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The novel concept of Spherical Fuzzy Sets provides a larger preference domain for decision makers to assign membership degrees since the squared sum of the spherical parameters is allowed to be at most 1.0. Spherical fuzzy sets are a generalization of Pythagorean Fuzzy Sets, picture fuzzy sets and neutrosophic sets. Spherical Fuzzy Sets are newly developed one of the extensions of ordinary fuzzy sets. In this paper, we proposed a MCDM method based on spherical fuzzy information. The method uses entropy theory to calculate the criteria weights, and calculates the similarity ratio of alternatives by using cosine similarity theory. Then alternatives are ranked according to their similarity ratio in descending order. To show the applicability of the proposed method, an illustrative example is given. We conclude that the proposed method is a useful tool for handling multi-period decision making problems in spherical fuzzy environment.

A patient-oriented model of assessment of cardiovascular (CV) health of men obtained as a result of medical observation and the observation itself is considered. The specificity of proposed methodology is determined by orientation toward men, by focus on selfobservation of CV health, by composition of indicators of men’s CV health as well as forms and methods of their estimation.A technique TAMECH of assessment of men’s cardiovascularhealthbased on a patient-oriented model, the theory of fuzzy sets, a formal conceptual analysis and linguistic summary is proposed and its application is considered.

One of the most relevant concepts in statistics is data variability or dispersion. We can find a wide number of studies related to the measurement of dispersion for quantitative data, however, the measurement of dispersion for qualitative data is being poorly developed despite the increasing weight in the Science of linguistic terms to manage information. In fact, only a few measures can be found within a qualitative framework, and their properties have not received much attention. In this chapter, we stress this terrible theoretical lack, exploring a desirable set of properties to be accomplished by an ordinal dispersion measure that allows a structured view of most existing ordinal dispersion measures and a better understanding of ordinal dispersion.

This work proposes an heuristic approach based on evolutionary computation, whose goal is to find a set of k-spanning trees with lowest costs in graphs that contain uncertainties in their parameters. In order to avoid the high complex ordinary resolution, this work presents a genetic approach to explore the space of solutions looking for satisfactory results, without the necessity of comparing all possible solutions.

The behaviour of concurrent systems has been classically specified by means of Labelled Transition Systems. Uncertainty can be modeled in LTS by means of non-determinism that can be used for modeling systems whose behaviour is not completely specified or for specifying unpredictable behaviours like, for instance, errors. However, such approach is not completely satisfactory. Indeed, it is not able to give a measure of such uncertainty. In this paper we propose a new variant of LTS, named Fuzzy Labelled Transition Systems (FLTS), where fuzziness is used for modeling uncertainty in concurrent systems. In FLTS, transition relation is defined in term of a L-Fuzzy Set that gives the membership degree of a given transition/computation. To reason about FLTS, a variant of Hennessy-Milner Logic is also proposed. The proposed logic will be used for specifying behavioural properties of systems for which a measure of the satisfaction is defined.

In this paper we highlight a few features of the semantic gap problem in image interpretation. We show that semantic image interpretation can be seen as a symbol grounding problem. In this context, ontologies provide a powerful framework to represent domain knowledge, concepts and their relations, and to reason about them. They are likely to be more and more developed for image interpretation. A lot of image interpretation systems rely strongly on descriptions of objects through their characteristics such as shape, location, image intensities. However, spatial relations are very important too and provide a structural description of the imaged phenomenon, which is often more stable and less prone to variability than pure object descriptions. We show that spatial relations can be integrated in domain ontologies. Because of the intrinsic vagueness we have to cope with, at different levels (image objects, spatial relations, variability, questions to be answered, etc.), fuzzy representations are well adapted and provide a consistent formal framework to address this key issue, as well as the associated reasoning and decision making aspects. Our view is that ontology-based methods can be very useful for image interpretation if they are associated to operational models relating the ontology concepts to image information. In particular, we propose operational models of spatial relations, based on fuzzy representations.

This paper deals with identification of romanized plaintexts of five Indian Languages - Hindi, Bengali, Manipuri, Urdu and Kashmiri. Fuzzy Pattern Recognition technique has been adopted for identification. Suitable features/characteristics are extracted from training samples of each of these five languages and represented suitably through fuzzy sets. Prototypes in the form of fuzzy sets are constructed for each of these five languages. The identification is based on computation of dissimilarity with prototypes of each of these languages. It is computed using a dissimilarity measure extracted through fuzzy relational matrices. The identifier proposed is independent of dictionary of any of these languages and can even identify plaintext without word break-ups. The identification can be used for automatic segregation of plain texts of these languages while analysing intercepted multiplexed interlieved Speech/Data/Fax communication on RF channel, in a computer network or Internet.

This paper presents an extended Branch-and-Bound algorithm for solving fuzzy linear bilevel programming problems. In a fuzzy bilevel programming model, the leader attempts to optimize his/her fuzzy objective with a consideration of overall satisfaction, and the follower tries to find an optimized strategy, under himself fuzzy objective, according to each of possible decisions made by the leader. This paper first proposes a new solution concept for fuzzy linear bilevel programming. It then presents a fuzzy number based extended Branch-and-bound algorithm for solving fuzzy linear bilevel programming problems.

This study focuses on the fundamental issues of granular information and information granulation, and discusses their role in pattern recognition. We demonstrate how to characterize information granules in terms of their size (dimension) and variability. We also show that these two essential aspects of information granules are closely linked: the increasing size of the granule implies increased variability. Two detailed models of the variability of information granules are included; the first exploits the notion of entropy, while the second expresses a mix between patterns from different classes. Finally, we elaborate on the development of granular neural classifiers, and outline the main advantages stemming from the usage of granular rather than numeric patterns.

