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.     

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).     

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.     

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.     

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.     

The Use of Ranking Veto Concept to Mitigate the Compensatory Effects of Additive Aggregation in Group Decisions on a Water Utility Automation Investment

The use of additive models for aggregating group decisions implies they have a compensatory effect in the process of aggregating all decision makers’ (DMs’) preferences. In this kind of model, the final result may produce some extremely undesirable alternatives for one or more DMs. Such alternatives may emerge with a higher ranking than desirable ones, thus generating conflicts and regrets. To overcome this problem the concept of ranking veto is introduced based on a reduction factor combined with the utility of the alternative in order to penalize conflicting alternatives and reduce disagreements in an additive model. A water utility problem was considered as a numerical application to illustrate the model. A decision group method based on MAUT, utility thresholds and a reduction factor is proposed to support group decision in selecting regions that will receive investments in automation over the next 4 years.     

A purchase decision support model considering consumer personalization about aspirations and risk attitudes

Ranking alternative products to help consumers make better purchase choices is a valuable research topic. Most previous decision support models cannot be well applied to heterogeneous consumers. This paper focuses on establishing a personalized interactive model to assist consumers make better buying decisions with less effort. For the alternative products provided by consumers, we collect online reviews and parameter configurations of alternative products and then obtain the fusing evaluative information. As consumers are dominated by bounded rationality, they only provide partially key attribute weights, based on which, we construct an optimizing model to obtain the optimal attribute weights of customers for products. Then, a satisfaction function is proposed by uniting aspiration levels and risk attitudes of consumers and a compensatory decision rules is established to rank and recommend the brands to consumers. Finally, practicability of this study is illustrated with a real car purchase case. Through the case study, it can be seen that the proposed decision support model generates a personalized list of alternatives based on consumer's own utility function about risk attitudes, aspiration levels, and preferences for product attributes, which further confirms that the proposed model can capture the personalized needs of consumers. Theoretical and managerial implications of this model as well as advantages are further illustrated.     

Monte Carlo Simulation Techniques in a Decision Support System for Group Decision Making

This paper describes a group decision support system based on an additive multi-attribute utility model for identifying a consensus strategy in group decision-making problems where several decision-makers or groups of decision-makers elicit their own preferences separately. On the one hand, the system provides procedures to quantify the DMs or group of DMs preferences separately. This involves assessing the DMs or group of DMs component utilities that represent their preferences regarding the respective possible attribute values and objective weights that represent the relative importance of the criteria. On the other hand, we propose Monte Carlo simulation techniques for identifying a consensus strategy. An iterative process will be carried out, where, after the simulations have been performed, the imprecise component utilities and weights corresponding to the different DMs or groups of DMs are tightened to output more meaningful information in the next simulations to achieve a consensus strategy. Finally, an application to the evaluation of remedial strategies for restoring contaminated aquatic ecosystems illustrates the usefulness and flexibility of this decision support tool.     

Are interactive decision aids better than passive decision aids? A comparison with implications for information providers on the internet

While much has been made of the ocean of information available on the Internet, much less emphasis has been placed on how Web surfers might actually be able to process it. This article compares an interactive (user-inputted attribute importance weights) linear computer–assisted decision aid (CADA) format with three passive CADA formats in two studies. The decision environments for these tests are difficult, involving 20 to 30 brands rated on 6 attributes, one of which is negatively correlated with the others. Because the Linear CADA rank order is based on user-inputted attribute weights, it is expected to be more in concordance with the user's preference and hence is predicted to offer higher decision quality and be better liked than the passive formats. Contrary to expectations, however, a passive Equal Weight format performed as well or better than the Linear format on all objective and subjective comparison criteria, while the other two passive formats were not significantly worse on several decision quality criteria. The implications of these findings for information providers on the Internet are also discussed.     

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.     

Conflicting Bifuzzy Multi-attribute Group Decision Making Model with Application to Flood Control Project

We propose a group decision making model based on conflicting bifuzzy sets (CBFS) where evaluation are bi-valued in accordance to the subjective assessment obtained from the experts for the positive and negative views. This paper discusses the weighting methods for particular attribute and subattribute with emphasis given to the unification of subjective and objective weights. The integration of CBFS in the model is naturally done by extending the fuzzy evaluation in parallel with the intuitionistic fuzzy. We introduce a new technique to compute the similarity measure, being the degree of agreement between the experts. We end up the paper by demonstrating the applicability of the proposed model to the empirical case of flood control project, one of the project selection problems.     

A Distance-Based Consensus Model with Flexible Choice of Rank-Position Weights

In this paper we propose a preference aggregation procedure for those cases in which the decision-makers express their preferences by means of a ranking of alternatives. Among the most applied methods for this purpose are those inspired by the Borda–Kendall rule, which attach to each alternative an aggregated value of the votes received in the different rank positions, and those based on distance measures between individual and collective preferences, which look for the solution that maximizes the consensus. The main idea here is to integrate these two approaches. Taking into account that the information about the values of weights or utilities assigned to each rank position is imprecise, we propose an evaluation of the alternatives using that vector of weights that minimizes the disagreement between DMs. In order to solve the problem, mixed-integer linear programming models are constructed. Two numerical examples are examined to illustrate the applicability of the proposed procedure.     

Ordered Weighted Disagreement Functions

In this paper a preference aggregation procedure is proposed for those cases in which decision-makers express their preferences by means of a ranking of alternatives. Among the most commonly applied methods for this purpose are those based on distance measures between individual and collective preferences, which look for the solution that minimizes the disagreement across decision-makers. Some models based on the minimization of the distance between rankings include weights to adjust the relative importance of the agents in the final decision, although in those cases, the weights are related with an a priori evaluation of the individuals and not with the behaviour of the agents in the group decision making process. In the model proposed here, a weighted disagreement function whose emphasis is on the ordered position of the individuals’ disagreement values is developed. In order to solve the problem, a mixed-integer linear programming model is constructed.     

