Top PDF An Extended LINMAP Method for Multi-Attribute Group Decision Making under Interval-Valued Intuitionistic Fuzzy Environment

An Extended LINMAP Method for Multi-Attribute Group Decision Making under Interval-Valued Intuitionistic Fuzzy Environment

An Extended LINMAP Method for Multi-Attribute Group Decision Making under Interval-Valued Intuitionistic Fuzzy Environment

The linear programming technique for multidimensional analysis of preference (LINMAP), developed by Srinivasan and Shocker [29], is one of the existing well-known method based on distance measure for MADM problems in crisp environments. The classical LINMAP method was developed to solve MAGDM problems in fuzzy environments [30–32], and further extended to develop a new methodology for solving MAGDM problems using AIFSs [33]. Intuitively, extending from AIFSs to IVIFSs furnishes additional capability to handle vague information because the membership and nonmembership degrees are only needed to be expressed as ranges of values rather than exact values. When the uncertainty in an IVIFS’s membership and nonmembership degrees diminishes to zero, the IVIFS is reduced to an IFS. Therefore, it motivates to further extend the LINMAP to develop a new methodology for solving MAGDM problems with IVIFSs, where each alternative is assessed on the basis of its distance to a positive ideal solution, which is known a priori. The weights of attributes are calculated by constructing a new linear programming model based on the group consistency and inconsistency index defined on the basis of pairwise comparison preference relations on alternatives given by the decision makers. The weighted distance of each alternative to the interval-valued intuitionistic fuzzy positive ideal solution (IVIFPIS) can be calculated to determine the ranking order of all alternatives for the decision makers, and the ranking order of alternatives and the best alternative(s) for the group are generated by using the Borda’s function.
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A Method for Multi-attribute Group Decision Making with Triangular Intuitionistic Fuzzy Numbers and Application to Trustworthy Service Selection

A Method for Multi-attribute Group Decision Making with Triangular Intuitionistic Fuzzy Numbers and Application to Trustworthy Service Selection

Abstract. The trustworthy service selection is a typical Multi-Attribute Group Decision- Making (MAGDM) problem. The aim of this paper is to develop a novel method for MAGDM with Triangular Intuitionistic Fuzzy Numbers (TIFNs) and apply it to the trustworthy service selection problem. Firstly, we dene the mean-index, variance-index, and standard deviation of TIFN. Moreover, a new distance measure of TIFNs is proposed, and the corresponding proofs are given. Based on these concepts of mean-index and standard deviation, a ranking method for TIFNs is developed considering the risk preference of Decision Maker (DM). Further, according to the crisp relative closeness coecient matrix with respect to the normalized TIFNs decision matrix, we use entropy measure to obtain attribute weights. The DMs' weights are calculated by the similarity between the individual and the average decisions. Then, a decision procedure is described to solve the MAGDM under triangular intuitionistic fuzzy environment. Finally, a real trustworthy service selection example is analyzed to verify the practicality and eectiveness of the developed method.
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Multi Criteria Decision Making Under Intuitionistic Fuzzy Environment Using Ranking Order of Soft TOPSIS

Multi Criteria Decision Making Under Intuitionistic Fuzzy Environment Using Ranking Order of Soft TOPSIS

Multiple criteria decision-making (MCDM) is considered as a complex decision-making (DM) tool involving both qualitativeand quantitative factors. In recent years, several MCDM techniques and approaches have been suggested for choosing the best probable options. De et al. 1 studied the Sanchez's approach for medical diagnosis and also they extended this concept which is a generalization of fuzzy set theorywith the notion of intuitionistic fuzzy set theory. The Boran 2 combined TOPSIS method with intuitionistic fuzzy set. They proposed a method to select best supplier in group decision making environment.
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Interval-valued Intuitionistic Fuzzy TODIM

Interval-valued Intuitionistic Fuzzy TODIM

The TODIM (an acronym in Portuguese for Interative Multi-criteria Decision Making) method has recently been extended firstly to fuzzy and next to intuitionistic fuzzy environments with promising results. In this paper, we further consider the extension of TODIM to interval-valued intuitionistic fuzzy (IVIF) environments. Two case studies are used to illustrate the approach to multi-criteria decision making. Experimental results show the effectiveness of the presented method.

