PARTHIBAN SELVAM | Vignan's University (original) (raw)

Papers by PARTHIBAN SELVAM

Trapezoidal fuzzy numbers have numerous advantages over triangular fuzzy numbers as they have mor... more Trapezoidal fuzzy numbers have numerous advantages over triangular fuzzy numbers as they have more generalized form. In this paper, two sample statistical test of hypothesis for means in normal population with interval data is given. The decision rules whether to accept or reject the null hypothesis or alternative hypothesis are given. Using numerical example, the test procedure is illustrated. The proposed test procedure has been extended to fuzzy valued statistical hypothesis testing for trapezoidal interval data.

Mathematical theory and modeling, 2015

Most of our traditional tools in descriptive and inferential statistics is based on crispness (pr... more Most of our traditional tools in descriptive and inferential statistics is based on crispness (preciseness) of data, measurements, random variable, hypotheses, and so on. By crisp we mean dichotomous that is, yes-or-no type rather than more-or-less type. But there are many situations in which the above assumptions are rather non-realistic such that we need some new tools to characterize and analyze the problem. By introducing fuzzy set theory, different branches of mathematics are recently studied. But probability and statistics attracted more attention in this regard because of their random nature. Mathematical statistics does not have methods to analyze the problems in which random variables are vague (fuzzy). In this regard, a simple and new technique for testing the hypotheses under the fuzzy environments is proposed. Here, the employed data are in terms of trapezoidal fuzzy numbers (TFN) which have been transformed into interval data using interval method and on the grou...

Trapezoidal fuzzy numbers have many advantages over triangular fuzzy numbers as they have more ge... more Trapezoidal fuzzy numbers have many advantages over triangular fuzzy numbers as they have more generalized form. In this paper, we have approached a new method where trapezoidal fuzzy numbers are defined in terms of α-level of trapezoidal interval data based on this approach, the test of hypothesis is performed.

This paper deals with the problem of two factor ANOVA test using Trapezoidal Fuzzy Numbers (TFNs)... more This paper deals with the problem of two factor ANOVA test using Trapezoidal Fuzzy Numbers (TFNs). The proposed ANOVA test is analysed under various types of trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function, Ranking Function, Total Integral Value and Graded Mean Integration Representation. Finally a comparative view of the conclusions obtained from various test is given. Moreover, two numerical examples having different conclusions have been given for a concrete comparative study.

Bulletin of Mathematical Sciences and Applications, 2016

This paper deals with the problem of three factor ANOVA model (Latin Square Design-LSD) test usin... more This paper deals with the problem of three factor ANOVA model (Latin Square Design-LSD) test using Trapezoidal Fuzzy Numbers (tfns.). The proposed test is analysed under various types of trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function, Ranking Function, Total Integral Value and Graded Mean Integration Representation. Finally a comparative view of the conclusions obtained from various test is given. Moreover, two numerical examples having different conclusions have been given for a concrete comparative study.

This paper deals with the problem of one factor ANOVA test using Trapezoidal Fuzzy N... more This paper deals with the problem of one factor ANOVA test using Trapezoidal Fuzzy Numbers (TFNs.). The proposed ANOVA test is analysed under various types of trapezoidal fuzzy models such as Alpha Cut Interval, Ranking Function, Total Integral Value and Graded Mean Integration Representation (GMIR). Finally a comparative view of all conclusions obtained from various tests is given. Moreover, two numerical examples having different conclusions have been illustrated for a concrete comparative study.

This paper proposes a method for testing hypotheses over two sample t-test under fuzzy environmen... more This paper proposes a method for testing hypotheses over two sample t-test under fuzzy environments using trapezoidal fuzzy numbers (tfns.). In fact, trapezoidal fuzzy numbers have many advantages over triangular fuzzy numbers as they have more generalized form. Here, we have approached a new method where trapezoidal fuzzy numbers are defined in terms of alpha level of trapezoidal interval data and based on this approach, the test of hypothesis is performed. Moreover the proposed test is analysed under various types of trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function, Ranking Function, Total Integral Value and Graded Mean Integration Representation. And two numerical examples have been illustrated. Finally a comparative view of all conclusions obtained from various test is given for a concrete comparative study.

This paper deals with the problem of Latin Square Design (LSD) that is three factor ANOVA test us... more This paper deals with the problem of Latin Square Design (LSD) that is three factor ANOVA test using Trapezoidal Fuzzy Numbers (tfns.). The proposed test is analysed under various types of trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function, Ranking Function, Total Integral Value and Graded Mean Integration Representation. Finally a comparative view of the conclusions obtained from various test is given. Moreover, two numerical examples having different conclusions have been given for a concrete comparative study.

This paper proposes a method for testing hypotheses over one sample t-test under fuzzy environmen... more This paper proposes a method for testing hypotheses over one sample t-test under fuzzy environments using trapezoidal fuzzy numbers (tfns.). In fact, trapezoidal fuzzy numbers have many advantages over triangular fuzzy numbers as they have more generalized form. Here, we have approached a new method where trapezoidal fuzzy numbers are defined in terms of alpha level of trapezoidal interval data and based on this approach, the test of hypothesis is performed. More over the proposed test is analysed under various types of trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function, Ranking Function, Total Integral Value and Graded Mean Integration Representation. And two numerical examples have been illustrated. Finally a comparative view of all conclusions obtained from various test is given for a concrete comparative study.

