A new method for solving fully fuzzy linear programming with. Representation, ranking, distance, and similarity of lr. In this paper, we introduce a fuzzy distance by using graded mean integration representation of generalized lr type fuzzy number and the span of fuzzy number, we also discuss the distance of the linguistic data of ldquogreater or less than xrdquo and ldquoabout xrdquo. Next, equivalent conditions for regular fuzzy numbers as well as regular lr fuzzy numbers can be given via the following theorems. In this section, we take the point of view that the distance between two fuzzy numbers should itself be fuzzy.
Pdf fuzzy arithmetic on lr fuzzy numbers with applications. Proposals are based on the strategy of characterization of a fuzzy. Ordering lr type generalized trapezoidal fuzzy numbers. In this group pdf of data has been assumed to have the form of.
Investigation of basic concepts of fuzzy arithmetic citeseerx. Science and technology, general fuzzy algorithms methods fuzzy logic fuzzy systems. Lrtype fuzzy numbers with unknown conditional probability density function. Any fuzzy number can be thought of as a function whose domain is a specified set usually the set of real numbers, and whose range is the span of nonnegative real numbers between, and including, 0 and. Pdf pentagonal fuzzy number iir publications academia.
A fuzzy number is a quantity whose value is imprecise, rather than exact as is the case with ordinary singlevalued numbers. A fuzzy number is a generalization of a regular, real number in the sense that it does not refer to one single value but rather to a connected set of possible values, where each possible value has its own weight between 0 and 1. Chen and others published representation, ranking, distance, and similarity of lr type fuzzy number and application find, read and cite all the research you. Similarly, lrtype fuzzy numbers are also used to describe data types for student and patient blood pressure data. A fuzzy number is of lr type if there exists a reference function for left and for right and scalar, with where is a real number whose membership value is 1, and are called the left and right spreads, respectively. On lr type interval valued fuzzy numbers in critical path. In the fuzzy number literature, there are many proposals for ordering left and right lrtype fuzzy numbers. An inventory model with allowable shortage using trapezoidal. A note on the revised method of ranking lr fuzzy number. To illustrate our method, a numerical example is solved. Recently, wang, liu, fan, and feng in press proposed an approach to overcome the limitations of the existing studies and simplify the computational procedures based on the lr deviation degree of fuzzy number. The method is able to rank every kind of fuzzy numbers that has. In this work, we have concentrated on the solution of rectangular games by principle of dominance using lr type trapezoidal fuzzy numbers. Here, using our recently developed approach for addition of mixed fuzzy numbers in tajdin 2010, we describe a methodology to multiply various fuzzy numbers using.
R 0, 1 and it has a fuzzy number a is a fuzzy set on the real. A new version of knn method is used to estimate conditional. Pdf fuzzy bayesian classification of lr fuzzy numbers. Countable fuzzy numbers, operations, regression and a specificity type ordering a. The nonlinear programming method is a precise method. Fuzzy clustering on lrtype fuzzy numbers with an application. Expert systems with applications, 37, 50565060 poi. Lr trapezoidal fuzzy number lr let a p 1 q 1 r 1, s 1. Lr type fuzzy numbers are quite common in practical life situations involving the triangular fuzzy number, the gaussian fuzzy number, cauchy fuzzy. Entropy and semientropies of lr fuzzy numbers linear. In the fuzzy number literature, there are many proposals for ordering lrleft and right type fuzzy numbers. Solution of rectangular fuzzy games by principle of dominance. In addition, well introduce special kind of fuzzy number such as triangular fuzzy number and trapezoidal fuzzy number.
The fuzzy set theory thus provides a strict mathematical framework in which vague conceptual phenomena can be precisely and rigorously studied. Cut approach for fuzzy product and its use in computing. Without loss of generality, let if,it can be transformed to the situation. A new distance function for lr type interval valued fuzzy. Note that, lrtype fuzzy numbers were first introduced by dubois and prade. Pdf fuzzy data is considered as an imprecise type of data with a source of uncertainty. Where are clear numbers, and are lr type fuzzy numbers. Fuzzy arithmetic on lr fuzzy numbers with applications to fuzzy programming article pdf available in journal of intelligent and fuzzy systems 301. In this paper, the distance between two generalized lr type fuzzy numbers based on the absolute value of difference of the graded mean integration. First of all, well look into interval, the fundamental concept of fuzzy number, and then operation of fuzzy numbers. In the above works, x is a crisp random variable and only its mean value is considered as a fuzzy number.
Fuzzy clustering on lr type fuzzy numbers with an application in taiwanese tea evaluation author links open overlay panel wenliang hung a miinshen yang b show more. A guide to the fuzzynumbers package for r cran r project. Afuzzy number a is of lr type if there exist reference functions land r,scalars. Fuzzy set theoryand its applications, fourth edition. In this paper, we use lrtype fuzzy numbers to approximate fuzzy numbers. Chapter 5 fuzzy number this chapter describes fuzzy numbers. Original article, report by advances in natural and applied sciences. In our paper we are developing an inventory model using trapezoidal fuzzy number for holding cost, ordering cost and shortage cost. On a similarity measure between lrtype fuzzy numbers and its.
Aggregating the results into the fp models with entropy or semientropies as risk measures, four meanentropy or meansemientropy optimization models are formulated. The aim of this paper is to find the formula for the elementary operations on lr fuzzy number. The revised method of ranking lr fuzzy number based on deviation degree. The next definition is related to the concept of lrtype fuzzy numbers throughout the text, we refer to lrtype fuzzy numbers simply as fuzzy number. Suppose two fuzzy numbers and, represented as lr fuzzy numbers of the form 3 the sum is again an lr fuzzy number of the form 4 with the modal value 5 and the spreads 6 in short we can write 7 the lefthand reference functions of both fuzzy numbers and have to be given by l, and the right hand reference functions by r. Pdf methods for ordering fuzzy numbers play an important role as decision criteria, with applications in areas such as optimization and data mining. A% is called lrtype fuzzy number, where m is called the center or mean of a%. Multiplication operation on fuzzy numbers is defined by the extension principle. The revised method of ranking lr fuzzy number based on. Fuzzy sets and fuzzy techniques lecture 9 fuzzy numbers. Jul 15, 2008 properties of fuzzy distance of lr type fuzzy numbers abstract. Representation, ranking, distance, and similarity of lr type. Fuzzy arithmetic on lr fuzzy numbers with applications to. Representation, ranking, distance, and similarity of lr type fuzzy.
Fuzzy shortest path problem based on level triangular lr. Fuzzy sets and systems special issue on fuzzy numbers and. Properties of fuzzy distance of lr type fuzzy numbers ieee. Regular lr fuzzy number a fuzzy number is said to be a regular lr fuzzy number if it is an lr fuzzy number with a regular credibility distribution. Based on extension principle, nonlinear programming method, analytical method, computer drawing method and computer simulation method are used for solving multiplication operation of two fuzzy numbers. We study some properties of our new method, comparing our results with those generated by other methods previously discussed in literature. We use also lr type fuzzy numbers and our model covers a wide class of fuzzy numbers, such as triangular fuzzy numbers. One approach for multiplication of fuzzy numbers is to employ. And suppose are both symmetric lr type fuzzy numbers for simplicity. Pdf a note on ranking of lr fuzzy numbers researchgate.
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