Group Decision-making Procedure Research Articles

Necessary and possible hesitant fuzzy sets: A novel model for group decision making

We propose an extension of Torra’s notion of hesitant fuzzy set, which appears to be well suited to group decision making. In our model, indecisiveness in judgements is described by two nested hesitant fuzzy sets: the smaller, called necessary, collects membership values determined according to a rigid evaluation, whereas the larger, called possible, comprises socially acceptable membership values. We provide several instances of application of our methodology, and accordingly design suitable individual and group decision procedures. This novel approach displays structural similarities with Atanassov’s intuitionistic fuzzy set theory, but has rather different goals. Our source of inspiration comes from preference theory, where a bi-preference approach has proven to be a useful extension of the classical mono-preference modelization in the fields of decision theory and operations research.

Linguistic intuitionistic fuzzy Hamacher aggregation operators and their application to group decision making

Linguistic intuitionistic fuzzy variables (LIFVs) can efficiently denote the qualitative preferred and non-preferred cognitions of decision makers. This paper researches group decision making with linguistic intuitionistic fuzzy information. To do this, several Hamacher operational laws on LIFVs are defined. To derive the comprehensive evaluating values of alternatives, several linguistic intuitionistic fuzzy Hamacher aggregation operators are proposed, including the linguistic intuitionistic fuzzy Hamacher weighted average operator, the linguistic intuitionistic fuzzy Hamacher weighted geometric mean operator, the linguistic intuitionistic fuzzy Hamacher ordered weighted average operator, the linguistic intuitionistic fuzzy Hamacher ordered weighted geometric mean operator, the linguistic intuitionistic fuzzy Hamacher hybrid weighted average operator, and the linguistic intuitionistic fuzzy Hamacher hybrid weighted geometric mean operator. Then, several of their desirable properties are researched to guarantee the rationality. Methods for determining the weights of criteria, decision makers as well as the ordered positions are offered, respectively. After that, a procedure for group decision making with linguistic intuitionistic fuzzy information is provided. Finally, a group decision-making problem is offered to illustrate the application of the new results.

Fit between humanitarian professionals and project requirements: hybrid group decision procedure to reduce uncertainty in decision-making

Choosing the right professional that has to meet indeterminate requirements is a critical aspect in humanitarian development and implementation projects. This paper proposes a hybrid evaluation methodology for some non-governmental organizations enabling them to select the most competent expert who can properly and adequately develop and implement humanitarian projects. This methodology accommodates various stakeholders’ perspectives in satisfying the unique requirements of humanitarian projects that are capable of handling a range of uncertain issues from both stakeholders and project requirements. The criteria weights are calculated using a two-step multi-criteria decision-making method: (1) fuzzy analytical hierarchy process for the evaluation of the decision maker weights coupled with (2) technique for order preference by similarity to ideal solution to rank the alternatives which provide the ability to take into account both quantitative and qualitative evaluations. Sensitivity analysis have been developed and discussed by means of a real case of expert selection problem for a non-profit organisation. The results show that the approach allows a decrease in the uncertainty associated with decision-making, which proves that the approach provides robust solutions in terms of sensitivity analysis.

Fair stable sets of simple games

Simple games are abstract representations of voting systems and other group-decision procedures. A stable set—or von Neumann–Morgenstern solution—of a simple game represents a “standard of behavior” that satisfies certain internal and external stability properties. Compound simple games are built out of component games, which are, in turn, “players” of a quotient game. I describe a method to construct fair—or symmetry-preserving—stable sets of compound simple games from fair stable sets of their quotient and components. This method is closely related to the composition theorem of Shapley (1963c), and contributes to the answer of a question that he formulated: What is the set G of simple games that admit a fair stable set? In particular, this method shows that the set G includes all simple games whose factors—or quotients in their “unique factorization” of Shapley (1967)—are in G, and suggests a path to characterize G.

Fair Stable Sets of Simple Games

Simple games are abstract representations of voting systems and other group-decision procedures. A stable set—or von Neumann-Morgenstern solution—of a simple game represents a “standard of behavior” that satisfies certain internal and external stability properties. Compound simple games are built out of component games, which are, in turn, “players” of a quotient game. I describe a method to construct fair—or symmetry-preserving—stable sets of compound simple games from fair stable sets of their quotient and components. This method is closely related to the composition theorem of Shapley (1963), and contributes to the answer of a question that he formulated: What is the set G of simple games that have a fair stable set? In particular, this method shows that the set G includes all simple games whose factors―or quotients in their “unique factorization” of Shapley (1967)―are in G, and suggests a path to characterize G.

