A Deviation-Based Approach to Intuitionistic Fuzzy Multiple Attribute Group Decision Making

The aim of this article is to investigate the approach to multiple attribute group decision making (MAGDM) with intuitionistic fuzzy information. We first introduce a deviation measure between two intuitionistic fuzzy numbers, and then utilize the intuitionistic fuzzy hybrid aggregation operator to aggregate all individual intuitionistic fuzzy decision matrices into a collective intuitionistic fuzzy decision matrix. Based on the deviation measure, we develop an optimization model by which a straightforward formula for deriving attribute weights can be obtained. Furthermore, based on the intuitionistic fuzzy weighted averaging operator and information theory, we utilize the score function and accuracy function to give an approach to ranking the given alternatives and then selecting the most desirable one(s). In addition, we extend the above results to MAGDM with interval-valued intuitionistic fuzzy information.     

Intuitionistic Fuzzy Ordered Weighted Cosine Similarity Measure

The aim of this paper is to introduce the intuitionistic fuzzy ordered weighted cosine similarity (IFOWCS) measure by using the cosine similarity measure of intuitionistic fuzzy sets and the generalized ordered weighted averaging (GOWA) operator. Some desirable properties and different families of the IFOWCS measure are investigated. The prominent characteristics of the IFOWCS measure are that not only it is a generalization of some widely used similarity measure, but also it can deal with the correlation of different decision matrices or multi-dimensional arrays for intuitionistic fuzzy values. We further generalize the IFOWCS measure and obtain the intuitionistic fuzzy ordered weighted similarity (IFOWS) measure. In the end, the IFOWS measure with existing similarity measures are compared with the IFOWCS measure by an illustrative example.     

Multiple Attribute Group Decision-Making Methods with Completely Unknown Weights in Intuitionistic Fuzzy Setting and Interval-Valued Intuitionistic Fuzzy Setting

The existing multiple attribute group decision-making approaches based on intuitionistic fuzzy sets (IFSs) or interval-valued intuitionistic fuzzy sets (IVIFSs) are considered as the situation that the weights of experts are given beforehand and the attribute weights are known or unknown. To better describe the uncertain decision environment and solve the corresponding decision problem, multiple attribute group decision-making methods with completely unknown weights of both experts and attributes are proposed in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting. Entropy weight models can be used to determine the weights of both experts and attributes from intuitionistic fuzzy decision matrices or interval-valued intuitionistic fuzzy decision matrices, and then the evaluation formulas of weighted correlation coefficients between alternatives and the ideal alternative are introduced in intuitionistic fuzzy setting and interval-valued intuitionistic fuzzy setting. The alternatives can be ranked and the most desirable one(s) can be selected according to the values of the weighted correlation coefficients for IFSs or IVIFSs. Finally, two numerical examples demonstrate the effectiveness of the proposed methods: they are capable for handling the multiple attribute group decision-making problems with completely unknown weights.     

Interval-Valued Intuitionistic Fuzzy WASPAS Method: Application in Reservoir Flood Control Management Policy

Interval-valued intuitionistic fuzzy sets (IVIFSs) are very flexible tool to cope with the uncertainty arises in multi-criteria decision making (MCDM) problems. In recent times, MCDM problems with interval-valued intuitionistic fuzzy information have achieved more attention from researchers in different areas and consequently, several MCDM methods have been extended for IVIFSs. In this paper, a novel approach based on WASPAS method is developed under IVIFSs. The developed method is based on the operators of IVIFSs, some amendments in the classical WASPAS method and a new process for calculation of criteria and decision experts’ weights. In process for calculating weights, new procedures is propoesd to compute the decision experts’ weights and criteria weights based on interval-valued intuitionistic fuzzy information measures (entropy, divergence and similarity measures) to achieve more realistic weights. Innovative information measures are developed based on the exponential function for IVIFSs to determine the weights of the criteria and decision experts. Since the uncertainty is an unavoidable feature of MCDM problems, the developed method can be a constructive tool for decision-making in an uncertain environment. Further, an uncertain decision making problem of reservoir flood control management policy is implemented with interval-valued intuitionistic fuzzy information, which reveals the effectiveness and reliability of the proposed IVIF-WASPAS method. To validate the result, comparative analysis with existing methods and sensitivity analysis are presented under interval-valued intuitionistic fuzzy environment.     

