Comparación entre el Índice de Yager y el Centroide para Reducción de tipo de un Número Difuso Tipo-2 de Intervalo

Context: There is a need for ranking and defuzzification of Interval Type-2 fuzzy sets (IT2FS), in particular Interval Type-2 fuzzy numbers (IT2FN). To do so, we use the classical Yager Index Rank (YIR) for fuzzy sets to IT2FNs in order to find an alternative to the centroid of an IT2FN.Method: We use a simulation strategy to compare the results of the centroid and the YIR of an IT2FN. This way, we simulate 1000 IT2FNs of the following three kinds: gaussian, triangular, and non symmetrical in order to compare their centroids and YIRs.Results: After performing the simulations, we compute some statistics about its behavior such as the degree of subsethood, equality and the size of the Footprint of Uncertainty (FOU) of an IT2FN. A description of the obtained results shows that the YIR is less wide than centroid of an IT2FN.Conclusions: In general, YIR is less complex to obtain than the centroid of an IT2FN, which is highly desirable in practical applications such as fuzzy decision making and control. Some other properties regarding its size and location are also discussed.Contexto: Hay una necesidad por defuzzificar y rankear Conjuntos Difusos Tipo-2 de Intervalo (IT2FS), en particular Números Difusos Tipo-2 de Intervalo (IT2FN). Para ello, usamos el Índice de Yager (YIR) para conjuntos difusos aplicado a IT2FNs con el fin de encontrar una alternativa al centroide de un IT2FN.Método: Usamos una estrategia de simulación para comparar los resultados del centroide y del YIR de un IT2FN. Así pues, simulamos 1000 IT2FNs de cada uno de los siguientes tres tipos: gausianos, triangulares y asimétricos para comparar sus centroides y YIRs.Resultados: Después de realizar las simulaciones, se calculan algunas estadísticas de su comportamiento como el grado de cobertura y de igualdad relativas del YIR respecto al centroide así como el tamaño de la Huella de Incertidumbre (FOU) de un IT2FN. La descripción de los resultados obtenidos muestra que el YIR es menos amplio que el centroide.Conclusiones: En general, el YIR es menos complejo de obtener que el centroide de un IT2FN, lo cual es altamente deseable en aplicaciones prácticas como toma de decisiones y control. Otras propiedades relacionadas con su tamaño y ubicación también son discutidas

Modelling and optimizing multiple attribute decisions by using fuzzy sets

The purpose of this paper is to present a coherent perspective of modeling and optimizing multiple attribute decisions by using fuzzy sets. In management practice we face most of the time the situation in which a problem have several possible solutions and each solution can be analyzed using multiple criteria models. In the same time, in real life decision making process there is a given level of uncertainty which makes difficult a clear cut analytical analysis. The object of this article is to build a model approach for making multiple criteria decision using fuzzy sets of objects. Elaborating multiple attribute decisions involves performing an assessment and selecting from a given and finite set of possible alternative courses of action in the presence of a given and finite, and usually conflicting set of attributes and criteria.decision making, fuzzy sets, modeling, multiple criteria optimization.

Ranking of fuzzy sets based on the concept of existence

AbstractVarious approaches have been proposed for the comparison or ranking of fuzzy sets. However, due to the complexity of the problem, a general method which can be used for any situation still does not exist. This paper formalizes the concept of existence for the ranking of fuzzy sets. Many of the existing fuzzy ranking methods are shown to be some application of this concept. An improved fuzzy ranking method is then introduced, based on this concept. This newly introduced method is expanded for treating both normal and nonnormal, convex and nonconvex fuzzy sets. Emphasis is placed on the use of the subjectivity of the decision maker, such as the optimistic or the pessimistic view points. An improved procedure for obtaining linguistic conclusions is also developed. Finally, some numerical examples are given to illustrate the approach

Fuzzy-assignment Model by Using Linguistic Variables

يتناول هذا البحث موضوع نماذج التخصيص المعتمدة على الكلف الضبابية حيث ان تقليل الكلف هو الهدف الاساسي المطلوب تحقيقه  في اية دراسة تخص نماذج التخصيص. فمن  الممكن استخدام الاعداد الضبابية المثلثية او الشبه منحرفة (كما تم في هذا البحث) لكل كلفة ضبابية بالاضافة الى ذلك يتم تطبيق نماذج التخصيص على المتغيرات اللغوية بعد تحويلها الى بيانات كمبة ضبابية باعتماد طريقة  Ranking Mothed Yager  . من خلال نتائج البحث فقد تبين ان المتغيرات اللغوية ذات تأثير مهم عند تطبيقها في النماذج الرياضية الضبابية.      This work addressed the assignment problem (AP) based on fuzzy costs, where the objective, in this study, is to minimize the cost. A triangular, or trapezoidal, fuzzy numbers were assigned for each fuzzy cost. In addition, the assignment models were applied on linguistic variables which were initially converted to quantitative fuzzy data by using the Yager’sorankingi method. The paper results have showed that the quantitative date have a considerable effect when considered in fuzzy-mathematic models

Comparing fuzzy numbers: The proportion of the optimum method

AbstractThe proportion of the optimum fuzzy number ranking procedure measures the consonance of the fuzzy number under comparison with the fuzzy ideals of max and min. This is accomplished by using three successive levels of analysis, where the number of levels utilized is dependent upon the difficulty of the ranking problem. This method is then compared to eight existing fuzzy number comparison methods. When evaluating all nine methods (using five examples) in terms of the method attributes of robustness, accuracy, and ease of use, the Lee-Li and proportion of the optimum methods are recommended. If, however, the decision maker desires the most flexible model, due to spread-preference differences, then the proportion of the optimum method is recommended

FUZZY COMPARATIVE CONCORDANCE ANALYSIS. Proposal and evaluation by a case study

In this paper it is proposed a fuzzy multiple attribute analysis, that we have called comparative concordance, as a help instrument to the decision-making process in an environment of lack of precise information as it generally is the decision-making in regional planning. Through an application to the selection of proceeding programs of the Environmental Plan of Andalusia, 1995-2000, it will be compared to other methods.fuzzy sets, multiple attribute decision, environmental planning