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Extended TODIM Method for MADM Problem under Trapezoidal Intuitionistic Fuzzy Environment

Extended TODIM Method for MADM Problem under Trapezoidal Intuitionistic Fuzzy Environment

At present, the theory and application of fuzzy numbers, such as triangular intuitionistic fuzzy number, trapezoidal intuitionistic fuzzy number, have been received great attention. But most of the existing decision-making methods do not consider the influence of the behavior of the decision-makers in the decision process, because they are assumed that the decision maker is completely rational. However, the actual decision-making process is often accompanied by the different psychological behavior of the decision-makers and the attitude of the risk and other factors of behavior. Kahneman and Tversky [13] proposed the prospect theory, which can describe the decision maker’s psychological behavior. Based on prospect theory, Gomes and Lima ( [6, 7]) developed a new MADM method named TODIM method, which has made many successful applications, such as material evaluation [34], green supplier selection [26], logistics outsourcing [30] etc. Fan et al. [5] proposed an extension of TODIM (H-TODIM) to solve the hybrid MADM problems in which attribute values have three forms: crisp numbers, interval numbers and fuzzy numbers. Qin [23] proposed a generalization of the TODIM method under triangular intuitionistic fuzzy environment. Ren et al. [25] extended the TODIM method to deal with the MADM problem in which attribute values are expressed with Pythagorean fuzzy numbers. Zhang et al. [33] developed the TODIM method to solve the MADM problem in which the attribute values are expressed with neutrosophic numbers. In this paper, we will develop a new extension of TODIM method to solve the MADM problem in which attribute values are expressed with TIFNs, and an application example is used to illustrate the validity and practicability of the proposed method.
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Group decision making process for early stage evaluations of infrastructure projects using extended VIKOR method under fuzzy environment

Group decision making process for early stage evaluations of infrastructure projects using extended VIKOR method under fuzzy environment

In addition to the AHP method, different methods were also conducted for the evaluation of linear infra- structure. Compromise programming techniques were used by Ballestero et al. [13] and Kosijer et al. [2]. Bal- lestero et al. [13] developed a Bayesian decision model based on utility maximisation as a standard method- ology to evaluate alternatives under non-strict uncer- tainty. The utility function was estimated objectively applying market-based social weighting. Probabilistic values for states of nature were subjectively determined based on interviews with decision makers. Five alterna- tives of a ring-road in Madrid metropolitan area were evaluated based on three cost criteria (investment costs, right of way costs, external costs of noise pollution) and two benefit criteria (savings in travelling costs and gains in real estates). Kosijer et al. [2] proposed a meth- odology for railway route planning and design based on multi-criteria decision making. As a case study, the VIKOR method was applied for ranking four railway route alternatives on the Pan-European Corridor X through Serbia. The alternatives were evaluated among three quantitative criteria (investments, operation costs and capacity) and two qualitative criteria (impacts on spatial development and environment). Anton and Grau [14] and Saat and Aguilar [15] investigated the use of the ELECTRE method providing an alternative selection of high speed rail (HSR) lines. Anton and Grau [14] focused on the Spain HSR network analysing the line between Madrid and Valencia as a case study. They evaluated three route alternatives using four standard criteria (investments, travel time, potential users and environmental impacts). Similarly, Saat and Aguilar [15] focused their research on the HSR devel- opment in Malaysia partly changing the set of criteria. Three route alternatives were evaluated using three cri- teria based on the following indicators: investments, total population and gross domestic product. Sperry et al. [3] developed a model based on weighted sum ap- proach as a part of methodology for the evaluation of HSR lines. The proposed model was applied on the case study of railway network in Texas considering 13 alter- native routes to connect two existing HSR corridors. The multi-criteria assessment of projects in transport sector applying weighting methods was also conducted by Delle Site and Fillippi [16]. Authors compared three methods within the multi-attribute value theory (MAVT): ratio with swings, Saaty scale with swings, and trade-off. In addition to the theoretical consider- ations on correlations among these methods, authors provided suggestions how MAVT should be applied to transport projects highlighting the differences among various weighting methods.
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Some Generalized Einstein Aggregation Operators Based on the Interval-Valued Intuitionistic Fuzzy Numbers and Their Application to Group Decision Making

