Fuzzy membership and graphic interpretation of fuzzy sets small, prime numbers, universal, finite, infinite. Postscript ps files are generated by substituting the call to pdf for the call to. Three new methods are proposed, and a notion of preference between alternatives is. Dubois and prade 7 introduced a ranking of fuzzy numbers in the setting of possibility theory, and chen 8 ranked fuzzy numbers using maximizing and minimizing sets. Prade, ranking fuzzy numbers in the setting of possibility theory, information sciences, vol. Another possibility is the utilization of possibility theory as described by dubois and prade.
Scheduling uncertain orders in the customersubcontractor. After that, zimmermann 1993 introduced recent application of fuzzy set theory. Fuzzy sets are also the cornerstone of a nonadditive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic. An approach to computerized processing of uncertainty, plenum press, new york. This article gives a survey of the fundamentals of fuzzy set theory and describes potential applications. The arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood. In this paper, we study the method of ranking intuitionistic fuzzy numbers.
This cited by count includes citations to the following articles in scholar. Fuzzy logic and probability theory university of waterloo. The method of superimposition of sets has been used to define arithmetic operations of fuzzy numbers. The consistency and effectiveness of these approaches in ranking fuzzy numbers are. Along with forward supply chain organization needs to consider the impact of reverse logistics due to its economic advantage, social awareness and strict legislations. Moewes fuzzy systems possibility theory 20091216 1 61. It corresponds to the most compact plausibility ranking of states induced by the rules 32. Fuzzy logic and possibility theory have widely been used in scheduling in order to represent the uncertainty or imprecision of processing times, but the existence of the manufacturing orders is not usually set into question. Possibility theory lies at the crossroads between fuzzy sets, probability. Informa tion sciences 69, 201217 1993 201 ranking fuzzy interval numbers in the setting of random sets s.
Firstly a possibility degree formula is defined to compare two intuitionistic fuzzy numbers. Ranking of fuzzy intervals seen through the imprecise probabilistic. This paper presents a new method for ranking fuzzy numbers named as possibilitybased comparison relation. Aggregation operators on triangular intuitionistic fuzzy. Fuzzy possibility graphs and their application to ranking fuzzy numbers, fuzzy sets and systems to appear. One modification of fuzzy topsis method, journal of. Prade, rankino of fuzzy numbers in the setting cf possibility theory. Fuzzy differentiation possibility theory, probability theory, and fuzzy set theory possibility theory fuzzy sets and possibility distributions possibility and necessity measures probability of fuzzy events probability of a fuzzy event as a scalar probability of a fuzzy event as a fuzzy set possibility vs. Fuzzy set theory soft computing introduction to fuzzy set, topics.
Note on ranking fuzzy triangular numbers note on ranking fuzzy triangular numbers facchinetti, gisella. Inequality relation between fuzzy numbers and its use in fuzzy optimization. Possibility theory and theory of evidence asuncion p. Fuzzy half spaces by applying fuzzy line and possibility ranking eliminate difficulty in definition of half planes and. Reflecting the tremendous advances that have taken place in the study of fuzzy set theory and fuzzy logic from 1988 to the present, this book not only details the theoretical advances in these areas, but considers a broad variety of applications of fuzzy sets and fuzzy logic as well. R fuzzy numbers based on possibility theory and the implication of possibilistic mean and possibilistic standard deviation.
Fuzzy equations were solved by using different standard methods. A study on ranking of trapezoidal intuitionistic fuzzy numbers. These results justify the use of symmetric triangular fuzzy numbers as fuzzy. We can use this function to create a fuzzy set for numbers near 6. Abstractthe notion of intuitionistic fuzzy numbers ifns. Even the ranking of fuzzy numbers by their crisp scores and ranking of fuzzy numbers by the distances of their centroids from the origin are widely accepted. Possibility theory lies at the crossroads between fuzzy sets. Spain abstract this paper explores the existing relationship between possibility theory and theory of evidence, when they are both applied. The aim of this work is to present some aggregation operators with triangular intuitionistic fuzzy numbers and study their desirable properties. Fuzzy arithmetic is a system of fuzzy operations on fuzzy numbers. Fuzzy numbers fns, introduced by dubois and prade in 10. Pdf this paper provides an overview of possibility theory. Possibility theory lies at the crossroads between fuzzy sets, probability and nonmonotonic reasoning. Golumbic, algorithmic graph theory and perfect graphs, academic.
Prade, ranking fuzzy numbers in the setting of possibility theory, information sciences 30 3 1983 183a224. The existing shortcomings are overcome by proposing a new possibility degree measure for ifns. There exist a large amount of literature involving the ranking of fuzzy numbers1,2,10,11,20 and decision making with fuzzy numbers1416. Fu abstract the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood. Ranking fuzzy numbers in the setting of possibility theory. However, there is no method which gives a satisfactory result to all situations. Possibility degree method for ranking intuitionistic fuzzy. In this paper, the problem of ranking multidimensional uncertain information based on fuzzy order is studied. The concept of possibility degrees of trapezoidal fuzzy numbers was introduced. The possibility theory derived from fuzzy sets theory is always compared with the probability theory. Most of the methods proposed so far are nondiscriminating and counterintuitive. Pdf a simulation study of bullwhip effect in a closed. Ranking of fuzzy numbers was also studied by bortolan and.
