Application Of Fuzzy Set Theory Research Articles

Data Bases with Fuzzy Information and Approximate Reasoning in Expert Systems

AND ORGANIZATION OF THE PAPER This short paper deals successively with two important fields of applications of fuzzy set and possibility theory:-data bases with fuzzy information and fuzzy queries-approximate/plausible reasoning in expert systems.The main ideas of a work in progress concerning a very general approach to the management of relational databases with fuzzy attribute values are presented. This approach makes an extensive use of the dual concepts of possibility and necessity measures.Besides the problem of the inference from uncertain/imprecise premises is discussed ; the unification of old and new results leads to the emergence of a coherent framework for dealing with this question ; the combination of uncertain or imprecise informations issued from different sources, which is another basic problem we have to deal with in production rule systems, is not addressed here.Proof are omitted for sake of brevity.

The Application of Fuzzy Sets Theory in Innovation Process Modelling

The requirements for innovation process model construction are characterized with respect of uncertain factors influencing the innovations. The possibilities of modelling under uncertainty and the applications of fuzzy sets theory is analysed. The general fuzzy model of the innovation is proposed and shortly discussed.

The application of Fuzzy set theory to the modeling of competition in ecological systems

This paper explores the application of fuzzy set theory for the modeling of within-phenotype niche width as it affects interspecific competition. Previous studies have used the Lotka-Volterra equations and calculated the competition coefficients @aij using @aij = (ui(s)ui(s) ds)/((ui(s))^2ds), where ui(s) is the utilization of resource s by species i. This assumes that variability in resource usage between organisms with different phenotypes and that within each individual phenotype can be treated identically. Within-phenotype variability in resource usage is modeled here by assigning a fuzzy set of optimal resources to each individual as a function of its phenotype, and competition between individuals is then assumed to be a measure of the intersection of the corresponding fuzzy sets of resources. Between-phenotype variability is still modeled using statistical techniques. This is intended as a conceptual model, serving to introduce fuzziness as a more appropriate method than probability for the modeling of within-phenotype niche variation. No experimental verification of the model is attempted. A particular instance of the model is solved numerically, and found to display a limit to the similarity of coexisting species similar to that found in previous Lotka-Volterra based models.

Entropy-coded hybrid differential pulse-code modulation

A hybrid differential pulse-code-modulation (DPCM) system is presented to demonstrate the application of fuzzy set theory in data compression. The system involves entropy coding, Laplacian quantiser and fuzzy enhancement operations as applied on the DPCM signal. Saving of about 0.5 bit is found to be obtained when a DPCM signal is quantised to 32-level, and then Huffman-coded.

An introduction to applications of possibility theory (+ commentaries by L.A. Zadeh, W. Bandler, T. Saaty, A. Kandel, D. Dubois & H. Prade, R.M. Tong and M. Kochen)

A new form of uncertainty called possibilistic uncertainty is introduced. As opposed to probabilistic uncertainty, which is based upon an additive measure and is applicable in cases of repeated experiments, possibilistic uncertainty is based upon a non-additive measure and is a generalization of the idea of ease of attainment in a situation. We discuss the properties of possibilistic uncertainty and describe some prototypical examples. We also discuss the idea of language as being a generator of possibilistic variables. We introduce fuzzy subsets as a means of translating linguistic values into possibility distributions and the idea of approximate reasoning as a means of simulating a large class of human reasoning operations. We introduce a measure of specificity of a possibility distribution and discuss applications of fuzzy set theory to intelligent quering of data bases and multiple criteria decision making. Finally, we introduce some ideas from fuzzy arithmetic.

Instructions and Opinions: The Use of Fuzzy Subjectivity

Architects receive and give instructions and are involved with opinions. Instructions and opinions are seldom treated objectively and yet clear communication is professionally essential. One application of fuzzy set theory is to provide a quantitative interpretation of verbally expressed, subjective statements which are meaningful and yet not always clearly defined. The fuzzy calculus leads to a better understanding of the statements without the loss of vagueness and imprecision which distinguish subjectivity from sharp objectivity. In this paper instructions involve fuzzy unions and intersects; opinions require the introduction of fuzzy relations and compositions to transform verbal statements into quantitative expressions.

Ecosystem analysis using fuzzy set theory

Ecosystem studies of environmental quality are complicated by the imprecise nature of many ecological interrelationships and the subjectivity which is inherent in judgements by field observers. Many analyses of ecosystems require hierarchical decision-making processes which involve variables from social, economic and ecological sectors that are seemingly incompatible. Fuzzy set theory has been developed for and applied to problems involving complex systems like ecosystems. For example, government agencies who make habitat evaluations for wildlife can use techniques developed in fuzzy set theory for the combination of disparate variables that are required for decision-making at an ecosystem level. Another application of fuzzy set theory has generated a classification scheme for wetlands which is based on the knowledge of wetland experts. Fuzzy compartmentalization of ecosystem components allows greater diversity of behavior tha deterministic or probabilistic methods.

Processing Vague Queries in Man-Machine Systems: A Fuzzy Set Approach

This short communication describes a possible application of fuzzy set theory to information retrieval systems. The aim is to improve the performances of such systems, namely the quality of selection, when all-or-nothing queries are unable to select a sufficiently small subset of items. The main idea is to rank the elements of this selected subset in term of the overall compatibility of each item with a fuzzy description expressing the user's preferences. This description is assumed of a semantic nature, i.e. with numerical features, as opposed to structural or syntactic ones. The latter features may however be used to select a subset of admissible items in a first step. Then, in a second step, the fuzzy description is simply built through a man-machine dialog. The paper focuses on this second step ; it deals with the representation of fuzzy specifications and their combination for the purpose of defining a compatibility index between the query and the objects stored in the data base.

