An Incentive Mechanism-Based Minimum Adjustment Consensus Model Under Dynamic Trust Relationship.

In traditional group decision making, the inconsistent experts are usually forced to make compromises toward the group opinion to increase the group consensus level. However, the strategy of reaching group consensus via an incentive mechanism encouraging adjustment of preferences is more effective than forcing, which is the aim of this article. Specifically, this article establishes a novel incentive mechanism to support group consensus under dynamic trust relationship. First, the supremum and infimum incentives-based rule driven by trust relationship is defined. Based on the assumption that if incentive conditions are met, then experts will be willing to adjust their preferences, the incentive behavior-driven minimum adjustment consensus model is developed to generate optimal incentive-based recommendation preferences. Thus, the proposed incentive mechanism can effectively reduce the preference adjustment cost and promote group consensus reaching. Third, the updated trust relationships between experts are shown to be strengthen by the proposed incentive-driven preference revision. Consequently, the optimization model based on trust interaction relationship is constructed to obtain the final group preference matrix. Finally, a supplier selection case of high-end medical equipment is provided to illustrate the proposed method and show the rationality and advantages of the proposed methodology with both a sensitivity analysis and a comparison analysis.

CD-BFT: Canonical Decomposition-Based Belief Functions Transformation in Possibility Theory.

Based on subjective possibilistic semantics, an agent's subjective probability mass function is dominated by a qualitative Possibility Mass Function (PossMF), which can also be transformed into a unique consonant mass function. However, the existing transformation method cannot maintain the consistency of combination rules, i.e., fusing PossMFs and consonant mass functions with same information content, respectively, the results no longer maintain the reversible transformation. To address the above issue, a novel belief functions transformation is proposed, which can be interpreted based on both Smets' canonical decomposition and Pichon's canonical decomposition. The proposed method is validated based on consistency of combination rules, the least commitment principle, and its application in the fusion of information. In addition, based on the two canonical decompositions, we extend the transformation to possibilistic belief structure, and offer a new perspective of relationship between possibilistic information and evidential information.

An approach to prevent weight manipulation by minimum adjustment and maximum entropy method in social network group decision making.

In social network group decision making (SN-GDM) problem, subgroup weights are mostly unknown, many approaches have been proposed to determine the subgroup weights. However, most of these methods ignore the weight manipulation behavior of subgroups. Some studies indicated that weight manipulation behavior hinders consensus efficiency. To deal with this issue, this paper proposes a theoretical framework to prevent weight manipulation in SN-GDM. Firstly, a community detection based method is used to cluster the large group. The power relations of subgroups are measured by the power index (PI), which depends on the subgroups size and cohesion. Then, a minimum adjustment feedback model with maximum entropy is proposed to prevent subgroups' manipulation behavior. The minimum adjustment rule aims for 'efficiency' while the maximum entropy rule aims for 'justice'. The experimental results show that the proposed model can guarantee the rationality of weight distribution to reach consensus efficiently, which is achieved by maintaining a balance between 'efficiency' and 'justice' in the mechanism of assigning weights. Finally, the detailed numerical and simulation analyses are carried out to verify the validity of the proposed method.

Fermatean fuzzy copula aggregation operators and similarity measures-based complex proportional assessment approach for renewable energy source selection.

Selecting the optimal renewable energy source (RES) is a complex multi-criteria decision-making (MCDM) problem due to the association of diverse conflicting criteria with uncertain information. The utilization of Fermatean fuzzy numbers is successfully treated with the qualitative data and uncertain information that often occur in realistic MCDM problems. In this paper, an extended complex proportional assessment (COPRAS) approach is developed to treat the decision-making problems in a Fermatean fuzzy set (FFS) context. First, to aggregate the Fermatean fuzzy information, a new Fermatean fuzzy Archimedean copula-based Maclaurin symmetric mean operator is introduced with its desirable characteristics. This proposed operator not only considers the interrelationships between multiple numbers of criteria, but also associates more than one marginal distribution, thus avoiding information loss in the process of aggregation. Second, new similarity measures are developed to quantify the degree of similarity between Fermatean fuzzy perspectives more effectively and are further utilized to compute the weights of the criteria. Third, an integrated Fermatean fuzzy-COPRAS approach using the Archimedean copula-based Maclaurin symmetric mean operator and similarity measure has been developed to assess and rank the alternatives under the FFS perspective. Furthermore, a case study of RES selection is presented to validate the feasibility and practicality of the developed model. Comparative and sensitivity analyses are used to check the reliability and strength of the proposed method.

Geospatial Modeling Using Dempster-Shafer Theory.

Uncertainty in spatial geometrical issues is represented using Dempster-Shafer (D-S) theory. Interval approaches are used for D-S uncertainty of spatial locations and the associated arithmetic operations on such intervals described. Categories of uncertainty for points and lines are defined using interval formulations. Based on these, approaches for calculation of geometric areas, line length and line slopes are given. Compatibility of imprecise point locations is discussed and potential aggregations for similar points considered. Finally, topological spatial relationships are described for objects with uncertain boundaries. This will provide a formal framework for the use of a D-S interval approach for uncertainty in spatial geometric issues.

