Fuzzy Information Measures with Multiple Parameters

Information theory deals with the study of problems concerning any system. This includes information processing, information storage, information retrieval and decision making. Information theory studies all theoretical problems connected with the transmission of information over communication channels. This includes the study of uncertainty (information) measures and various practical and economical methods of coding information for transmission. In this chapter, the introduction of a new generalised measure of fuzzy information involving two real parameters is given. The proposed measure satisfies all the necessary properties of being a measure. Some additional properties of the proposed measure have also been studied. Further, the monotonic nature of generalised fuzzy information measure with respect to the parameters is studied and validity of the same is checked by constructing the computed tables and plots on taking different fuzzy sets and different values of the parameters. Also, a new generalised fuzzy information measure involving three parameters has been introduced

Some New Correlation Coefficient Measures Based on Fermatean Fuzzy Sets using Decision Making Approach in Pattern Analysis and Supplier Selection

Fermatean fuzzy set (FFS) is an effective tool to depict expert reasoning information in the decision‐making process than fuzzy sets (FS), intuitionistic fuzzy sets (IFS), and Pythagorean fuzzy sets (PFS). Keeping in mind the importance of correlation coefficient and application in medical diagnosis, decision making and pattern recognition, several studies on correlation coefficient measures have been proposed in the literature. As there does not exist any study concerning correlation coefficient measures for FFS, in this communication, we propose novel entropy-correlation measures for Fermatean fuzzy sets and applied it decision making problems of pattern analysis and multi-criteria decision making for supplier selection. With the help of proposed correlation coefficient, we establish some weighted measures for FFS. Using numerical computations, we determine the efficacy of the suggested measures over other measures. The aim of this study is to propose a novel and efficient methodology for evaluation of supplier’s selection with uncertain information. Finally, we establish the comparative study of our developed measures over the existing correlation coefficient measures. The analysis showed that the suggested methodology is reliable, flexible, and consistent with the existing techniques

Statistical mechanics and information-theoretic perspectives on complexity in the Earth system

This review provides a summary of methods originated in (non-equilibrium) statistical mechanics and information theory, which have recently found successful applications to quantitatively studying complexity in various components of the complex system Earth. Specifically, we discuss two classes of methods: (i) entropies of different kinds (e.g., on the one hand classical Shannon and R´enyi entropies, as well as non-extensive Tsallis entropy based on symbolic dynamics techniques and, on the other hand, approximate entropy, sample entropy and fuzzy entropy); and (ii) measures of statistical interdependence and causality (e.g., mutual information and generalizations thereof, transfer entropy, momentary information transfer). We review a number of applications and case studies utilizing the above-mentioned methodological approaches for studying contemporary problems in some exemplary fields of the Earth sciences, highlighting the potentials of different techniques

Integration of Link and Semantic Relations for Information Recommendation

Information services on the Internet are being used as an important tool to facilitate discovery of the information that is of user interests. Many approaches have been proposed to discover the information on the Internet, while the search engines are the most common ones. However, most of the current approaches of information discovery can discover the keyword-matching information only but cannot recommend the most recent and relative information to users automatically. Sometimes users can give only a fuzzy keyword instead of an accurate one. Thus, some desired information would be ignored by the search engines. Moreover, the current search engines cannot discover the latent but logically relevant information or services for users. This paper measures the semantic-similarity and link-similarity between keywords. Based on that, it introduces the concept of similarity of web pages, and presents a method for information recommendation. The experimental evaluation and comparisons with the existing studies are finally performed

A fuzzy-QFD approach for the enhancement of work equipment safety: a case study in the agriculture sector

The paper proposes a design for safety methodology based on the use of the Quality Function Deployment (QFD) method, focusing on the need to identify and analyse risks related to a working task in an effective manner, i.e. considering the specific work activities related to such a task. To reduce the drawbacks of subjectivity while augmenting the consistency of judgements, the QFD was augmented by both the Delphi method and the fuzzy logic approach. To verify such an approach, it was implemented through a case study in the agricultural sector. While the proposed approach needs to be validated through further studies in different contexts, its positive results in performing hazard analysis and risk assessment in a comprehensive and thorough manner can contribute practically to the scientific knowledge on the application of QFD in design for safety activities

Ranking Alternatives on the Basis of the Intensity of Dominance and Fuzzy Logic within MAUT

We introduce dominance measuring methods to derive a ranking of alternatives to deal with incomplete information in multi-criteria decision making problems on the basis of Multi-Attribute Utility Theory (MAUT). We consider the situation where the alternative performances are represented by uniformly distributed intervals, and there exists imprecision concerning the decision-makers¿ preferences, by means of classes of individual utility functions and imprecise weights represented by weight intervals or fuzzy weights, respectively. An additive multi-attribute utility model is used to evaluate the alternatives under consideration, which is considered a valid approach in most practical cases. The approaches we propose are based on the dominance values between pairs of alternatives that can be computed by linear programming, which are then transformed into dominance intensities from which a dominance intensity measure is derived. The methods proposed are compared with other existing dominance measuring methods and other methodologies by Monte Carlo simulation techniques. The performance is analyzed in terms of two measures of efficacy: hit ratio, the proportion of all cases in which the method selects the same best alternative as in the TRUE ranking, and the Rank-order correlation, which represents how similar the overall rank structures of alternatives are in the TRUE ranking and in the ranking derived from the method. The approaches are illustrated with an example consisting on the selection of intervention strategies to restore an aquatic ecosystem contaminated by radionuclides

An evaluation methodology for ergonomic design of electronic consumer products based on fuzzy axiomatic design

This article is posted with permission of OCP Science imprint. Copyright @ 2008 Old City Publishing Group.The development life cycle of software and electronic products has been shortened by the growth of rapid prototyping techniques. The evaluation of electronic consumer products should consider hardware and software as well as the ergonomic usability, emotional appeal and aesthetic integrity of the design. This research follows a systematic approach to develop an evaluation methodology for electronic mobile products on ergonomic design. The proposed methodology is based on fuzzy multi attribute decision making and fuzzy axiomatic design realized in three steps; determination of ergonomic attributes for electronic consumer products, determination of a representative set of alternatives, and selection of the best alternative in terms of ergonomic design by utilizing fuzzy axiomatic design. A case study is also provided to support the proposed methodology

Subjective Versus Objective Economic Measures, A fuzzy logic exercise

It is rather evident that there is much more (statistical) information about objective aggregates, such as inflation, output or unemployment than that concerning subjective aggregates, such as well-being, satisfaction, confidence or even expectations. Due to its characteristics, fuzzy logic can and should indeed be used to understand how some of those subjective measures can be approximated by objective ones. This task is accomplished in the paper by the use of Portuguese data on consumer confidence - the subjective economic measure - and on the unemployment rate - the objective economic measure -. The results clearly indicate that to be a worthwhile exercise as the clear importance of unemployment on confidence is only revealed by the fuzzy logic approximation