Uninorm Aggregation Operator Research Articles

A novel consensus model for multi-attribute large-scale group decision making based on comprehensive behavior classification and adaptive weight updating

Consensus reaching process (CRP) has received increasing attention in recent years, as the demand for decision results with mutual agreement has greatly grown. With the current tendency to introduce e-democracy and public participation into decision making for public issues, decision makers from various backgrounds are more likely to encounter conflict when attempting to reach a consensus, especially under a multi-attribute large-scale group decision making framework. In order to improve the efficiency of the CRPs, different consensus models have been proposed. Specific patterns of behaviors presented by decision makers, such as non-cooperative behaviors and minority opinions, are also strictly supervised in these models. However, not every type of behaviors is specifically defined and given directed treatment, this includes the behavior of highly-weighted clusters, which may seriously bias group consensus. In this paper, we present a novel CRP model named uninorm-based comprehensive behavior classification (UBCBC) model with enhanced efficiency and rationality. First, a behavior classification model based on the calculation of a cooperative index and a non-cooperative index is proposed to classify three kinds of modification behaviors. Second, decision weights in the next iteration of the CRP are updated using a uninorm aggregation operator to reward or penalize the behaviors of clusters. Furthermore, a floating neutral element is introduced into the uninorm aggregation operator to lay stricter supervision upon highly-weighted clusters. Finally, an illustrative example and a numerical simulation are implemented to prove that this model is of high efficiency and feasibility.

A dynamic multi-criteria decision making model with bipolar linguistic term sets

Real world decision making problems under uncertainty face different challenges. These challenges include lack of information, the necessity of quick decisions, and problems may change across time. When the uncertainty involved is due to fuzziness and vagueness, the use of fuzzy linguistic information can facilitate the elicitation of decision makers’ preferences of alternatives by allowing assessment of alternatives in unipolar scales. However, in some cases decision makers need to express negative, positive and neutral attitudes that cannot be modeled by unipolar scales. This paper aims at developing a dynamic linguistic multi-criteria decision making model dealing with bipolar linguistic scales in which both alternatives and criteria may vary across time. In order to consider the historical evolution of alternatives leading up to the current assessments, a fusion process based on transformation functions and uninorm aggregation operator is proposed to deal with the membership functions of bipolar linguistic assessments. Finally the performance of this model is compared with a non-dynamic method in a supplier selection problem.

Managing experts behavior in large-scale consensus reaching processes with uninorm aggregation operators

In many real-life large scale group decision making problems, it can be necessary and convenient a consensus reaching process, which is an iterative procedure aimed at seeking a high degree of agreement amongst experts’ preferences before making a group decision. Although a wide variety of models and approaches have been proposed and developed to support consensus reaching processes, in large groups there are some important aspects that still require further study, such as the treatment of experts’ behaviors that could hamper reaching the wanted agreement. More specifically, it would be necessary an approach to deal with experts properly, based on the overall behavior they present during the discussion process, as well as reinforcing repeated patterns of cooperative (or uncooperative) behavior adopted by experts. This paper presents an expert weighting methodology for consensus reaching processes in large-scale group decision making, that incorporates the use of uninorm aggregation operators. Such operators, which are characterized by their property of full reinforcement, are used in the proposed methodology to allow the experts’ weighting based on their overall behavior during the consensus process and the behavior evolution across the time. This proposal is integrated in a consensus model for large-scale group decision making problems under uncertainty, and it is put in practice to show an illustrative example of its effectiveness and improvements with respect to other approaches.

To reach consensus using uninorm aggregation operator: A gossip-based protocol

Gossip-based protocols for group communication have attractive scalability and reliability properties. This paper presents a gossip-based protocol that enables agents to reach a consensus based on a specific uninorm aggregation operator. We theoretically analyze the convergence, the speed and the randomness features of this protocol as well as its extensions. This model can be used to handle the uncertainty and the fast convergence characteristic of collective decision dynamics. The experimental results show that this protocol is efficient, scalable, and resilient against the failures under various network sizes, and topologies. © 2012 Wiley Periodicals, Inc.

Aggregation of ordinal information

Our interest is with the fusion of information which has an ordinal structure. Information fusion in this environment requires the availability of ordinal aggregation operations. Basic ordinal operations are first introduced. Next we investigate conjunctive and disjunction aggregations of ordinal information. The idea of a pseudo-log in the ordinal environment is presented. We discuss the introduction of a zero like point on an ordinal scale along with the related ideas of bipolarity (positive and negative values) and uni-norm aggregation operators. We introduce mean like aggregation operators as well weighted averages on a ordinal scale. The problem of selecting between ordinal models is considered.

On the determination of strength of belief for decision support under uncertainty—Part II: fusing strengths of belief

Valuation functions are used in decision making under uncertainty to enable comparisons of alternatives. They are based on a weighted averaging of the n possible payoffs available under an alternative. The weighting vectors used are a reflection of the decision-making agent's strength of belief a given outcome will occur. Our concern is with developing methods to fuse multiple sources of these weighting vectors. We first suggest a method based on a normalized product. Some methods are suggested for handling completely conflicting beliefs. We abstract the basic features of this product fusion method. Particularly notably among these properties is the fact that a source with all weights equal, 1/ n, acts as an identity in the fusion process. We consider next a fusion method using a uninorm aggregation operator with identity 1/ n. We carefully look at this new type of method for multi-source fusion and suggest some generations and modifications. Finally we consider the situation when the contributing sources have differing credibilities.

Defending against strategic manipulation in uninorm-based multi-agent decision making

We consider the problem of multi-agent group decision making. We describe the possible use of the uninorm aggregation operator as a way of combining individual agents' preference functions to obtain a group preference function. We then discuss the possibility of an agent using a type of strategic manipulation of the preference information it provides in order to get the group to select its most preferred alternative. A mechanism is then suggested for modifying the construction of the group decision function to defend against this type of strategic manipulation. In addition to considering the case where the preference information is provided numerically we consider the case of ordinal preference information.

The structure of continuous uni-norms

The concept of uni-norm aggregation operators ( uni-norms) was introduced by Yager and Rybalov to unify and generalize the t-norms and t-conorms. Considering that uni-norms continuous on [0,1] 2 must be t-norms or t-conorms, we concentrate our attention on uni-norms continuous in (0,1) 2 in this paper. We mainly investigate their properties, representation and structure.

Remarks on uninorm aggregation operators

It is proved that continuous uninorm aggregation operators are only t-norms or t-conorms. Some general constructions about uninorm aggregation operators are given.

Weak uninorm aggregation operators

By weakening the identity condition of uninorm, a general class of associative aggregation operators called weak uninorm is introduced. It is proved that continuous weak uninorms are the combination of continuous t-norm and continuous t-conorm through a median operator. The representation theorem for Archimedean weak uninorm is also given. Finally, the counting number of the identity elements of weak uninorm is also investigated.

Uninorm aggregation operators

A generalization of the t-norm and t-conorm called the uni-norm is defined. These operators allow for an identity element lying anywhere in the unit interval rather than at one or zero as in the case of t-norms and t-conorms, respectively. Various important properties of these uni-norms are investigated. We next introduce two particular families of these uni-norms, R ∗ and R ∗ , study their behavior and suggest some semantics. Finally, withdrawing the requirement of associativity, we introduce a class of operators called R Q-star aggregation operators which are useful for aggregations guided by imperatives such as “if most of the scores are above the identity take the Max else use the Min”.