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).     

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.     

A Study on Aggregation of TOPSIS Ideal Solutions for Group Decision-Making

The technique for order preference by similarity to ideal solution (TOPSIS) has become a popular multi-criteria decision making (MCDM) technique, since it has a comprehensible theoretical structure and is able to provide an exact model for decision making. For the use of TOPSIS in group decisions, the common approaches in aggregating individual decision makers’ judgments are the geometric and the arithmetic mean methods, although these are too intuitive and do not consider either preference levels or preference priorities among alternatives for individual decision makers. In this paper, a TOPSIS group decision aggregation model is proposed in which the construction consists of three stages: (1) The weight differences are calculated first as the degrees of preferences among different alternatives for each decision maker; (2) The alternative priorities are then derived, and the highest one can be denoted as the degree to which a decision maker wants his most favorite alternative to be chosen; (3) The group ideal solutions approach in TOPSIS is used for the aggregation of similarities obtained from different decision makers. A comparative analysis is performed, and the proposed aggregation model seems to be more satisfactory than the traditional aggregation model for solving compromise-oriented decision problems.     

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.     

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 risk-based decision support framework for selection of appropriate safety measure system for underground coal mines

In the context of underground coal mining industry, the increased economic issues regarding implementation of additional safety measure systems, along with growing public awareness to ensure high level of workers safety, have put great pressure on the managers towards finding the best solution to ensure safe as well as economically viable alternative selection. Risk-based decision support system plays an important role in finding such solutions amongst candidate alternatives with respect to multiple decision criteria. Therefore, in this paper, a unified risk-based decision-making methodology has been proposed for selecting an appropriate safety measure system in relation to an underground coal mining industry with respect to multiple risk criteria such as financial risk, operating risk, and maintenance risk. The proposed methodology uses interval-valued fuzzy set theory for modelling vagueness and subjectivity in the estimates of fuzzy risk ratings for making appropriate decision. The methodology is based on the aggregative fuzzy risk analysis and multi-criteria decision making. The selection decisions are made within the context of understanding the total integrated risk that is likely to incur while adapting the particular safety system alternative. Effectiveness of the proposed methodology has been validated through a real-time case study. The result in the context of final priority ranking is seemed fairly consistent.     

A Fuzzy Stochastic Multi-Attribute Group Decision-Making Approach for Selection Problems

The purpose of this paper is to demonstrate how the fuzzy and stochastic approaches as well as multi-attribute group decision-making techniques can be effectively utilized for selection problems in different kinds of uncertainty situations. A group of the decision makers describes a value for an alternative with respect to an attribute by the use of linguistic variables. The rating of each alternative is aggregated, which can be expressed as triangular fuzzy numbers. Then Monte Carlo simulation is applied to generate the performance distribution of alternatives with respect to different attributes in an uncertain environment. Finally, a stochastic compromise ranking technique, known as the VIKOR technique, is developed to evaluate probability distributions for each alternative on each attribute and to prioritize them. The proposed fuzzy stochastic approach is suitable to compromise a solution among the conflicting tangible and intangible attributes under the group decision-making process. In addition, an application of the proposed approach is provided to solve the important risk selection problem in a highway project. The results illustrate its real-life applicability and suitability in discrete group decision-making under uncertainty.     

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.     

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.     

The relative importance of time and dollar values in new product introduction decisions

This study investigates managerial sensitivity to timing differences in new product introduction decisions. Using a case scenario as the research setting, the study finds that in managerial decisions involving a choice between two-attribute alternatives (dollar value and time), respondents shifted their emphasis between attributes when they were personally affected by the decision outcome. Specifically, it was found that an additive constant manipulation (adding a constant to the dollar amount of each alternative) caused respondents to place more emphasis on the time attribute, and a multiplicative constant manipulation (multiplying the dollar amount of each alternative by a constant) caused them to place more emphasis on the dollar-value attribute.The study asks 108 subjects to assume the role of product manager in a case scenario and choose from among three two-attribute alternatives proposed by the case. The personal relevance of the decision was manipulated by telling respondents that the CEO in the decision scenario had stated publicly that the career of the decision maker would be (would not be) affected. The results show that the additive constant and multiplicative constant effects were only found when the decision outcomes would affect the respondents' career.     

An Integrated Group Decision-Making Method Dealing with Fuzzy Preferences for Alternatives and Individual Judgments for Selection Criteria

Organizations often require decisions to be made by a group, and decision makers often have fuzzy preferences for alternatives and individual judgments when attempting to reach an optimal solution. In order to deal with the fuzziness of preference of decision makers, this paper proposes an integrated fuzzy group decision-making method. This method allows group members to express fuzzy preferences for alternatives and individual judgments for solution selection criteria. It also allowed for the weighting of group members. The method then aggregates these elements into a compromise group decision which is the most acceptable for the group as a whole. This method has been implemented and tested. An example is presented to illustrate the method.     

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.     

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.     

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.     

A Relative Entropy Approach to Group Decision Making with Interval Reciprocal Relations Based on COWA Operator

A new approach has been presented based on relative entropy to rank all the alternatives in the group decision making with interval reciprocal relations. First we introduced the continuous ordered weighted averaging operator and used it to aggregate all individual interval reciprocal relations to derive the priority vector. Then we define the consensus indicator of the interval reciprocal relations to determine the weights of experts in the group decision making. Based on the conception of relative entropy, we construct an optimization model to minimize the difference between the group priority vector and all individual priority vectors. We also give the solution to the optimal model, in which we obtain the formula to rank the given alternatives in the group decision making for the collective reciprocal relations and select the most desirable one. Finally, a numerical example shows that the developed approach is feasible and the result is credible.     

Some Hesitant Fuzzy Aggregation Operators with Their Application in Group Decision Making

Hesitancy is the most common problem in decision making, for which hesitant fuzzy set can be considered as a suitable means allowing several possible degrees for an element to a set. In this paper, we study the aggregation of the hesitancy fuzzy information. Several series of aggregation operators are proposed and the connections of them are discussed. To reflect the correlation of the aggregation arguments, two methods are proposed to determine the aggregation weight vectors. Based on the support degrees among aggregation arguments, the weight vector of decision makers are obtained more objectively. To deal with the correlation of criteria, we apply the Choquet integral to get the weights of criteria. A method is also proposed for group decision making under hesitant fuzzy environment.     

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.     

Market Share Overestimation and the Noncomplementarity Effect

Recent research indicates that people tend to overestimate the likelihood of an alternative, particularly when an alternative is considered in isolation rather than as part of a set of alternatives. The present experiment shows that subjective market share overestimation and noncomplementary market share estimates are more likely to be observed for individuals who are high (vs. low) in concern about cognitive closure or when a small (vs. large) set of alternatives is considered. Implications of the results for understanding managerial decision making are discussed.     

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.     

模糊多属性决策法在配送中心选址中的应用

依据配送中心选址的主要因素,从基础设施、自然环境、社会效益、费用以及服务水平等几个方面建立多级评判指标体系,并提供两种模糊多属性决策法对备选配送中心进行优选和排序。最后一个算例方法客观反映实际情况,具有可行性。