Shapes Of Fuzzy Numbers Research Articles

On the analysis of interval data based game theoretical problem under various symmetric fuzzy environments

In a real world environment, the payoffs of a matrix game are varying between two fixed values because of uncertainty. This type of payoffs may not be defined as a crisp numbers. In order to model such uncertainty, the payoffs can be represented as interval numbers. A matrix game with payoffs of such interval numbers are called interval data based matrix game. This work takes an initiative to solve the interval data based matrix game in an uncertain environment. In order to find the optimum solution of the interval matrix game without the knowledge of interval arithmetic, the fuzzy set theory is used in various symmetric environments. Finally the analysis is made on the solutions obtained through various symmetric fuzzy environments with the help of different shapes of fuzzy numbers.

Error analysis between two different fuzzy multiplication operations on Triangular Fuzzy Number

One of the basic contents of fuzzy mathematics is the mathematical operations of fuzzy numbers. But still some of the fuzzy mathematical operations are not determined. There are some operations between fuzzy numbers are exact and there are approximated operations. In this paper, a comparison has been presented between two different fuzzy multiplication operations. One of these two fuzzy multiplication operations is exact with using interval arithmetic cut method and the other one is an approximation method which uses a standard approximation. In the two different methods, the fuzzy numbers will be defined as triangular fuzzy numbers because the triangular fuzzy number is the most popular one between the other shapes of fuzzy numbers. A numerical example has been presented with graphical result to show the difference between them and to analyze the error.

Multi Criteria Decision Making Based on Classical α-Cut Approach

Multi Criteria Decision Making (MCDM) is the process to find the best alternatives among a set of available alternatives in presence of various conflicting criteria. In this paper MCDM method is presented using α-cut approach and it is observed that α-cut approach is general enough to deal with MCDM methods. Here first fuzzy numbers have been assigned to quantify different qualitative criteria of alternatives and then their α-cut values are evaluated and then performed some arithmetic operation to order ranking of the alternatives. Finally, a decision making problem is carried out with different case studies by using different shapes of fuzzy numbers. Keywords: Multi criteria decision making, fuzzy numbers, α-cut of fuzzy number.

The law of large numbers and renewal process for T-related weighted fuzzy numbers on [formula omitted

This paper considers the law of large numbers for T-related weighted fuzzy variables whose underlying spaces are Rp. We provide new sufficient conditions that do not depend on the shape of fuzzy numbers and the additive generator of a t-norm T for the law of large numbers for T-related weighted fuzzy variables. The results provide a far-reaching generalization of previous findings on the law of large numbers for T-related fuzzy numbers. In addition, we prove T-related fuzzy renewal theorems in which the inter-arrival time is characterized as weighted fuzzy numbers under t-norm-based fuzzy operations on Rp by using the law of large numbers for weighted fuzzy variables on Rp. We also investigate the law of large numbers and the renewal process for T-related fuzzy numbers on Rp with respect to the credibility measure, the chance measure, and the expected value.

A new fuzzy multicriteria decision making method and its application in diversion of water

Taking account of uncertainty in multicriteria decision making problems is crucial due to the fact that depending on how it is done, ranking of alternatives can be completely different. This paper utilizes linguistic values to evaluate the performance of qualitative criteria and proposes using appropriate shapes of fuzzy numbers to evaluate the performance of quantitative criteria for each problem with respect to its particular conditions. In addition, a process to determine the weights of criteria using fuzzy numbers, which considers their competition to gain greater weights and their influence on each other is described. A new fuzzy methodology is proposed to solve such a problem that utilizes parametric form of fuzzy numbers. The case study of diversion of water into Lake Urmia watershed, which is defined using triangular, trapezoidal, and bell-shape fuzzy numbers demonstrates the utility of the proposed method.

ON SOME STRUCTURES OF FUZZY NUMBERS

The operations in the set of fuzzy numbers are usually obtained by the Zadeh extension principle. But these definitions can have some disadvan- tages for the applications both by an algebraic point of view and by practical aspects. In fact the Zadeh multiplication is not distributive with respect to the addition, the shape of fuzzy numbers is not preserved by multiplication, the indeterminateness of the sum is too increasing. Then, for the applications in the Natural and Social Sciences it is important to individuate some suitable variants of the classical addition and multiplication of fuzzy numbers that have not the previous disadvantage. Here, some possible alternatives to the Zadeh operations are studied.

THE USE OF STEAM REGRESSION WITH CLEAR PARAMETERS ON FUZZY NUMBERS TO MODEL THE EXPERT MONETARY VALUATION OF LAND PLOTS

The urgency of modeling of land assessment expert procedure is shown. The complexities, which is arising during application of usual mathematical methods to data, which has expert origin, are analyzed. Limitations in usage of existing fuzzy regression methods are analyzed. It has been offered fuzzy regression method, which does not apply limitations on the shape of fuzzy numbers.