Fuzzy Logic with Linguistic Quantifiers in Group Decision Making

A novel approach to a human centric support of a consensus reaching process in a group of agents who present their testimonies as individual fuzzy preference relations is proposed. The concept of a degree of consensus is used which is meant as the degree to which, for instance, most of important agents agree as to almost all of relevant options. The fuzzy majorities are equated with linguistic quantifiers and Zadeh's calculus of linguistically quantified propositions is used. The new concepts of a consensory and dissensory agent is introduced. The authors' approach of using linguistic data summaries for a comprehensive summarization of how the agents' current testimonies look like is then employed for the consensory and dissensory agents to obtain suggestions to the agents on changes of specific preferences that could lead to a higher degree of consensus. An explicit inclusion of opinions of the consensory and dissensory agents is shown to be an important step towards a fairness type attitude of the moderator as opinions of all agents are accounted for.

An interactive multi-user decision support system for consensus reaching processes using fuzzy logic with linguistic quantifiers

There are alternative ways of decomposing a given fuzzy weak preference relation into its antisymmetric and symmetric components. In this paper I have provided support to one among these alternative specifications. It is shown that on this specification the fuzzy analogue of the General Possibility Theorem is valid even when the transitivity restrictions on the individual and the social preference relations are relatively weak. In the special case where the individual preference relations are exact but the social preference relation is permitted to be fuzzy it is possible to distinguish between different degrees of power of the dictator. This power increases with the strength of the transitivity requirement.

This paper is an extension of work published by Kacprzyk in 1983 in which, by using a fuzzy-logic-based calculus of linguistically quantified propositions, some generalizations of multistage decision making and control have been proposed. Namely, a new class of models has been developed that make it possible, roughly speaking, to find an optimal sequence of controls best satisfying (fuzzy) constraints and goals at, say, most (or any other suitable linguistic quantifier, for example ‘almost all’, ‘at least a few’) of the control stages. In this paper we further extend the above-mentioned approach by introducing discounting (a variable importance of particular control stages, in principle ‘the earlier the more important’). We propose a new model that can find an optimal sequence of controls best satisfying the (fuzzy) constraints and goals at, say, most of the earlier control stages. We employ a fuzzy-logic-based calculus of linguistically quantified propositions and develop a branch-and-bound algo...

We present a new type of a query with a fuzzy linguistic quantifier that makes it possible to account for a variable quality of pieces of data involved. We assume the so called horizontal quantification query introduced in our works (cf. Kacprzyk and Ziolkowski [10] and Kacprzyk, Ziolkowski and Zadrozny [9]), an additional degree of the quality of a piece of data (corresponding to a particular query condition), and then use some extended OWA (ordered weighted aggregation) operator with importance (weight) qualification for the implementation of a linguistic quantifier driven aggregation of satisfaction of the particular query conditions. Finally, we show how the new approach can be accommodated in our FQUERY for Access database querying system.

We present an idea of supporting the consensus reaching process, and its related group decision making process in a small group of autonomous decision makers (agents). Our approach is based on some fuzzy-logic-based representations, involving the use of fuzzy preference structure and linguistic quantifiers in a soft measure of the consensus, proposed by Kacprzyk and Fedrizzi, that is the degree to which: "most of agents agree with their preferences to the most of options". The focus is on the consensus reaching process which is run by a moderator. This process is enhanced and accelerated by applying various modern concepts and techniques that are based on the use of some additional higher-level information. Here, we combine the use of a natural language knowledge representation and the concept of an ideal and anti-ideal point, and its related TOPSIS method which determines a solution with the longest distance from the anti-ideal solution and the shortest distance to the ideal one. The improvement of obtaining a higher degree of consensus within the group of agents by using the enhanced moderated consensus reaching support system is illustrated with a numerical example.

We discuss first the concept of a linguistic summary of a time series in the setting proposed by the authors1 and then its extension to cover some additional types of summaries that concern the duration of (partial) trends identified here as straight line segments of a piece-wise linear approximation of a time series. Then, we use the features that characterize the trends: the slope of the line segment, the goodness of approximation and the length of the trend. The derivation of a linguistic summary of a time series is then related to a linguistic quantifier driven aggregation of trends. For this purpose we employ the classic Zadeh's calculus of linguistically quantified propositions in its basic form with the minimum operation. We present some results of a linguistic summarization of time series data on daily quotations of an investment fund over an eight year period, i.e. some best linguistic summaries with their associated degrees of truth (validity). The results obtained provide much insight into the very essence of the time series data, and prove to be promising.

One of the most widely adopted approaches to define weights for Ordered Weighting Averaging (OWA) operators consists of using biparametric linear increasing fuzzy linguistic quantifiers. However, several shortcomings appear when using these quantifiers because depending on the values of these parameters, the aggregations could be biased or the extreme values might be completely ignored. In this contribution, the use of Extreme Values Reductions (EVRs) as fuzzy linguistic quantifiers is proposed to define weights for OWA operators in order to provide more realistic aggregations. First, the impact of the parameters of these linear fuzzy linguistic quantifiers in the OWA aggregations is studied. After that, EVR-OWA operators are introduced as those OWA operators whose weights are computed by using an EVR as fuzzy linguistic quantifier. It will be shown that when using EVR-OWA operators to fuse information, the aggregations are non-biased, take into account more information and the intermediate values are prioritized before the extreme ones. After proposing several families of EVRs, the generalising potential of the EVR-OWA operators is shown by proving that every family of symmetric weights for OWA operators that prioritize the intermediate information are the weights obtained from a certain EVR. Finally, an illustrative example is provided.