In the field of military intelligence, data to be fused are numerous and heterogeneous. Therefore an automatic decision aid method to reproduce intelligence officer reasoning is useful. We model data as fuzzy sets and we use an aggregation method based upon management of priorities between criteria. On top of that, a multi-agents architecture lying on modelisation of processes as competing agents provides an efficient and adaptive implementation. As an example, we describe hereafter an application aimed at helping artillery localization.

We present two methods of modelling ordered datasets using Baldwin's mass assignment. The first method generates a simplified memory-based fuzzy belief updating model. Results are given in application to particle classification and facial feature detection. The second method uses a new, high level, fuzzy trend feature based on a set of fuzzy trend prototypes. These prototypes are closely related to human perceptions of shape in ordered series. The models generated using this method are concise and linguistically clear glass box models. Results are given in application to sunspot and simple sinewave data series.

We show here some of our results on intuitionistic fuzzy topological spaces. In 1983, K.T. Atanassov proposed a generalization of the notion of fuzzy set: the concept of intuitionistic fuzzy set. D. Çoker constructed the fundamental theory on intuitionistic fuzzy topological spaces, and D. Çoker and other mathematicians studied compactness, connectedness, continuity, separation, convergence and paracompactness in intuitionistic fuzzy topological spaces. Finally, G.-J Wang and Y.Y. He showed that every intuitionistic fuzzy set may be regarded as an L-fuzzy set for some appropriate lattice L. Nevertheless, the results obtained by above authors are not redundant with other for ordinary fuzzy sense. Recently, Smarandache defined and studied neutrosophic sets (NSs) which generalize IFSs. This author defined also the notion of neutrosophic topology. We proved that neutrosophic topology does not generalize the concept of intuitionistic fuzzy topology.

We propose a new method for ranking alternatives represented by Atanassov's intuitionistic fuzzy sets (A-IFSs) which takes into account the amount of information related to an alternative (expressed by a distance from the ideal positive alternative) and the reliability of information (how sure the information is).

Type-1 OWA operator provides us with a new technique for directly aggregating linguistic variables expressing human experts' opinions or preferences by fuzzy sets via OWA mechanism in soft decision making. However, the existing Direct Approach to performing type-1 OWA operation involves high computational overhead. In this paper, a fast approach, called α-level Approach, is suggested to implement the type-1 OWA operator. Experimental results have shown that the α-level Approach can achieve much higher computing efficiency in performing type-1 OWA operation than the Direct Approach.

Bilevel decision techniques are developed for decentralized decision problems, which may be defined by fuzzy coefficients. Based on a fuzzy linear bilevel (FLBL) model and two FLBL algorithms, this research develops a FLBL decision support system (FLBLDSS). It first introduces a satisfactory-degree-adjustable FLBL model. Then, the system structure and function modules of this FLBLDSS are presented. Finally the key algorithms are illustrated.

Fabric-hand evaluation is one of the key features and measures in textile material selection for fashion design. Fabric-hand evaluation requires considering multiple criteria with in a group of evaluators. The evaluation process often involves fuzziness in the weights of criteria and the judgments of evaluators. This study first develops a multi-level textile material fabric-hand evaluation model. It then proposes a fuzzy multi-criteria group decision-making (FMCGDM) method for the evaluation. A fuzzy multi-criteria group decision support system (FMCGDSS) is developed to implement the proposed method and applied in textile material fabric-hand evaluation.

We present a soft computing approach to character recognition from printed documents. For feature extraction, we define a number of fuzzy sets on the Hough transform of character pattern pixels and synthesize additional fuzzy sets by t-norms. The height of each t-norm constitutes a feature element and a set of 'n' such feature elements form an n-dimensional feature vector for the character. A 3n-dimensional vector is then generated from the n-dimensional feature vector by defining three linguistic fuzzy sets, namely, weak, moderate and strong. These 3n-dimensional vectors form a Multilayer Perceptron (MLP) input for training by back propagation. The MLP outputs represent fuzzy sets denoting the belongingness of an input pattern to a number of fuzzy pattern classes. The feature set is chosen by optimizing a Feature Quality Index (FQI) using genetic algorithm. A two-state Markov chain is used to model degraded document images for simulation tests. The system can recognize characters with an accuracy of 98%.

We introduce a notion of partial order for fuzzy sets in connection with their greater or smaller fuzziness. This allows us to give a simple basis to the theory of fuzziness measures.

Sugeno's integral permits to build very large classes of fuzziness measures.

This extended abstract of the thesis “Computational Intelligence in Image Segmentation”, explains the formulation of the objectives and expected contributions, a short outline of the problem domain's current knowledge, some proposed solutions to the problem, preliminary results obtained so far, and conclusions.

In this work, we did the construction of a fuzzy mathematical model wich it was developed to predict the pathological stage of prostate cancer.⁵ The intention is to help the specialists on the decision process about stage of the disease, to avoid surgery and intensive treatments unnecessary. The model consists on a system founded in fuzzy rules, that it combine the pre-surgical data (clinic state, PSA level and Gleason score) availing of a set of linguistic rules made with base on informations of the existents nomograms. Herewith we hoped to get the chance of the individual, with certain clinical features, be in each stage of the tumor extension: localized, advanced locally and metastatic. Simulations were made with patient's data of the Clinics Hospital/UNICAMP and the results were compared with Kattan's probabilities⁸ that are used on the medicals decisions. A software was developed from this model and is a graphic interface that makes interaction with the subroutines that make the calculations. Its source code was written in Java and software has been tested on Windows and Linux / GNU.