The personalization of security selection: An application of fuzzy set theory

We apply the theory of fuzzy subsets to the multiple objective decision problem of stock selection. We allow our objectives to have varying degrees of importance. We discuss various criteria used in selecting stocks. We indicate some procedures for subjectively evaluating the membership functions associated with these criteria.

Some considerations on fuzzy conditional inference

In much of human reasoning, the form of reasoning is approximate rather than exact as in ‘A red apple is ripe and this apple is more or less red. Then this apple is more or less ripe.’ L.A. Zadeh and E.H. Mamdani suggested methods for such a fuzzy reasoning as an application of fuzzy set theory. The method involves an inference rule and a conditional proposition which contains fuzzy concepts. In this paper we point out that the consequence inferred by their methods does not always fit our intuitions and we suggest the improved methods which fit our intuitions under several criteria.

Fuzzy Sets and Decision Analysis

The applicability of fuzzy set theory to decision analysis (DA) is examined. It extends the ideas of an earlier paper Fuzzy decision by Watson et al. [33]. Particular emphasis is placed on justifying the use of Zadeh's fuzzy calculus to model impression, and an axiomatic system is suggested towards this end. This is seen as an attempt at extending Savage's axioms of subjective probability to produce approximate probabilities. It is argued that the method proposed by Watson et al. for comparing decision options is unsatisfactory, and several alternative methods are developed. Some computational anomalies are pointed out which severely limit the potential of this methodology. It is suggested that, for individual decisionmaking, fuzzy decision analysis should be viewed as an automatic sensitivity analysis, but that fuzzy sets may be useful with another interpretation for group decisionmaking. The conclusions are that the methodology has too many limitations to be of use for isolated decisions but that it may have a value for often repeated generic decisions.

On the satisfaction of a fuzzy relation by a set of inputs

Some applications of Fuzzy Set theory require an indication of how well a set of fuzzy sets satisfy a relation: where the relation represents a connection between the spaces on which the fuzzy sets are defined, perhaps in the form of a hypothesis. Two measures of such satisfaction, one a scalar and one a function, are compared in this paper: and the derivation of the scalar from the function is given. The relevance of these measures to applications, approximate reasoning in particular, is indicated.

On measuring fuzziness: a comment on "A fuzzy set approach to modifiers and vagueness in natural language".

Hersh and Caramazza's application of fuzzy set theory to vagueness in natural language is criticized for including in their measures of fuzziness response variability due to experimental and statistical procedures.

An application of fuzzy sets theory to bus transportation network modification

An application of fuzzy sets theory to bus transportation network modification

LEVEL FUZZY SETS

Abstract In practical applications of fuzzy set theory, e.g., in pattern recognition, information retrieval, etc., the reader is not advised-for the reasons of the amount of the considered object universal set and the capacity of computer memory involved-to consider fuzzy sets defined in the whole universal set, when it is sufficient-from the point of view of a given process description exactness-to take into consideration fuzzy sets determined in the universal subsets. Such a type of fuzzy set called a level fuzzy set is defined in the paper, definitions of basic operations performed on level fuzzy sets are given, and properties of these operations are presented.

On Some Applications of Fuzzy Algorithm in Man-Machine Communication Research

Present paper ennuuciates some practical applications of fuzzy set theory in problems of man-machine communication. Problems are recognition of vowel speech sounds and identification of speakers from spoken words. Data used are derived from acoustic-phonetic and spectrographs analysis of large number of Hindi and Telugu (two of the major Indian Languages) speech sounds. It is explained that Fuzzy set theory provides a suitable algorithm which is substantively different from the conventional quantitative methods of system analysis yet presents an approximate but effective means of describing the behaviour of systems which are too ill-defined for precise mathematical analysis. In this paper, two decision algorithmic methods developed from fuzzy set theory and applied for machine recognition of vowels and identification of speakers with Telugu and Hindi speech sounds are presented along with the results of experiments.

Fuzzy sets for man-machine interaction

A new type of experiment is'proposed to better understand the fuzzy behaviour of a human operator in a man-machine system. The published applications of fuzzy set theory to the control of a simple steam engine are used as a convenient example to illustrate how some of the current applications of fuzzy set theory may be modified to carry out this type of experiment. The rationale for this proposal is developed by reviewing studies of the classification of human height and applications of fuzzy set theory to handwritten character recognition and control system design. Based on this brief review, both the results to be expected from such an experiment and how they might be analyzed are discussed. A key result is that such experiments ought to provide a much better understanding of the operator's fuzzy algorithm for adapting his experience to the development of the fuzzy algorithm for the new task.

FUZZY SETS IN COMMUNICATION SYSTEMS AND IN CONSENSUS FORMATION SYSTEMS

Abstract In this paper we shall examine some applications of fuzzy set theory in the area of communications and information systems. With the advent of computers, the telephone and the television, there are potentialities of all kinds of communication services into the home. Fuzzy problems are very likely to occur with user groups requesting methods to understand fuzzy needs. Thus problems in fuzzy communication, fuzzy problem-solving, fuzzy information retrieval, and fuzzy teleconferencing have direct applications of fuzzy set theory, which are considered.

Application of Fuzzy Set Theory to Syntactic Pattern Recognition of Handwritten Capitals

An algorithm for automatic recognition of handwritten capital letters is described in terms of formal grammars. The formalism is used for a priori computer time and memory optimization. Moreover, the syntactic recognition scheme is extended by introducing the concept of fuzzy sets instead of the usual probabilistic approach.

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

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.