Some Generalized Einstein Aggregation Operators Based on the Interval-Valued Intuitionistic Fuzzy Numbers and Their Application to Group Decision Making

In this paper, we explored some generalized Einstein aggregation operators based on IVIFNs and applied them to the multi-attribute group decision making problems where attribute values are the IVIFNs. Firstly, Interval-Valued Intuitionistic Fuzzy General- ized Einstein Weighted Averaging (IVIFGEWA) oper- ator, Interval-Valued Intuitionistic Fuzzy Generalized Einstein Ordered Weighted Averaging (IVIFGEOWA) operator, and Interval-Valued Intuitionistic Fuzzy Gen- eralized Einstein Hybrid Weighted Averaging (IV- IFGEHWA) operator were proposed. Some of their general properties such as idempotency, commutativ- ity, monotonicity, and boundedness, were studied, and some special cases of them were analyzed. Further- more, a method to multi-criteria group decision making based on these operators was developed, and the operational processes were illustrated in detail. Finally, an illustrative example was given to show the decision steps of the proposed method and to demonstrate their eectiveness. In further research, it is necessary and signicant to give the applications of these operators to the other domains such as pattern recognition, fuzzy cluster analysis, uncertain programming, etc.
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Interval-Valued Hesitant Fuzzy Method based on Group Decision Analysis for Estimating Weights of Decision Makers

Interval-Valued Hesitant Fuzzy Method based on Group Decision Analysis for Estimating Weights of Decision Makers

In this study, a new soft computing group decision making method has been proposed to specify the decision makers (DMs)’ weights for multi-criteria group decision making (MCGDM) which could be implemented to solve industrial selection problems. For this purpose, the weight of each criterion was computed by hybridizing a non-linear programming concept and the opinion of each DM about the relative significance of selected criteria. In addition, the interval-valued hesitant fuzzy positive ideal solution (IVHF-PIS) / interval-valued hesitant fuzzy negative ideal solution (IVHF-NIS) matrices were established. Then, the interval-valued hesitant fuzzy average group score (IVHF-AGS) and the interval-valued hesitant fuzzy worst group score (IVHF-WGS) values were determined by using the n-dimensional Euclidean distance measure under interval-valued hesitant fuzzy environment. Also, a novel IVHF-CI based on the compromise ratio concept was introduced to appraise each DM and determine the weight of each DM. For industrial selection problems, the best site selection for building the new factory has indicated the verification and feasibility of the proposed soft computing group decision method. The presented method was compared with three recent literature studies to shows the feasibility of the proposed approach. Moreover, a comparative analysis is established based on six criteria to clear representation of the advantages and merits of each method. The proposed soft computing group decision method has some uniqueness characteristics under hesitant situations. The IVHF-decision matrix and the opinions of the DMs about the relative importance of each criterion were expressed by linguistic variables to help the DMs for assigning the membership degrees. For future direction, the presented method can be enhanced by considering the hierarchical structure in criteria. In addition, the proposed DMs’ weight method can be considered in process of a new extended ranking method to help the IVHFS literature for solve the group decision problems, precisely.
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Dynamic intuitionistic fuzzy multi-attribute decision making

