based on the intuitionistic fuzzy sets and interval valued intuitionistic fuzzy. An interval valued intuitionistic fuzzy set a m a,n a of sris called an. In application such as weak consistency judgment of an interval valued intuitionistic fuzzy judgment and multiattribute decisionmaking, the comparison operator is needed. In section 4, we study the interval valued multiplicative intuitionistic fuzzy group. The operational laws of intuitionistic fuzzy numbers are useful in dealing with the problems under intuitionistic fuzzy circumstances. Generalized intervalvalued neutrosophic graphs type1. Intuitionistic fuzzy number and its arithmetic operation with application on system failure.
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