Evaluating Belief Structure Satisfaction to Uncertain Target Values.

We describe the basic properties of the Dempster-Shafer belief structure and introduce the associated measures of plausibility and belief. We look at the role of these structures for providing a model of imprecise probabilistic information. We next consider the problem of calculating the satisfaction of target values by a variable V whose value is expressed by a belief structure. We first look at the simplest case when the target is expressed as subset of the domain of V . We then look at the situation when the target is expressed by more complex uncertain structures. Among those considered are a probability distribution, another belief structure, measure, and possibility distribution. At a formal level this paper involves the extension of the concepts of plausibility and belief associated with D-S structures from being mappings of subsets of the underlying domain of V into unit interval to be mappings of these more complex structures into the unit interval.

On prioritized multiple-criteria aggregation.

We describe multicriteria aggregation and discuss its central role in many modern applications. The concept of aggregation imperative is introduced to indicate the description of how the individual criteria satisfactions should be combined to obtain the overall score. We focus on a particular type of aggregation imperative called prioritized aggregation that is characteristic of situations where lack of satisfaction to criteria denoted as higher priority cannot be compensated by increased satisfaction by those denoted as lower priority. We discuss two approaches to the formulation of this type of aggregation process. One of these uses the prioritized aggregation operator, and the second is based on an integral-type aggregation using a monotonic set measure to convey the prioritized imperative.

Intuitionistic fuzzy Bonferroni means.

The Bonferroni mean (BM) was originally introduced by Bonferroni and then more recently generalized by Yager. The desirable characteristic of the BM is its capability to capture the interrelationship between input arguments. Nevertheless, it seems that the existing literature only considers the BM for aggregating crisp numbers instead of any other types of arguments. In this paper, we investigate the BM under intuitionistic fuzzy environments. We develop an intuitionistic fuzzy BM (IFBM) and discuss its variety of special cases. Then, we apply the weighted IFBM to multicriteria decision making. Some numerical examples are given to illustrate our results.

Modeling prioritized multicriteria decision making.

We consider the problem of multicriteria decision making (MCDM) in the situation in which there exists a prioritization of criteria. A good example of prioritization among criteria occurs in the case of air travel, where concerns about passenger safety have a higher priority then economic concerns. Tradeoffs between saving on gasoline usage and jeopardizing passenger safety are unacceptable. We show how this prioritization of criteria can be modeled by using importance weights in which the weights associated with the lower priority criteria are related to the satisfaction of the higher priority criteria. We provide some models that allow for the formalization of these prioritized MCDM problems using both the Bellman-Zadeh paradigm for MCDM and the ordered weighted averaging (OWA) operator method.

OWA aggregation over a continuous interval argument with applications to decision making.

We briefly describe the ordered weighted average (OWA) operator. We discuss its role in decision making under uncertainty. We provide an extension of the OWA operator to the case in which our argument is a continuous valued interval rather than a finite set of values. We look at some examples of this type of aggregation. We show how it can be used in some tasks that arise in decision making. We consider the extension of the continuous interval argument OWA operator to the more general case in which the argument values have importance weights. We use this to introduce the idea of an attitudinal-based expected value associated with a continuous random variable.

Cumulative distribution functions from Dempster-Shafer belief structures.

We discuss the Dempster-Shafer belief structure. We introduce the idea of a cumulative distribution induced by a Dempster-Shafer belief structure. We call these belief-cumulative distribution (B-CDs) functions. We study the properties of these distribution functions and show that they are interval functions. We investigate the possibility of using these distribution functions as a tool for knowledge representation.

On the retranslation process in Zadeh's paradigm of computing with words.

We discuss Zadeh's paradigm of computing with words and indicate the three important stages. We focus on the retranslation process, selecting a term from our prescribed vocabulary to express information represented using fuzzy sets. A number of criteria of concern in this retranslation process are introduced. Some of these criteria can be seen to correspond to a desire to accurately reflect the given information. Other criteria may correspond to a desire, on the part of the provider of the information, to give a particular perception or "spin." These types of criteria can be of particular importance in many types of information warfare. We discuss some methods for combining these criteria to evaluate potential retranslations.

On the role of anxiety in decisions under possiblistic uncertainty.

We focus on situations in which we must decide on what time to take an action. The action is not in question it is the time of action. We call these "time for action decisions," a prototypical example being deciding when to leave on a journey. We point out that during this type of decision process, the decision-maker recognizes two groups of forces acting on him: one that pushes him to act now and other that pushes him act later. We note that the strength of these forces depends on the information available about various uncertainties associated with the situation. It also strongly depends upon the personality of the decision-maker. We observe that as time passes these conflicting forces tend to build up an anxiety in the decision-maker resulting in an action being taken at a time of most intense anxiety. In this paper using the ideas of possibility and necessity measures to enable different interpretations of uncertain information we investigate the temporal profile of the decision-maker's anxiety as a function of their decision attitude. We investigate the role of maximization of anxiety as decision paradigm. One of our goals here is to try to understand role of the nature and the quality information plays in these types of decisions as well as its interaction with anxiety.