Compatibility Analysis of Intuitionistic Fuzzy Preference Relations in Group Decision Making

Compatibility analysis is an efficient and important tool used to measure the consensus of opinions within a given group of individuals. In this paper, we give a compatibility measure between intuitionistic preference values and a compatibility measure between intuitionistic preference relations, respectively, and study their properties. It is shown that each individual intuitionistic preference relation and the collective intuitionistic preference relation is perfectly compatible if and only if all the individual intuitionistic preference relations are perfectly compatible. Based on the compatibility measures, a consensus reaching procedure in group decision making with intuitionistic preference relations is developed, and a method for comparing intuitionistic fuzzy values is pointed out, by which the considered objects are ranked and selected. In addition, we extend the developed measures, procedure and method to accommodate group decision making situations with interval-valued intuitionistic preference relations. Numerical analysis on our results through an illustrative example is also carried out.     

Multi-criteria Group Decision-Making Method Based on Intuitionistic Interval Fuzzy Information

For problems in multi-criteria group decision-making (MCGDM), this paper defines intuitionistic interval numbers, and the operational laws and comparison method of it. Some intuitionistic interval information aggregation operators are proposed, such as intuitionistic interval weighted arithmetic averaging operator, intuitionistic interval weighted geometric averaging operator, intuitionistic interval ordered weighted averaging operator, intuitionistic interval heavy averaging operator and intuitionistic interval aggregating operator. Then, based on intuitionistic interval fuzzy information, a method is developed to handle the problems in MCGDM. In this method, by applying the knowledge level of the experts to the decision making problem, the model of maximizing comprehensive membership coefficient is constructed to determine the weights of decision makers. By calculating the distances to the ideal and negative ideal solutions, the comprehensive attribute values and the rank of the alternatives can be obtained. Finally, an example is provided to demonstrate the feasibility and effectiveness of the proposed method.     

Uncertain Power Average Operators for Aggregating Interval Fuzzy Preference Relations

In this paper, we investigate group decision making problems based on interval fuzzy preference relations. We define an uncertain power weighted average (UPWA) operator and an uncertain power ordered weighted average (UPOWA) operator, on the basis of the power average operator of Yager (IEEE Trans Syst Man Cybern A 31:724–731, 1988) and the uncertain geometric mean. In the situations where the weights of experts are known, we develop a method based on the UPWA operator for group decision making with interval fuzzy preference relations; and in the situations where the weights of experts are unknown, we develop a method based on the UPOWA operator for group decision making with interval fuzzy preference relations.     

Multiple Attribute Group Decision Making Method Based on Utility Theory Under Interval-Valued Intuitionistic Fuzzy Environment

In this paper, a kind of multiple attribute group decision making problem is studied, where there is no original information about the weights of importance of the attributes and the decision makers (DMs), and the attribute values are given in the form of interval-valued intuitionistic fuzzy numbers (IVIFNs). To solve this problem, a new method is proposed based on utility theory. In the proposed method, the weights of importance of the DMs and the attributes are all determined by using the intuitionistic indexes of related IVIFNs. And then, the alternatives are compared by using their composite interval indexes which are generated based on utility theory. Finally, two numerical examples are proposed to demonstrate the effectiveness of the proposed method.     

Fuzzy Group Decision Making for the Selection of Facility Location

In this paper, fuzzy group decision making based on extension of TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method which was proposed by Chen (Fuzzy Sets Syst, 114:1–9, 2000) is adopted for facility location selection. In this method, the ratings of various alternatives versus various subjective criteria and the weights of all criteria are assessed in linguistic variables represented by fuzzy numbers. By fuzzy numbers, it has been tried to resolve the ambiguity of concepts that are associated with human being’s judgments. To determine the order of the alternatives, closeness coefficient is defined by calculating the distances to the fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS). In Chen’s approach, the distance between two fuzzy numbers is calculated with vertex method. But in this study, different distance measurement methods are used and the results are compared. Finally the proposed method has been applied to a facility location selection problem of a textile company in Turkey.     

Multicriteria Group Decision-Making Method Using Vector Similarity Measures For Trapezoidal Intuitionistic Fuzzy Numbers

Based on the extension of the Jaccard, Dice, and cosine similarity measures, three vector similarity measures between trapezoidal intuitionistic fuzzy numbers (TIFNs) are proposed in the vector space and are applied to the fuzzy multicriteria group decision-making problem, in which the criteria weights and the evaluated values in decision matrix are expressed by TIFNs. Through the weighted similarity measures between each alternative and the ideal alternative, the ranking order of all the alternatives can be determined and the best one(s) can be easily identified as well. A practical example of the developed approaches is given to select the investment alternatives. The decision results of different similarity measures demonstrate that the three similarity measures have better similarity identification. The illustrative example shows that the proposed methods are applicable.     