Dynamic intuitionistic fuzzy multi-attribute decision making

decision making based on IFSs. Liu and Wang [13] gave an eval- uation function for the decision making problem to measure the degrees to which alternatives satisfy and do not satisfy the decision maker’s requirement. Then, they introduced the intuitionistic fuzzy point operators, and defined a series of new score functions for the multi-attribute decision making problems based on intui- tionistic fuzzy point operators and evaluation function. Xu [14] defined some new intuitionistic preference relations, such as the consistent intuitionistic preference relation, incomplete intuitionistic preference relation and acceptable intuitionistic preference relation, and studied their properties. We also developed a method for group decision making based on intuitionistic preference relations and a method for group decision making based on incomplete intuitionistic preference relations, respectively. All these studies are focused on the deci- sion making problems where all the original decision information are provided at the same period. However, in many decision areas, such as multi-period investment decision making, medical diagnosis, personnel dynamic examination, and military system efficiency dynamic evaluation, etc., the original decision informa- tion are usually collected at different periods. Thus, it is necessary to develop some approaches to dealing with these issues. In this paper, we shall study the fuzzy multi-attribute decision making problems where all the attribute values are expressed in intuitionistic fuzzy numbers collected at different periods (for convenience, we call this kind of problems dynamic intuitionistic fuzzy multi-attribute decision making (DIF-MADM) problems). To do that, we first introduce the notion of intuitionistic fuzzy variable and develop an aggregation operator called dynamic intuitionistic fuzzy weighted averaging (DIFWA) operator. Then, we introduce some methods such as the basic unit-interval monotonic (BUM) function based method, normal distribution based method, exponential distribution based method and average age method, to determine the weight vectors asso- ciated with the operator, and develop a procedure for DIF-MADM. Furthermore, we extend the developed operator and procedure to deal with the situations where all the attribute values are expressed in interval-val- ued intuitionistic fuzzy numbers collected at different periods. At last, an illustrative example is given. 2. Preliminaries
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Multi-criteria trapezoidal valued intuitionistic fuzzy decision making with Choquet integral based TOPSIS

Multi-criteria trapezoidal valued intuitionistic fuzzy decision making with Choquet integral based TOPSIS

very important in group decision making problems to perform evaluation process. Group decision making involves weighted aggregation of all individual decisions to obtain a single collective decision. In [44], aggregation operator of intuitionistic fuzzy group decision making is proposed with the weights of decision makers. The weights of decision makers plays an important role in the process of aggregation. In [46], [47] and [64], aggregation of the interval-valued intuitionistic fuzzy group decision making environment with the Choquet integral is studied. Until now, we do not have any aggregation of the trapezoidal-valued intuitionistic fuzzy group de- cision making environment with Choquet integral. In this paper, we …rst develop a generalized trapezoidal-valued intuitionistic fuzzy geometric aggregation operator for aggregating all individual decision makers’ opinions under trapezoidal-valued intuitionistic fuzzy group decision making environment. Combining this operator with TOPSIS on Choquet integral-based distance, a multi-criteria trapezoidal- valued intuitionistic fuzzy group decision making is proposed, where interaction phenomena among the decision making problem and weights of decision makers are taken into account.
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Multi-criterion multi-attribute decision-making for an EOQ model in a hesitant fuzzy environment

Multi-criterion multi-attribute decision-making for an EOQ model in a hesitant fuzzy environment

[5,6] . Since then, a large number of research articles on inventory management problems that consider this topic have been pub- lished. In such problems, the membership and non-membership functions are used to determine a score. De and Sana [19] have developed a backlogging model using IFSs with the score of the objective function. De et al. [18] have studied an EOQ model with backorder that considers the interpolation bypass technique as an alternative to the Pareto optimality technique for intuitionistic fuzzy sets. On decision-making problems, a trapezoidal-valued IFS has been studied by Beg and Rashid [8] ; interval-valued intuition- istic fuzzy sets have been developed by Wei et al. Wei et al. [44] , and geometric aggregation rules have been analysed by Wei [45] . Au- thors such as Takeuti and Tinani [36] , Atanassov and Gargov [4] , Dabois et al. [16] , Dymova and Sevastjanov [24] , Angelov [3] have studied current issues in decision-making problems using IFSs in inventory management. In an intuitionistic fuzzy environment, De
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Study on the Development of Decision Making Using Intuitionistic Fuzzy Set (IFS) and Interval Valued Intuitionistic Fuzzy Set (IVIFS)

Study on the Development of Decision Making Using Intuitionistic Fuzzy Set (IFS) and Interval Valued Intuitionistic Fuzzy Set (IVIFS)