Several New Interval-Valued Intuitionistic Fuzzy Hamacher Hybrid Operators and Their Application to Multi-Criteria Group Decision Making

Interval-valued intuitionistic fuzzy sets (IVIFSs) contain three ranges, namely the membership degree range, the non-membership degree range, and the hesitancy degree range, and they are very suitable for depicting uncertain or fuzzy information. In the course of decision making with IVIFSs, interval-valued intuitionistic fuzzy aggregation operators play a very important role and have received considerable attention in recent years. In this paper, we note the drawbacks of existing aggregation operators for IVIFNs. Some new interval-valued intuitionistic fuzzy Hamacher hybrid aggregation operators, such as the interval-valued intuitionistic fuzzy Hamacher hybrid arithmetical averaging operator and the interval-valued intuitionistic fuzzy Hamacher hybrid arithmetical geometric operator, are introduced to overcome the drawbacks of the existing operators. All of these newly developed operators can weigh both the interval-valued intuitionistic fuzzy arguments and their ordered positions simultaneously, and they have several desirable properties, such as idempotency, boundedness, and monotonicity. To show the applications of our proposed hybrid aggregation operators, we propose a simple procedure for multi-criteria group decision making with interval-valued intuitionistic fuzzy information and then use a numerical example to illustrate the validity and applicability of the proposed procedure and operators.

Group Decision Procedure to Model the Dependency Structure of Complex Systems: Framework and Case Study for Critical Infrastructures

This paper proposes a group decision framework to model the dependency structure of a complex system based on expert surveys. The proposed framework is designed to systematically populate a dependency matrix whose entry indicates the degree that its row element is influenced by its column element. The degree of dependency is assessed based on two different perspectives-of the influencing element and of the influenced element-and the assessments with the two perspectives are separately compiled and compared in the initial round survey. Entries with large assessment gaps are classified as discussion items and a group decision procedure to reduce the gaps in these items is applied in the consensus round survey. A case study for dependency modeling of critical infrastructures of South Korea was conducted using the proposed framework and its effectiveness was demonstrated. The analysis on the results of the case study discovered an insight that the opinions from the influenced elements are more convincing and respected in the consensus round than those from the influencing elements.

Levels of incomplete information in group decision models – A comprehensive simulation study

We present a comprehensive computational study on the effects of providing different forms of incomplete preference information in additive group decision models. We consider different types of information on individual preferences, and on weights of the group members, and study their effects on conclusiveness, efficiency and fairness of outcomes at the group level. Furthermore, we analyze possible violations of the axiom of independence of irrelevant alternatives (IIA) as well as the impact of problem characteristics, in particular initial agreement between group members. Our results indicate that providing information in the form of a ranking of differences between consecutive alternatives comes close to providing exact cardinal preference information in several outcome dimensions. However, group decision procedures based on incomplete preference information also show a significant amount of violations of the IIA axiom.

Some Hesitant Fuzzy Information Aggregation Operators Based on Einstein Operational Laws

The performance and development review (PADR) evaluation in a company is a complex group decision-making problem that is influenced by multiple and conflicting objectives. The complexity of the PADR evaluation problem is often due to the difficulties in determining the degrees of an alternative that satisfies the criteria. In this paper, we present a hesitant fuzzy multiple criteria group decision-making methods for PADR evaluation. We first develop some operations based on Einstein operations. Then, we proposed some aggregation operators to aggregate hesitant fuzzy elements and the relationship between our proposed operators and the existing ones are discussed in detail. Furthermore, the procedure of multicriteria group decision making based on the proposed operators is given under hesitant fuzzy environment. Finally, a practical example about PADR evaluation in a company is provided to illustrate the developed method.

Automatic procedures for group decision making with intuitionistic fuzzy preference relations

The intuitionistic fuzzy preference relation (IFPR), whose elements are intuitionistic fuzzy values, is a powerful structure in expressing the comprehensive preference information of a person. In this paper, after reviewing different kinds of consistency for IFPR, we construct a mathematical model to derive the underlying crisp weighting vector from a multiplicative consistent IFPR. Such method is very easy to be understood. As to multiplicative inconsistent IFPR, we claim that there are two ways to repair it, which are interactive method and automatic method. When the expert does not want to interact with the analyst, or if the analyst cannot find the initial expert to re-evaluate and alter his/her preferences, or if consistency must be urgently obtained, the proposed automatic algorithm is efficient and useful. Finally, we propose a procedure for group decision making with IFPRs based on the multiplicative consistency of IFPRs. It is proven that if all individual IFPRs are multiplicative consistent, their overall IFPR fused by IFWG operator is also multiplicative consistent. Some numerical examples are given to illustrate the validity and applicability of the proposed methods.