Continuous Ordered Weighted Distance Measure and Its Application to Multiple Attribute Group Decision Making

We develop a new distance measure called the continuous ordered weighted distance (COWD) measure by using the continuous ordered weighted averaging (COWA) operator in the interval distance. We study some properties and different families of the COWD measure. We further generalize the COWD measure. The prominent characteristics of the COWD measure are that it is not only a generalization of some widely used distance measures and the continuous generalized OWA operator, but also it can deal with interval deviations in aggregation on interval arguments by using a controlled parameter. The desirable characteristics make the COWD measure be suitable to wide range situations, such as decision making, engineering and economics. In the end, we develop the new approach to group decision making in investment selection.     

A linguistic decision process in group decision making

Assuming a set of linguistic preferences representing the preferences of the individuals, a linguistic choice process is presented. This is developed using the concept of fuzzy majority for deriving a collective linguistic preference, and the concept of nondominated alternatives for deriving the selected alternatives in the linguistic choice process. The fuzzy majorities are equated with fuzzy linguistic quantifiers. The collective linguistic preference is derived by means of a linguistic ordered weighted averaging operator whose weights are defined using a fuzzy linguistic quantifier. In order to obtain the nondominated alternatives, we present a novel reformulation of Orlovski's nondominance degree under linguistic information.     

An Acceptable Consistency-Based Framework for Group Decision Making with Intuitionistic Preference Relations

This article studies acceptable consistency of intuitionistic preference relations (IPRs) and examines how to aggregate individual IPRs into a collective judgment in a group decision making (GDM) context. A consistency index is first introduced to measure the consistency level, thereby defining acceptable consistency for IPRs. If a decision-maker is unwilling or unavailable to revise his/her judgment for an IPR with unacceptable consistency, an automated approach is developed to improve its consistency to an acceptable level. The acceptably consistent IPRs are subsequently aggregated into a group opinion by using an induced ordered weighted averaging operator. A procedure is then proposed to solve GDM problems with IPRs. An illustrative example is presented to demonstrate the effectiveness and applicability of the proposed approach.     

The Continuous Quasi-OWA Operator and its Application to Group Decision Making

In this paper, we extend the Quasi-OWA operator to the case in which the input argument is a continuous valued interval and present the continuous Quasi-OWA (C-QOWA) operator, which generalizes a wide range of continuous operators such as the continuous ordered weighted averaging (C-OWA) operator, the continuous generalized OWA operator (C-GOWA) and the continuous generalized ordered weighted logarithm aggregation (C-GOWLA) operator. Then an orness measure to reflect the or-like degree of the C-QOWA operator is proposed. Moreover, some desirable properties of the C-QOWA operator associated with its orness measure are investigated. In addition, we apply the C-QOWA operator to the aggregation of multiple interval arguments and obtain the weighted C-QOWA operator, the ordered weighted C-QOWA (OWC-QOWA) operator, the combined C-QOWA (CC-QOWA) operator. Finally, a CC-QOWA operator-based approach for multi-attribute group decision making problem is presented, and a numerical example shows that the developed approach is feasible and the results are credible.     

Consistency in MCGDM Problems with Intuitionistic Fuzzy Preference Relations Based on an Exponential Score Function

This paper investigates an approach for multiple criteria decision making problems with intuitionistic fuzzy preference relations (IFPRs). An exponential score function for intuitionistic fuzzy numbers is developed. Its novelty is that it can convert an IFPR into a multiplicative preference relation. Then, the exponential score preference relation is introduced and its associated optimal transfer matrix is proposed. The optimal transfer matrix can guarantee the consistency via the additive transitivity property. Furthermore, an optimal model for aggregating group IFPRs to reach consistency is proposed. Finally, a group decision making approach and a multi-criteria decision making approach with IFPRs are presented.     

Generalized Hybrid Aggregation Operators Based on the 2-Dimension Uncertain Linguistic Information for Multiple Attribute Group Decision Making

With respect to the multiple attribute decision making problems in which the attribute values take the form of the 2-dimension uncertain linguistic information, a new method based on the generalized hybrid operators is proposed. Firstly, the definition, properties, expectations and ranking method of 2-dimension uncertain linguistic information are introduced, and the operational laws the 2-dimension uncertain linguistic information are defined. Then some aggregation operators, including 2-dimension uncertain linguistic generalized weighted average operator, 2-dimension uncertain linguistic generalized ordered weighted average operator, and 2-dimension uncertain linguistic generalized hybrid weighted average operator, are developed, and some properties and special cases of them are also discussed. Finally, these operators are applied to multi-criteria decision making and an illustrative example is given to verify the developed approach and to demonstrate its effectiveness.     