Minimizing Group Discordance Optimization Model for Deriving Expert Weights

This paper focuses on the problem of how to determine expert weights in multiple attribute group decision making. We first aggregate all the individual decision matrices into the collective decision matrix by means of the weighted arithmetic averaging operator, and then from the angle of minimizing group discordance, we establish a general nonlinear optimization model based on deviation function, and employ a genetic algorithm to solve our model so as to find the optimal expert weights. Moreover, we extend our model to uncertain multiple attribute group decision making, where the attribute values are interval numbers, and finally, apply our model to the plan evaluation of new model of cars of an investment company.     

An Integrated Group Decision Making Support Model for Corporate Financing Decisions

The essential goal of corporate finance is to maximize corporate value while reducing a firm’s financial risks. Corporate financing decision is a kind of multi-criteria based group decision making that embodies major approaches to handle qualitative criteria and quantitative limitations. However, in literature related to financing decision making, very little research uses decision making trial and evaluation laboratory (DEMATEL) and analytic network process (ANP) methods to consider the impact and dependency of its factors, or uses Goal programming (GP) to find the satisfactory financing decision under the related financial constraints. This study proposes an integrated group decision making support (GDMS) model to assist corporate financing group decision makers (DMs) in obtaining a satisfactory group solution. ANP, DEMATEL and GP are combined in this GDMS model. By using this model, the group DMs can systemically structure a multi-criteria network framework and derive priority weights of those criteria, and then deal with the quantitative financial constraints for a satisfactory group solution. An illustrative case is demonstrated for the effectiveness and practicability of this GDMS model.     

Attribute Identities Matter: Subjective Perceptions of Attribute Characteristics

Recent research indicates that attributes vary along multiple dimensions with implications for how trade-offs are resolved during choice. We present an exploratory study of the dimensionality underlying naïve subjects ratings of attributes on the characteristics commonly discussed in the literature on tradeoff resolution and decision difficulty. Factor analysis of attribute characteristic assessments indicates that subjects view decision attributes in a multi-dimensional fashion, including an importance/loss aversion dimension, an emotional potential/protection from tradeoffs dimension, and a cognitive difficulty dimension. These results suggest that a one-dimensional measure of attribute characteristics, such as a standard attribute importance rating, may obscure some factors determining individual responses to attributes during decision processing. However, the results also suggest that developing a relatively succinct set of scales in order to characterize the dimensions along with subjects response to attributes is a viable goal for future research.     

A Sample Survey Based Linguistic MADM Method with Prospect Theory for Online Shopping Problems

In MADM problems, the attributes are often rated in linguistic variables, some researchers transform them into numerical values through some formulas. However, it might be inconsistent with real human thinking in some extent. In order to deal with such problems, a sample survey based MADM method with prospect theory is proposed. Firstly, through sampling survey, we collect the data in single point format corresponding to the words, and establish the codebook by mapping words into fuzzy sets, after that fuzzy operation rules are suitable for them. Secondly, based on the reference points, the gain and/or loss matrix is obtained, in accordance with the value function, the prospect value matrix is constructed. Finally, if the attributes are independent, the weighted prospect value of each alternative is computed, if the attributes are dependent, the Choquet integral based prospect value of each alternative is computed. The alternatives are ranked in descending order respect to the defuzzified values. The first alternative is chosen as the best decision result. The feasibility of the proposed method is illustrated through an application in online shopping problem from real life.     

Generalized Ordered Weighted Reference Dependent Utility Aggregation Operators and Their Applications to Group Decision-Making

To quantify the influence of decision makers’ psychological factors on the group decision process, this paper develops a new class of aggregation operators based on reference-dependent utility functions (RUs) in multi-attribute group decision analysis. RUs include S-shaped RU and non-S-shaped RU. Each RU affords a framework where the psychological factors explicitly enter the decision problem via the basic utility function, reference point and loss aversion coefficient. Under the general framework, we derive a generalized ordered weighted S-shaped RU proportional averaging (GOSP) operator and a generalized ordered weighted non-S-shaped RU proportional averaging (GONSP) operator, respectively. The GOSP operator implies the risk attitude of the DM for relative losses is risk-seeking, while GONSP operator indicates the risk attitude in this case is risk-averse. As a special case, GONSP operator can degenerate into GOWPA operator which means that the attitude of the DM is risk-neutral. Each operator satisfies the desirable properties of general operator, i.e., monotonicity, commutativity, idempotency and boundedness. Furthermore, we consider hyperbolic absolute risk aversion (HARA) function as the basic utility function, and define an S-shaped HARA and a non-S-shaped HARA utility functions. Based on the two new RUs, we propose GOSP–HARA operator and GONSP–HARA operator. Every operator covers many existing aggregation operators. To ascertain weights of such operators, the paper builds an attribute-deviation weight model and a DMs-deviation weight model. Based on these RU operators and weight models, an approach is addressed for solving multiple attribute group decision-making problem. At last, an example is provided to show the feasible of our approach.     

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.     

Sensitivity of multiattribute decision models to alternative specifications of weighting parameters

The issue of attribute weighting in multiattribute decision models is examined. Results are presented which show that the outputs produced by linear multiattribute models are extremely robust with respect to alternative specifications of the weighting parameters unless the number of attributes included in the models is small, the average correlation among the attributes is low, and the dispersion of the weights is large relative to their mean. Implications of these results are discussed for three different types of weighting schemes-regression weighting, equal weighting, and subjective weighting—which are used in multiattribute decision modeling.