A parametric representation of linguistic hedges in Zadeh’s fuzzy logic

This paper proposes a model for the parametric representation of linguistic hedges in Zadeh’s fuzzy logic. In this model each linguistic truth-value, which is generated from a primary term of the linguistic truth variable, is identified by a real number r depending on the primary term. It is shown that the model yields a method of efficiently computing linguistic truth expressions accompanied with a rich algebraic structure of the linguistic truth domain, namely De Morgan algebra. Also, a fuzzy logic based on the parametric representation of linguistic truth-values is introduced.     

On consistency measures of linguistic preference relations

Inspired by the concept of deviation measure between two linguistic preference relations, this paper further defines the deviation measure of a linguistic preference relation to the set of consistent linguistic preference relations. Based on this, we present a consistency index of linguistic preference relations and develop a consistency measure method for linguistic preference relations. This method is performed to ensure that the decision maker is being neither random nor illogical in his or her pairwise comparisons using the linguistic label set. Using this consistency measure, we discuss how to deal with inconsistency in linguistic preference relations, and also investigate the consistency properties of collective linguistic preference relations. These results are of vital importance for group decision making with linguistic preference relations.     

基于语言真值格值一阶逻辑系统Lv(n×2)F(X)中两种模型的不确定性推理

在语言真值格值一阶逻辑系统的框架下,讨论了两种推理模型中的不确定性推理理论与方法,并针对不同的推理规则得到了推理算法,其推理算法既有合理的语义解释又有严密的语法论证.     

Multi-criteria decision aid for the formulation of sustainable technological energy priorities using linguistic variables

Implementation of new and innovative energy technologies is a key mean towards a sustainable energy system. Currently, governments have to decide from an increasingly diverse mix of them, the ones which warrant support, including funding and other incentives for private sector efforts. However, appraising energy technologies in terms of their sustainability is a really complex task, considering the series of uncertainties and implications that have to be encountered so as to obtain realistic and transparent results. In this context, the main aim of this paper is to present a direct and flexible multi-criteria decision making approach, using linguistic variables, to assist policy makers in formulating sustainable technological energy priorities. Furthermore, its software realization will be applied to a number of technologies, in the context of the Greek Technology Foresight Programme, and the results will be presented and discussed.     

导出的纯语言OWGA算子及其在的群决策中的应用

研究属性权重、专家权重和属性值均为纯语言变量的多属性群决策问题,利用纯语言变量的运算规律,提出一种新的数据信息集成算子:导出的纯语言有序加权几何平均(IPLOWGA)算子。并且给出纯语言环境下基于IPLOWGA算子和PLOWGA算子的一种群决策方法。最后,进行实例分析,说明该方法的实用性和有效性。     

Fuzzy logic in measurements

Our main interest in this paper is to translate from “natural language” into “system theoretical language”. This is of course important since a statement in system theory can be analyzed mathematically or computationally. We assume that, in order to obtain a good translation, “system theoretical language” should have great power of expression. Thus we first propose a new frame of system theory, which includes the concepts of “measurement” as well as “state equation”. And we show that a certain statement in usual conversation, i.e., fuzzy modus ponens with the word “very”, can be translated into a statement in the new frame of system theory. Though our result is merely one example of the translation from “natural language” into “system theoretical language”, we believe that our method is fairly general.     

基于模糊语言判断矩阵和FIOWA算子的有限方案决策法

定义一种模糊的导出有序加权平均(FIOWA)算子，给出方案之间比较的模糊语言标度。运用模糊语言标度构造出模糊语言判断矩阵，并提出一种基于模糊语言判断矩阵和FIOWA算子的有限方案决策方法。该法利用FIOWA算子对模糊语言信息进行集结，并利用已有的三角模糊数排序公式求得决策方案的排序。     

Rule-based models of multivariable functions

This study is devoted to fuzzy rule based modelling of multiple-input single-output nonlinear numerical relationships. The model under investigation is viewed as a collection of conditional statements “if state Ω_i then y = g_i(x, a_i)”, i = 1, 2,…, N with Ω_i being a fuzzy relation defined in the space of the input variables. In contrast to the commonly encountered identification approach that is dwelled upon discrete experimental data, the one proposed in this study is concerned with explicitly articulated nonlinear input-output relationship. The main thrust is in the development of a fuzzy partition of the input variables completed through a sequence of fuzzy relations rather than Cartesian products of fuzzy sets. This approach allows us to maintain the number of necessary rules under control and avoid a combinatorial explosion otherwise inevitable in situations of highly multivariable functions. Introduced are criteria of separability and function variability whose objective is to guide a distribution and granularity of the linguistic labels forming the condition part of the rules.     

Fuzzy cardinality and the modeling of imprecise quantification

The concept of cardinality of a fuzzy set has received attention from several researchers and has been defined in several apparently independent manners. A systematic investigation of this notion is performed which unifies and improves previous attempts. The cardinality of a fuzzy set, viewed as a fuzzy integer, is related to scalar cardinality indices. The closely related question of the probability of a fuzzy event is dealt with. Lastly, the usefulness of fuzzy cardinality for meaning representation of statements or queries involving fuzzy linguistic quantifiers is emphasized.     

The case for an interval-based representation of linguistic truth

This paper develops an interval-based approach to the concept of linguistic truth. A special-purpose interval logic is defined, and it is argued that, for many applications, this logic provides a potentially useful alternative to the conventional fuzzy logic.The key idea is to interpret the numerical truth value v(p) of a proposition p as a degree of belief in the logical certainty of p, in which case p is regarded as true, for example, if v(p) falls within a certain range, say, the interval [0.7, 1]. This leads to a logic which, although being only a special case of fuzzy logic, appears to be no less linguistically correct and at the same time offers definite advantages in terms of mathematical simplicity and computational speed.It is also shown that this same interval logic can be generalized to a lattice-based logic having the capacity to accommodate propositions p which employ fuzzy predicates of type 2.