An Extended PROMETHE II Multi-Criteria Group Decision Making Technique Based on Intuitionistic Fuzzy Logic for Sustainable Energy Planning

The implementations of Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE) category to complex multi-criteria group decision making (MCGDM) scenarios have been included in thousands areas. Outranking methods such as PROMETHEE II are also greatly employed in energy planning application. In MCGDM methods if decision makers (DMs) are not able to treat precise data in order to define their preferences, the intuitionistic fuzzy set (IFS) theory enables them. IFS attributes are connected with the degree of membership and non-membership, and can be used to draw uncertainty in group decision-making situations. In this paper, a new version of the PROMETHEE II method is proposed, aiming at solving MCGDM problems. Linguistic variables are expressed in the membership function and non-membership function of IFS which are used to assess the weights of all criteria and the ratings of each alternative with respect to each criteria. Conditional normalized Euclidean distance measure is adopted to measure deviations between alternatives on intuitionistic fuzzy set. Then, a ranking algorithm is applied to indicate the order of superiority of alternatives. Finally, a practical example is given to an application of sustainable energy planning to verify our proposed method. Additionally, a comparative analysis is done among the proposed PROMETHEE II method and the intuitionistic fuzzy technique for order preference by similarity to ideal solution (IF-TOPSIS) method and elimination and choice translating reality method (IF-ELECTRE).     

Prioritization and Aggregation of Intuitionistic Preference Relations: A Multiplicative-Transitivity-Based Transformation from Intuitionistic Judgment Data to Priority Weights

This article proposes a goal programming framework for deriving intuitionistic fuzzy weights from intuitionistic preference relations (IPRs). A new multiplicative transitivity is put forward to define consistent IPRs. By analyzing the relationship between intuitionistic fuzzy weights and multiplicative consistency, a transformation formula is introduced to convert normalized intuitionistic fuzzy weights into multiplicative consistent IPRs. By minimizing the absolute deviation between the original judgment and the converted multiplicative consistent IPR, two linear goal programming models are developed to obtain intuitionistic fuzzy weights from IPRs for both individual and group decisions. In the context of multicriteria decision making with a hierarchical structure, a linear program is established to obtain a unified criterion weight vector, which is then used to aggregate local intuitionistic fuzzy weights into global priority weights for final alternative ranking. Two numerical examples are furnished to show the validity and applicability of the proposed models.     

Generalized Multiple Averaging Operators and their Applications to Group Decision Making

In this paper, we present a new operator called the generalized ordered weighted multiple averaging (GOWMA) operator based on a minimization problem with penalty function, which unifies the geometric mean and the generalized ordered weighted averaging operator with the generalized ordered weighted harmonic averaging operator in the same formulation. We study different properties and families of the GOWMA operator and develop a generalization of this operator called the generalized hybrid multiple averaging operator. To determine the GOWMA operator weights, we propose the generalized least squares method which does not follow a regular distribution. Finally, we give a numerical example of an investment selection to illustrate the application of the GOWMA operator to multiple attribute group decision making.     

A Note on Linguistic Hybrid Arithmetic Averaging Operator in Multiple Attribute Group Decision Making with Linguistic Information

In this paper, we propose a linguistic hybrid arithmetic averaging (LHAA) operator, which is based on linguistic weighted arithmetic averaging (LWAA) operator and extended ordered weighted averaging (EOWA) operator, and study some desirable properties of the LHAA operator. The LHAA operator can not only reflect the importance degrees of both the given argument and its ordered position, but also relieve the influence of unfair arguments on the decision results by weighting these arguments with small values. Based on the LWAA and LHAA operators, we develop a practical approach to multiple attribute group decision making under linguistic environment. The approach first aggregates the individual linguistic preference values into a collective linguistic preference value for each alternative by using the LWAA and LHAA operators (it is worth pointing out that the aggregation process does not produce any loss of linguistic information), and then orders the collective linguistic preference values to obtain the best alternative(s). Finally, an illustrative example is also given to verify the approach and to demonstrate its feasibility and practicality.