Ranking fuzzy numbers in the setting of possibility theory 8 s the necessity measure is a set function defined by s let the complementary set of a, and a possibility measure, the necessary measure can be defined by s if the possibility measure derived from a normalized membership function. Note on ranking fuzzy triangular numbers, international. Most of the ranking methods discuss only triangular fuzzy numbers or trapezoidal fuzzy numbers. Ghanas institute of industrial engineering and management, technical university of wroclaw, poland m. Department of mathematics, indian institute of technology, patna, india. We suggest a method allowing to take into account the uncertainty of subcontracted orders. To achieve it, we first present some shortcomings of the existing possibility degree method and score function of ifns. This paper provides an overview of possibility theory, emphasizing its historical roots and its recent developments.
Information sciences 30, 183224 1983 183 ranking fuzzy numbers in the setting of possibility theory didier dubois department of automatics dera, c. Herrera and verdegay 1995 present methods to solve fuzzy integer linear. Debates have been taking place, in the literature, between two classes of researchers. How different are ranking methods for fuzzy numbers.
Perhaps youre already aware of this, but chapters 3, 7 and 9 of george j. The central concept of fuzzy measure theory is the fuzzy measure also capacity, see which was introduced by choquet in 1953 and independently defined by sugeno in 1974 in the context of fuzzy integrals. In this paper we consider the problem of ranking a set of intuitionistic fuzzy numbers. Fuzzy possibility graphs and their application to ranking fuzzy. One modification of fuzzy topsis method one modification of fuzzy topsis method zivojin prascevic. Ranking fuzzy numbers are an important aspect of decision making in a fuzzy environment. A novel approach for finding a shortest path in a mixed. We adopt a statistical viewpoint and interpret each intuitionistic fuzzy number as an ensemble of ordinary fuzzy numbers. Possibility theory can be cast either in an ordinal or in a numerical setting. Ranking fuzzy numbers in the setting of possibility theory, information sci.
An invitationto study fuzzy and generalized uncertainty. A possibilitybased method for ranking fuzzy numbers and. Equally important for application purposes is the problem of ranking. In the present paper, we define an improved possibility degree method to rank the different intuitionistic fuzzy numbers ifns. This enables us to define a fuzzy rank and a characteristic vagueness factor for each intuitionistic fuzzy number. This paper presents a discriminative analysis of approaches to ranking fuzzy numbers for decision making in a fuzzy environment. In this article, it has been shown that the fuzzy equation, where a, x, b are fuzzy numbers can be solved by using the method of superimposition of sets. What is the difference between probability and fuzzy logic. Since their inception in 1965, many authors have proposed different methods for ranking fuzzy numbers.
Ottovonguericke university of magdeburg faculty of computer science department of knowledge processing and language engineering r. New ranking method for fuzzy numbers by their expansion. Fuzzy set theory and its applications second, revised edition. Ranking fuzzy interval numbers in the setting of random. The proportion of the optimum fuzzy number ranking procedure measures the. Dubois, the role of fuzzy sets in decision sciences. Home about us subject areas contacts advanced search help help. Ranking of intuitionistic fuzzy number by centroid point. Hwang, fuzzy multiple attribute decision making methods and applications, lecture notes in economics and mathematical systems, springer, new york, 1992. In this paper, we develop a system dynamics framework for a closedloop supply chain with fuzzy demand and fuzzy collection rate by incorporating product exchange policy in forward channel and various recovery options in reverse. A modified approach based on ranking fuzzy numbers for fuzzy integer programming with equality constraints.
Ranking of znumbers and its application in decision making. There are also ranking methods for fuzzy numbers available in the literature. Ranking fuzzy numbers with a distance method using. Theory and applications 1995 provide indepth discussions on the differences between the fuzzy and probabilistic versions of uncertainty, as well as several other types related to evidence theory, possibility distributions, etc. Firstly, the score function and the accuracy function of triangular intuitionistic fuzzy number are given, the method for ranking triangular intuitionistic fuzzy. In mathematics, fuzzy measure theory considers generalized measures in which the additive property is replaced by the weaker property of monotonicity. Possibility theory lies at the crossroads between fuzzy sets, probability and. A guide to the fuzzynumbers package for r fuzzynumbers.
Dynamic ranking of multidimensional uncertain information. In this paper, we will introduce a new method of ranking generalized l. Information security investment decisionmaking based on. A znumberbased decision making procedure with ranking fuzzy numbers method, proc. A discriminative analysis of approaches to ranking fuzzy. Return to website theory, crisp and noncrisp sets representation, capturing uncertainty, examples. A theory of fuzzy arithmetic is presented towards a fuzzy. A modified approach based on ranking fuzzy numbers for. The method is based on cut sets and comparison relation on interval values.