__________________________________________________________________________________________ Abstract: Out of several higher order fuzzy sets [1], the concept of an intuitionistic fuzzy set (IFS) [2] introduced by Atanassov has been found to be highly useful to deal with vagueness and imprecision. IFS theory has been extensively applied to areas like Artificial Intelligence, networking, Soft decision making, Programming logic, operational research etc. One the promising role of IFS has been emerged in Decision making problems specially group decision making and multi-attribute decision making. In some real-life situations, decision makers may not be able to accurately express their view for the problem as they may not possess a precise or sufficient level of knowledge of the problem or the decision makers are unable to discriminate explicitly the degree to which one alternative are better than others in such cases, the decision maker may provide their preferences for alternatives to a certain degree, but it is possible that they are not so sure about it [3]. Thus, it is very suitable to express the decision maker preference values with the use of fuzzy/intuitionistic fuzzy values rather than exact numerical values or linguistic variables [4]. To satisfy the need of decision making problem with imprecision and uncertainty many researchers have been concentrated on IFS theory. In this paper we reviewed the development of different approaches for solving decision making problem using IFS theory and a brief introduction on the role of Interval Valued IF sets (IVIFS) [5] in multiattribute decision making.
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Solving robot selection problem by a new interval-valued hesitant fuzzy multi-attributes group decision method

Solving robot selection problem by a new interval-valued hesitant fuzzy multi-attributes group decision method

In this respect, to solve the industrial robot se- lection problem based on decision-making anal- ysis under the fuzzy environment, Devi [7] de- veloped VIKOR method under an intuitionis- tic fuzzy environment, in which the evaluating the candidate robots and the attributes weights are defined by triangular intuitionistic fuzzy sets. Samantra et al. [24] presented an interval-valued trapezoidal fuzzy VIKOR method to deal with uncertainty in solving the decision-making prob- lems. Vahdani et al. [27] developed a com- plex proportional assessment method based on the interval-valued fuzzy sets regarding to the objective information and subjective judgments. Rashid et al. [23] proposed a generalized interval- valued trapezoidal fuzzy TOPSIS method accord- ing to the subjective judgment and objective in- formation. In their method, the experts opinions are aggregated on different attributes.
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Supplier selection with multi-criteria group decision making based on interval-valued intuitionistic fuzzy sets (case study on a project-based company)

Supplier selection with multi-criteria group decision making based on interval-valued intuitionistic fuzzy sets (case study on a project-based company)

aggregation (IIFWA) operator, the interval-valued intuitionistic fuzzy ordered weighted aggregation (IIFOWA) operator, and the interval- valued intuitionistic fuzzy hybrid aggregation (IIFHA) operator in order to aggregate interval-valued intuitionistic preference information. Meanwhile, Wei and Wang (2007), Ze-Shui (2007a) and Xu and Chen (2007b), presented some operators in terms of geometrics, such as the interval-valued intuitionistic fuzzy weighted geometric (IIFWG) operator, the interval-valued intuitionistic fuzzy ordered weighted geometric (IIFOWG) operator, and the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator. According the results, all these numbers are still IVIFSs. Obviously, there are different indications on arithmetic aggregation operators and geometric aggregation operators; Such that the former indicates the group’s influence, whereas the later indicates the individual influence. To evaluate IVIFSs, score function and accuracy function have been developed with the capability of comparing criteria values expressed by IVIFSs in order to generate a permutation and give ordered weights to the corresponding criteria values. The accuracy functions proposed by Xu and Da (2003), do not give sufficient information about alternatives and may lead to difficult conditions in the decision making processes. So, more attentions to other measuring functions is made. Therefore Ze-Shui (2007a), proposed a score function and Lakshmana Gomathi Nayagam, Muralikrishnan, and Sivaraman (2011), proposed a new novel accuracy function to discriminate between the IVIFSs. With this enhanced studies on IVIFNs, researchers have turned their attention to decision problems whereas some input decision data are provided as IVIFNs (Wang, Li, & Wang, 2009; Z. Xu & Yager, 2008; Ze-Shui, 2007a). However, there are a few studies on MCDM involving multiple decision-makers in an interval-valued intuitionistic fuzzy environment. In order to avoid partial judgment caused by individual opinion’s, group decision-making is used to integrate different opinions. Comparing with individual decision making, group decision making can elicit more complete information about the problem and provide more selective alternatives(T.-Y. Chen, Wang, & Lu, 2011).The risk attitude of a decision maker is an important parameter in the decision process, especially in multi-criteria group decision making (MCGDM) that can influences the process results, but it is generally neglected in the existing research on MCGDM with IVIFN assessments. In this paper, we proposed an approach to deal with the multi-criteria group decision making (MCGDM) problem based on the interval-valued intuitionistic fuzzy preference relation and the interval-valued intuitionistic fuzzy decision matrix, while the main focus is to contribute the risk attitude of decision group members in MCGDM process.
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MULTI-CRITERIA GROUP DECISION-MAKING USING AN EXTENDED EDAS METHOD WITH INTERVAL TYPE-2 FUZZY SETS

