Fuzzy number

About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.

A fuzzy set approach to modifiers and vagueness in natural language.

Abstract: SUMMARY Recent developments in semantic theory, such as the work of Labov (1973) and Lakoff (1973), have brought into question the assumption that meanings are precise. It has been proposed that the meanings of all terms are to a lesser or greater degree vague, such that, the boundary of the application of a term is never a point but a region where the term gradually moves from being applicable to nonapplicable. Developments in fuzzy set theory have made it possible to offer a formal treatment of vagueness of natural language concepts. In this article, the proposition that natural language concepts are represented as fuzzy sets of meaning components and that language operators—adverbs, negative markers, and adjectives— can be considered as operators on fuzzy sets was assessed empirically. In a series of experiments, we explored the application of fuzzy set theory to the meaning of phrases such as very small, sort of large, and so on. In Experiment 1, subjects judged the applicability of the set of phrases to a set of squares of varying size. The results indicated that the group interpretation of the phrases can be characterized within the framework of fuzzy set theory. Similar results were obtained in Experiment 2, where each subject's responses were analyzed individually. Although the responses of the subjects, in general, could be interpreted in terms of fuzzy logical operations, one subject responded in a more idiomatic style. Experiments 3 and 4 were attempts to influence the logical-idiomatic distinction in interpretatio n by (a) varying the presentation mode of the phrases and by (b) giving subjects only a single phrase to judge. Overall, the results were consistent with the hypothesis that natural language concepts and operators can be described more completely and more precisely using the framework of fuzzy set theory.

Possibility theory in constraint satisfaction problems: Handling priority, preference and uncertainty

Abstract: In classical Constraint Satisfaction Problems (CSPs) knowledge is embedded in a set of hard constraints, each one restricting the possible values of a set of variables. However constraints in real world problems are seldom hard, and CSP's are often idealizations that do not account for the preference among feasible solutions. Moreover some constraints may have priority over others. Lastly, constraints may involve uncertain parameters. This paper advocates the use of fuzzy sets and possibility theory as a realistic approach for the representation of these three aspects. Fuzzy constraints encompass both preference relations among possible instantiations and priorities among constraints. In a Fuzzy Constraint Satisfaction Problem (FCSP), a constraint is satisfied to a degree (rather than satisfied or not satisfied) and the acceptability of a potential solution becomes a gradual notion. Even if the FCSP is partially inconsistent, best instantiations are provided owing to the relaxation of some constraints. Fuzzy constraints are thus flexible. CSP notions of consistency and k-consistency can be extended to this framework and the classical algorithms used in CSP resolution (e.g., tree search and filtering) can be adapted without losing much of their efficiency. Most classical theoretical results remain applicable to FCSPs. In the paper, various types of constraints are modelled in the same framework. The handling of uncertain parameters is carried out in the same setting because possibility theory can account for both preference and uncertainty. The presence of uncertain parameters leads to ill-defined CSPs, where the set of constraints which defines the problem is not precisely known.

A Fuzzy Linguistic Approach Generalizing Boolean Information Retrieval: a Model and its Evaluation

Abstract: The generalization of Boolean Information Retrieval Systems (IRS) is still an open research field; in fact, though such systems are diffused on the market, they present some limitations; one of the main features lacking in these systems is the ability to deal with the “imprecision” and “subjectivity” characterizing retrieval activity. However, the replacement of such systems would be much more costly than their evolution through the incorporation of new features to enhance their efficiency and effectiveness. Previous efforts in this area have led to the introduction of numeric weights to improve both document representation and query language. By attaching a numeric weight to a term in a query, a user can provide a quantitative description of the “importance” of that term in the documents he or she is looking for. However, the use of weights requires a clear knowledge of their semantics for translating a fuzzy concept into a precise numeric value. Our acquaintance with these problems led us to define, starting from an existing weighted Boolean retrieval model, a linguistic extension, formalized within fuzzy set theory, in which numeric query weights are replaced by linguistic descriptors which specify the degree of importance of the terms. This fuzzy linguistic model is defined and an evaluation is made of its implementation on a Boolean IRS. © 1993 John Wiley & Sons, Inc.

Computer-aided machine-tool selection based on a Fuzzy-AHP approach

Abstract: Investment evaluation methods play an important role in today's competitive manufacturing environment. Shrinking profit margins and diversification require careful analysis of investments and decisions regarding these investments are crucial for the survival of the manufacturing industry. Both economic evaluation criterion and strategic criteria such as flexibility, quality improvement, which are not quantitative in nature, are considered for evaluation. Much has been written about the deficiencies of traditional models for justifying advanced manufacturing systems. The use of fuzzy set theory allows incorporating unquantifiable, incomplete and partially known information into the decision model. In this paper, an analytic hierarchical process (AHP) based on fuzzy numbers multi-attribute method is proposed for the evaluation and justification of an advanced manufacturing system. Finally, an example of machine tool selection is used to illustrate and validate the proposed approach.

Defuzzification in Fuzzy Controllers

Abstract: An important subject in fuzzy control theory is tuning of a fuzzy controller. If one wants to tune a fuzzy controller, one can focus on the choice of rules, membership functions, number of input and output fuzzy sets and their degree of overlapping, implication, and connection operations, and defuzzification method. All these choices are closely related and in no way independent of each other. We describe six important defuzzification methods and their respective merits and shortcomings, dependent on the rules, domains, etc. Further, we give an alternative approach for the case in which the output fuzzy sets have different shapes or are asymmetrical. We illustrate this by several examples.