INTUITIONISTIC FUZZY PRIORITIZED OPERATORS AND THEIR APPLICATION IN MULTI-CRITERIA GROUP DECISION MAKING

Intuitionistic fuzzy set is a very useful tool to depict uncertainty. Lots of multi-criteria group decision making methods under intuitionistic fuzzy environment have been developed. Current methods are under the assumption that the criteria and the decision makers are at the same priority level. However, in real group decision making problems, criteria and decision makers have different priority level commonly. In this paper, multi-criteria group decision making problems where there exists a prioritization relationship over the criteria and decision makers are studied. First, the intuitionistic fuzzy prioritized weighted average (IFPWA) and the intuitionistic fuzzy prioritized weighted geometric (IFPWG) operators are proposed. Then, some of their desirable properties are investigated in detail. Furthermore, the procedure of multi-criteria group decision making based on the proposed operators is given under intuitionistic fuzzy environment. Finally, a practical example about talent introduction is provided to illustrate the developed method.

A fuzzy-normalisation-based group decision-making approach for prioritising engineering design requirements in QFD under uncertainty

Quality function deployment (QFD) is often implemented to transform customer requirements (CRs) into the engineering design requirements (DRs) of a new product. Prioritising engineering DRs is essential to reasonably allocate resources for the new product development, and often must be done under uncertainty due to the vagueness and impreciseness of the judgments made by customers and QFD team members, and is a typical group decision behaviour that requires the active participation of multiple customers and multiple QFD design team members. Fuzzy set theory provides a theoretical basis for solving such group decision-making problems under uncertainty. Existing approaches for prioritising DRs under uncertainty usually simplify the group decision-making problem as non-group decision making for solution by simply aggregating individuals’ opinions using their arithmetic averages. This paper proposes a different fuzzy group decision-making procedure for prioritising DRs under uncertainty. The proposed approach does not aggregate the individual judgments of customers and QFD design team members, but rather aggregates the technical importance ratings of DRs, and can produce more rational and robust priority rankings for DRs through fuzzy normalisation. A real design case of a flexible manufacturing system (FMS) is examined to show the effectiveness and the potential applications of the proposed approach. Results are compared with those obtained by two known approaches.

Hesitant fuzzy prioritized operators and their application in multi-criteria group decision making

Hesitant fuzzy set is a very useful technique in the situations where there are some difficulties in determining the membership of an element to a set. Some aggregation methods have been developed for hesitant fuzzy information. Current aggregation methods are under the assumption that the criteria are at the same priority level. However, in real decision making problems, criteria have different priority level commonly. In this paper, we investigated multi-criteria group decision making problems where a prioritization relationship existed over the criteria under hesitant fuzzy environment. Firstly, we propose the hesitant fuzzy prioritized weighted average (HFPWA) and the hesitant fuzzy prioritized weighted geometric (HFPWG) operators. Then, some of their desirable properties are studied in detail. Furthermore, the procedure of multi-criteria group decision making based on the proposed operators is given under hesitant fuzzy environment. Finally, a practical example about talent introduction is provided to illustrate the developed method. Key words: Group decision making, hesitant fuzzy set, hesitant fuzzy prioritized weighted average operator, hesitant fuzzy prioritized weighted geometric operator.

On Consensus of Group Decision Making with Interval Utility Values and Interval Preference Orderings

Uncertainty is a common phenomenon in our real world. Interval utility values and interval preference orderings are two of the simplest and most convenient tools to describe uncertain preferences in decision making. In this paper, we investigate consensus problems in group decision making with interval utility values and interval preference orderings. We first establish their transformation relations, and give a formula for calculating the association coefficients of individual uncertain preferences and group ones. We then develop a consensus procedure for group decision making with interval utility values and interval preference orderings, which takes interval utility values as the uniform preference representation. This procedure can be reduced to a series of processes for dealing with some special group decision making situations, such as: group decision making with utility values and preference orderings, group decision making with interval utility values, group decision making with interval preference orderings, etc. Finally, we illustrate the applications of the developed procedures with two practical examples.