We propose a novel approach to the moderator supported consensus reaching process in a group of agents. We assume the agents' testimonies to be fuzzy preference relations, a fuzzy majority, and the concept of a degree of consensus meant as the degree to which, e.g., most of important agents agree as to almost all of relevant options. We use to handle fuzzy majorities Zadeh's calculus of linguistically quantified propositions. We propose a new concept of a (fuzzy sets of) consensory and dissensory agents, and use our approach of using linguistic data summaries for a comprehensive summarization of how the agents' testimonies look like, separately for the consensory and dissensory agents to obtain a deeper view that can be useful for the moderator to suggest the agents changes of specific preferences that could lead to a higher degree of consensus. An explicit inclusion of opinions of the consensory and dissensory agents is a reflection of a fairness type attitude of the moderator as opinions of all agents are accounted for.

Applying fuzzy linguistic quantifier to select supply chain partners at different phases of product life cycle

In this paper, a model for Group Decision Making is defined in a linguistic context. A multi-person decision problem is considered, in which a group of experts is involved in the evaluation of a set of alternatives. The objective is to identify the alternative which is judged the best by a majority of the experts. Alternatives’ evaluations are expressed in the form of preference relations. Both the experts’ preference relations and the degree of consensus on each alternative are expressed linguistically. An overall preference of each alternative with respect to a fuzzy majority of the other alternatives as well as a “soft” consensus degree referred to a fuzzy majority of the experts are proposed based on the concept of linguistic quantifier. The entire process is modeled within fuzzy set theory by Ordered Weighted Average operators.

We present a new, human consistent approach to the summarization of numeric time series aimed at capturing the very essence of what occurs in the data in terms of an increase, decrease and stable values of data, when relevant changes occur, and how long are periods of particular behavior types exemplified by an increase, decrease and a stable period, all with some intensity. We use natural language descriptions that are derived by using tools of Zadeh’s computing with words and perceptions paradigm, notably tools and techniques involving fuzzy linguistic quantifiers. More specifically, we use the idea of fuzzy logic based linguistic summaries of data(bases) in the sense of Yager, later developed by Kacprzyk and Yager, and Kacprzyk, Yager and Zadrozny. We extend that idea to a dynamic setting, to the summarization of trends in time series characterized by: dynamics of change, duration and variability. For the aggregation of partial trends, which is crucial element in the problem considered, we apply the traditional Zadeh’s fuzzy logic based calculus of linguistically quantified propositions and the Sugeno integral. Results obtained are promising.

The theory of fuzzy sets has been applied to social choice primarily in the contexts where one is given a set of individual fuzzy preference relations and the aim is to find a non-fuzzy choice set of winners or best alternatives. We discuss the problem of composing multi-member deliberative bodies starting from a set of individual fuzzy preference relations. We outline methods of aggregating these relations into a measure of how well each candidate represents each voter in terms of the latter's preferences. Our main goal is to show how the considerations discussed in the context of individual non-fuzzy complete and transitive preference relations can be extended into the domain of fuzzy preference relations.

In each hesitant fuzzy linguistic preference relation, experts may express their opinions through comparison linguistic information combined with a discrete fuzzy number. In this paper, a hesitant fuzzy linguistic computational model based on discrete fuzzy numbers whose support is a subset of consecutive natural numbers is proposed, which enriches the flexibility of group decision‐making. First, some main concepts related to discrete fuzzy numbers and an aggregation function of individual subjective linguistic preference relations are introduced. Then, a consistency measure is presented to check and improve the consistency in a given matrix. Further, in order to achieve the predefined degree of consensus and to arrive at the final result, a consensus‐reaching process based on the interactive feedback mechanism is defined. Meanwhile, a revised formula is introduced to calculate the consistency and the degree of consensus in a preference relation matrix. Besides, an illustrative example and comparative analysis are conducted through the proposed calculation process and the optimization algorithm. Finally, the analysis on the threshold values is made to help the decision‐maker determine critical consensus level. The proposed method can address both consistency and consensus, and the results confirmed the effectiveness of the proposed method and its potential use in the qualitative decision‐making problems.

We describe the aggregation process of the typical artificial neuron. We introduce the concept of a fuzzy linguistic quantifier and describe the process for determining the truth of propositions containing linguistic quantifiers. We show how this truth value can be viewed as the firing level of an artificial neuron. We show the relationship between fuzzy sets and neural inputs. A new class of neurons called owa-neurons is described. A learning algorithm for this class of neurons is presented. We provide a methodology for processing information in non-numeric neural networks. © 1992 John Wiley & Sons, Inc.