Orderings of fuzzy sets based on fuzzy orderings. Part I: the basic approach

The aim of this paper is to present a general framework for comparing fuzzy sets with respect to a general class of fuzzy orderings. This approach includes known techniques based on generalizing the crisp linear ordering of real numbers by means of the extension principle, however, in its general form, it is applicable to any fuzzy subsets of any kind of universe for which a fuzzy ordering is known|no matter whether linear or partialPeer Reviewe

A new lexicographical approach for ranking fuzzy numbers

In the literature many ranking methods have been proposed for comparing the fuzzy numbers, most of them suffer from plenty of shortcomings such as complex calculations, inconsistency with human intuition. To overcome such shortcomings, a new ranking method is proposed for L-R flat fuzzy numbers which is based on the lexicographical ordering approach. It is shown that proposed ranking method satisfies all the reasonable properties of the ordering fuzzy quantities proposed by Wang & Kerre (Fuzzy Sets and Systems 118(2001) 375-385). Finally a comprehensive comparison is done between the existing ranking methods with the proposed one to demonstrate the effectiveness of the proposed ranking method. Keywords: Ranking method, L-R flat fuzzy number

Fuzzy Risk Analysis for a Production System Based on the Nagel Point of a Triangle

Ordering and ranking fuzzy numbers and their comparisons play a significant role in decision-making problems such as social and economic systems, forecasting, optimization, and risk analysis problems. In this paper, a new method for ordering triangular fuzzy numbers using the Nagel point of a triangle is presented. With the aid of the proposed method, reasonable properties of ordering fuzzy numbers are verified. Certain comparative examples are given to illustrate the advantages of the new method. Many papers have been devoted to studies on fuzzy ranking methods, but some of these studies have certain shortcomings. The proposed method overcomes the drawbacks of the existing methods in the literature. The suggested method can order triangular fuzzy numbers as well as crisp numbers and fuzzy numbers with the same centroid point. An application to the fuzzy risk analysis problem is given, based on the suggested ordering approach

A new approach for the sequence spaces of fuzzy level sets with the partial metric

In this paper, we investigate the classical sets of sequences of fuzzy numbers by using partial metric which is based on a partial ordering. Some elementary notions and concepts for partial metric and fuzzy level sets are given. In addition, several necessary and sufficient conditions for partial completeness are established by means of fuzzy level sets. Finally, we give some illustrative examples and present some results between fuzzy and partial metric spaces

Applicazioni della matematica fuzzy per la selezione dei progetti conservativi nei siti archeologici

The Authors deal with the problem of a standardised but clear and easily understood framework for the strategic decisions involved in the selection among the diverse projects for the conservation and cultural and economic enhancement of archaeological sites. The aim of the paper is to explore the possibility of the use of fuzzy logic to create a hierarchy among the different projects. We propose the use of fuzzy numbers mathematics for the joint treatment of technical, landscape impact, economic and humanistic aspects in selecting the best conservation projects. The basic elements for the definition and the arithmetic of fuzzy numbers are given and a procedure based on the ordering is implemented. Finally, an application relating to an archaeological site on the Mediterranean Sea (Nora, Sardinia) is presented

Program Linier Fuzzy Penuh Dengan Algoritma Multi Objective Linear Programming

In the linear programming there is one of the certainty assumptions, where each parameters has been known with certainty, but in this real life, the parameters is often can not be stated with certainty, so that the linear programming developed into fully fuzzy linear programming (FFLP). This paper discusses the problem solving FFLP problem with Multi Objective Linear Programming Algorithm. FFLP problem will be converted to MOLP problem with three objective functions by using a new lexicographic ordering on triangular fuzzy numbers and then it is solved by lexicographic method. The value of the fuzzy optimal solution obtained is used to find the optimal value of fuzzy objective function and then do defuzzification to obtain crisp optimal solution

ORDENAMIENTO DE N aMEROS DIFUSOS USANDO CENTROIDES: ASPECTOS TE 3RICOS

En el presente trabajo se exploran diferentes m\ue9todos de ordenamiento que se han propuesto para los n\ufameros difusos. Adem\ue1s, se presenta una propuesta basada en la abscisa del centroide de cada n\ufamero difuso. Se compara el ordenamiento propuesto con otro que tambi\ue9n usa el c\ue1lculo del centroide mostrando las mejoras obtenidas. Este ordenamiento satisface, en la mayor\ueda de los casos, la intuici\uf3n por lo que es \ufatil para consultas en bases de datos. Palabras clave: n\ufameros difusos, ordenamiento, centroide, bases de datos, intuici\uf3n. ABSTRACT In this work some ordering methods proposed for fuzzy numbers are explored. Furthermore, a proposal based on the abscissa of the centroid of each fuzzy number is presented. The proposed method is compared with another one that also uses the centroid calculation method, showing its improvements. This ordering method satisfies intuition in most cases, making it useful for database queries. Keywords: fuzzy numbers, ordering, centroid, databases, intuition. <br