MULTI-CRITERIA GROUP DECISION-MAKING USING AN EXTENDED EDAS METHOD WITH INTERVAL TYPE-2 FUZZY SETS

Type-1 fuzzy sets are effi cient in modeling the multi-criteria decision-making problems and have many applications for extending MCDM methods in an uncertain environment. However, we may confront with situations that more degrees of fl exibility are needed to deal with the decision-making process. Type-2 fuzzy sets (T2FSs), which was introduced by Zadeh (1975), are more fl exible than type-1 fuzzy sets in the modeling of uncertainty. Interval type-2 fuzzy sets (IT2FSs) are a special type of T2FSs. Some basic defi nitions of IT2FSs were proposed by Mendel et al. (2006). IT2FSs have increasingly been considered by researchers in applications and extensions of multi-criteria decision-making methods. Chen and Lee (2010) developed a new ranking method for interval type-2 fuzzy sets and used it in a new fuzzy MCDM method. Chen et al. (2012) proposed a new ranking method and a new multi-criteria decision-making method with interval type-2 fuzzy sets. Wang et al. (2012) introduced a multi-criteria group decision-making (MCGDM) method in type- 2 fuzzy environment, which can be used with incomplete information about criteria weights. Hu et al. (2013) developed a new ranking method based on the possibility degree for IT2FSs and applied it in multi-criteria decision- making process. Keshavarz Ghorabaee et al. (2014) presented a new fuzzy ranking method and extended COPRAS (Complex Proportional Assessment) method in the context of IT2FSs to evaluate suppliers in a supply chain. Celik et al. (2014) proposed an interval type-2 fuzzy MCDM method to identify and evaluate critical success factors for humanitarian relief logistics management. Balin and Baraçli (2015) developed a fuzzy MCDM methodology based on the IT2FSs for evaluating renewable energy alternatives in Turkey. Chen (2015) proposed a new likelihood-based interval type-2 fuzzy
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Dynamic multi-attribute decision making model based on triangular intuitionistic fuzzy numbers

Dynamic multi-attribute decision making model based on triangular intuitionistic fuzzy numbers

Multiple-Attribute Decision Making (MADM) methods have been extensively applied to various areas, such as society, management science, economics, military research and public administration [ 1–5 ]. However, most MADM methods focus on decision making problems at the same period, such as those proposed by Ye [ 6 ] who developed a MADM model with interval-valued, intuitionistic, fuzzy numbers, and Jaskowski et al. [ 7 ] who presented an extended fuzzy AHP model for group decision making, at the same period. Greco et al. [ 8 , 9 ] and Blaszczynski et al. [ 10 ] extended the rough set theory into a multi-attribute decision making method, and Hu et al. [ 11 ] also extended a rough set MADM model to solve a multi-attribute decision making problem at the same period.
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Study on Interval Intuitionistic Fuzzy Multi-Attribute Group Decision Making Method based on Choquet Integral

Study on Interval Intuitionistic Fuzzy Multi-Attribute Group Decision Making Method based on Choquet Integral