Personnel selection based on computing with words and fuzzy MULTIMOORA

Personnel selection process is aimed at choosing the best candidate to fill the defined vacancy in a company. It determines the input quality of personnel and thus plays an important role in human resource management. Given the uncertain, ambiguous, and vague nature of personnel selection process, it requires the application of multi-criteria decision making (MCDM) methods for robust recruitment. This paper hence is aimed at extending the fuzzy MULTIMOORA for linguistic reasoning under group decision making. The fuzzy MULTIMOORA was further modified in this study. The fuzzy MULTIMOORA for group decision making (MULTIMOORA–FG) enables to aggregate subjective assessments of the decision-makers and thus offer an opportunity to perform more robust personnel selection procedures. A personnel selection problem illustrated the group decision-making procedure according to MULTIMOORA–FG: the enterprise has formed an executive committee consisting of four decision-makers to choose the best candidate from another four participants to fill the vacancy. The committee has decided to consider eight qualitative attributes expressed in linguistic variables. The numerical example exhibited possibilities for improvement of human resources management as well as any other business decision area by applying MULTIMOORA–FG.

MULTIMOORA-FG: A Multi-Objective Decision Making Method for Linguistic Reasoning with an Application to Personnel Selection

This paper aims to extend fuzzy MULTIMOORA with linguistic reasoning and group decision-making (MULTIMOORA-FG). The new method consists of the three parts, namely the fuzzy Ratio System, the fuzzy Utopian Reference Point, and the fuzzy Full Multiplicative Form offering a robust comparison of alternatives against multiple objectives. In addition, MULTIMOORA-FG is designed to deal with triangular fuzzy numbers which, in turn, can resemble linguistic variables. MULTIMOORA-FG is a proper instrument for linguistic reasoning under fuzzy environment. In our study an application of personnel selection illustrates the group decision-making procedure according to MULTIMOORA-FG. Given the uncertainties peculiar of personnel selection, the application of multi-objective decision making (MODM) is required in this area. Fuzzy MULTIMOORA enables to aggregate subjective assessments of the decision-makers and thus offer an opportunity to perform a more robust personnel selection. The committee decided to consider eight qualitative characteristics expressed in linguistic variables. A numerical example exhibited possibilities for improvement of human resources management or any other business decision-making by applying MULTIMOORA-FG.

A note on group decision-making procedure based on incomplete reciprocal relations

In a very recent paper by Xu and Chen (Soft Comput 12:515–521, 2008), a novel procedure for group decision making with incomplete reciprocal relations was developed. In this note, we examine the function between the fuzzy preference relation and its corresponding priority vector developed by Xu and Chen with a numerical example and show that the function does not hold in general cases. Then, we deduce an exact function between the additive transitivity fuzzy preference relation and its corresponding priority vector. Based on this, we develop a procedure for the decision making with an incomplete reciprocal relation and also develop a procedure for the group decision making with incomplete reciprocal relations. In order to compare the performances of our method with Xu and Chen’s method in fitting the reciprocal relation, we introduce some criteria. Theoretical analysis and numerical examples have shown that the function deduced by us is more reasonable and effective than Xu and Chen’s.

Interactive group decision making procedure based on uncertain multiplicative linguistic preference relations

Group decision making problems are investigated with uncertain multiplicative linguistic preference relations. An unbal- anced multiplicative linguistic label set is introduced, which can be used by the experts to express their linguistic preference informa- tion over alternatives. The uncertain linguistic weighted geometric mean operator is utilized to aggregate all the individual uncer- tain multiplicative linguistic preference relations into a collective one, and then a simple approach is developed to determining the experts' weights by utilizing the consensus degrees among the individual uncertain multiplicative linguistic preference relations and the collective uncertain multiplicative linguistic preference re- lations. Furthermore, a practical interactive procedure for group decision making is proposed based on uncertain multiplicative lin- guistic preference relations, in which a possibility degree formula and a complementary matrix are used to rank the given alterna- tives. Finally, the proposed procedure is applied to solve the group decision making problem of a manufacturing company searching the best global supplier for one of its most critical parts used in assembling process.

Group Decision-making in Child Welfare and the Pursuit of Participation

In institutional social work, decision-making is a core task that increasingly involves more than one professional as well as, frequently, the clients. Group decision-making is fundamentally different from individual decision-making in that it is an inherently social activity calling for the communicative competencies of those involved. In this article, we describe group decision-making procedures for a specific setting of German child welfare. Condensing our findings into an idealised model of decision-making, we attempt to show how communicative and interactive exigencies conflict with decision-making rationalities. We go on to discuss the consequences this conflict has on the participation of clients in the decision-making process, arguing that social workers are likely to address both rationales separately. We show that accordingly, participation in the interaction does not necessarily safeguard a partaking in the decision.

A recursive group decision-making procedure for choosing qualified individuals

A recursive group decision-making procedure for choosing qualified individuals