Multiple attribute group decision making problem is the process that a group of decision makes (DMs) to select the best alternative from the overall feasible alternatives. Interval intuitionistic attribute group decision making problem is a special case of MAGDM, in which the attribute value takes the form of interval intuitionistic fuzzy number. In GDM problem, how to aggregate the expert opinions and how to obtain the interactive among the attributes are two important problems which should be deeply considered. In the following, based on the interval intuitionistic fuzzy entropy and interval intuitionistic fuzzy measure we have mentioned above, a new approach is proposed to solve interval intuitionistic attribute group decision making problem, we construct two models to determine the fuzzy measure which are used to calculate the interactive importance measure of attributes and correlation measure of the experts (e.g. absolute measure, relative measure). First, we describe the interval intuitionistic fuzzy multiple attribute group decision making problems in this paper. For an interval intuitionistic fuzzy multiple attribute group decision making problems, let M = {A 1 , A 2 , · · · A m } be the set of alternatives, N =
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An Extended TOPSIS Method for Multiple Attribute Group Decision Making Based on Generalized Interval-valued Trapezoidal Fuzzy Numbers

An Extended TOPSIS Method for Multiple Attribute Group Decision Making Based on Generalized Interval-valued Trapezoidal Fuzzy Numbers

(NLP) solution procedure by considering triangular fuzzy numbers. Liu and Zeng [9] proposes a new TOPSIS method to deal with the fuzzy multiple attribute group decision making problem based on the expected value operator of the trapezoidal fuzzy number when the fuzzy decision matrixes and the weights of the decision attributes and decision makers are all given by the trapezoidal fuzzy number. Tsaur et al. [10] convert the fuzzy MCDM problem into a crisp one via centroid defuzzification and then solve the non-fuzzy MCDM problem by the TOPSIS method. Chu and Lin [11] changed the fuzzy MCDM problem into a crisp one. Differing from the others, they first derive the membership functions of all the weighted ratings in a weighted normalized decision matrix and then convert them to crisp values by defuzzifying and then use TOPSIS method to solve this problem.
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Extended TOPSIS method for multi-criteria group decision-making problems under cubic intuitionistic fuzzy environment

Extended TOPSIS method for multi-criteria group decision-making problems under cubic intuitionistic fuzzy environment

Abstract. The objective of this work is to present a novel Multi-Criteria Group Decision- Making (MCGDM) method under the Cubic Intuitionistic Fuzzy (CIF) environment by integrating it with the extended TOPSIS method. In the existing studies, uncertainties, which are present in the data, are handled with either Interval-Valued Intuitionistic Fuzzy Sets (IVIFS) or Intuitionistic Fuzzy Set (IFS) information, which may lose some useful information of alternatives. On the other hand, CIF Set (CIFS) handles the uncertainties by considering both the IVIFS and IFS simultaneously. Thus, motivated by this, in the present work, some series of distance measures between the pairs of CIFSs were presented, and their various relationships were investigated. Further, under this environment, a group decision-making method based on the proposed measure was presented by considering the dierent priority pairs of the decision-makers. A practical example was provided to verify the developed approach and, demonstrate its practicality and feasibility, their results were compared with those of the several existing approaches.
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Interval-valued Trapezoidal Intuitionistic Fuzzy Generalized Aggregation Operators and Application to Multi-attribute Group Decision Making

Interval-valued Trapezoidal Intuitionistic Fuzzy Generalized Aggregation Operators and Application to Multi-attribute Group Decision Making

Since the three characteristic functions of IVTrIFNs are all piecewise continuous, their function images are the plain regions, as depicted in Figure 1. We view them as sheets with uniform density and calculate their barycentric coordinates. For the MAGDM in intuitionistic fuzzy environments, the ranking of in- tuitionistic fuzzy numbers plays an important role. In order to compare the IVTrIFNs, it is necessary to develop a method to rank the IVTrIFNs. Mo- tivated by the score and accuracy functions of IFS [48], we dene the expectation and expectant score of IVTrIFNs and thereby propose a new ranking method of IVTrIFNs.
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