The 2 power 2 factorial experiment using Trapezoidal Fuzzy Numbers (tfns.) is proposed here. And ... more The 2 power 2 factorial experiment using Trapezoidal Fuzzy Numbers (tfns.) is proposed here. And the proposed test is analysed under various types of trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function,
Ranking Function, Total Integral Value and Graded Mean Integration Representation. Finally a comparative view of the conclusions obtained from various test is given. Moreover, two numerical examples having different conclusions have been illustrated for a concrete comparative study.

This paper deals with the problem of three factor ANOVA model (Latin Square Design-LSD) test usin... more This paper deals with the problem of three factor ANOVA model (Latin Square Design-LSD) test
using Trapezoidal Fuzzy Numbers (tfns.). The proposed test is analysed under various types of
trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function, Ranking Function,
Total Integral Value and Graded Mean Integration Representation. Finally a comparative view of
the conclusions obtained from various test is given. Moreover, two numerical examples having
different conclusions have been given for a concrete comparative study.

This paper deals with the problem of Latin Square Design (LSD) test using Trapezoidal Fuzzy Numbe... more This paper deals with the problem of Latin Square Design (LSD) test using Trapezoidal Fuzzy Numbers (tfns.). The proposed test is analysed under various types of trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function, Ranking Function, Total Integral Value and Graded Mean Integration Representation. Finally a comparative view of the conclusions obtained from various test is given. Moreover, two numerical examples having different conclusions have been given for a concrete comparative study.

Trapezoidal fuzzy numbers have numerous advantages over triangular fuzzy numbers as they have mor... more Trapezoidal fuzzy numbers have numerous advantages over triangular fuzzy numbers as they have more
generalized form. In this paper, two sample statistical test of hypothesis for means in normal population with interval data
is given. The decision rules whether to accept or reject the null hypothesis or alternative hypothesis are given. Using
numerical example, the test procedure is illustrated. The proposed test procedure has been extended to fuzzy valued
statistical hypothesis testing for trapezoidal interval data.

Trapezoidal fuzzy numbers have many advantages over triangular fuzzy numbers as they have more ge... more Trapezoidal fuzzy numbers have many
advantages over triangular fuzzy numbers as they have
more generalized form. In this paper, we have
approached a new method where trapezoidal fuzzy
numbers are defined in terms of α - level of
trapezoidal interval data based on this approach, the
test of hypothesis is performed.

This paper deals with the problem of two factor ANOVA test using Trapezoidal Fuzzy Numbers (TFNs)... more This paper deals with the problem of two factor ANOVA test using Trapezoidal Fuzzy Numbers (TFNs). The proposed ANOVA test is analysed under various types of trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function, Ranking
Function, Total Integral Value and Graded Mean Integration Representation. Finally a comparative view of the conclusions obtained from various test is given. Moreover, two numerical examples having different conclusions have been given for a concrete comparative study.

Most of our traditional tools in descriptive and inferential statistics is based on crispness (pr... more Most of our traditional tools in descriptive and inferential statistics is based on crispness (preciseness) of data, measurements, random variable, hypotheses, and so on.
By crisp we mean dichotomous that is, yes-or-no type rather than more-or-less type. But there are many situations in which the above assumptions are rather non-realistic such that we need some new tools to characterize and analyze the problem. By introducing
fuzzy set theory, different branches of mathematics are recently studied. But probability and statistics attracted more attention in this regard because of their random nature. Mathematical statistics does not have methods to analyze the problems in which random
variables are vague (fuzzy).
In this regard, a simple and new technique for testing the hypotheses under the fuzzy environments is proposed. Here, the employed data are in terms of trapezoidal
fuzzy numbers (TFN) which have been transformed into interval data using α-cut interval method and on the grounds of the transformed fuzzy data, the one-factor ANOVA test is executed and decisions are concluded. This concept has been illustrated
by giving two numerical examples.

Most of our traditional tools in descriptive and inferential statistics is based on crispness (pr... more Most of our traditional tools in descriptive and inferential statistics is based on crispness (preciseness) of data, measurements, random variable, hypotheses, and so on.
By crisp we mean dichotomous that is, yes-or-no type rather than more-or-less type. But
there are many situations in which the above assumptions are rather non-realistic such that we need some new tools to characterize and analyze the problem. By introducing
fuzzy set theory, different branches of mathematics are recently studied. But probability and statistics attracted more attention in this regard because of their random nature. Mathematical statistics does not have methods to analyze the problems in which random variables are vague (fuzzy).
In this regard, a simple and new technique for testing the hypotheses under the
fuzzy environments is proposed. Here, the employed data are in terms of trapezoidal fuzzy numbers (TFN) which have been transformed into interval data using α-cut
interval method and on the grounds of the transformed fuzzy data, the one-factor ANOVA test is executed and decisions are concluded. This concept has been illustrated by giving two numerical examples.

Mathematical theory and modeling, 2015

Bulletin of Mathematical Sciences and Applications, 2016

This paper deals with the problem of three factor ANOVA model (Latin Square Design-LSD) test usin... more This paper deals with the problem of three factor ANOVA model (Latin Square Design-LSD) test
using Trapezoidal Fuzzy Numbers (tfns.). The proposed test is analysed under various types of
trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function, Ranking Function,
Total Integral Value and Graded Mean Integration Representation. Finally a comparative view of
the conclusions obtained from various test is given. Moreover, two numerical examples having
different conclusions have been given for a concrete comparative study.

Trapezoidal fuzzy numbers have numerous advantages over triangular fuzzy numbers as they have mor... more Trapezoidal fuzzy numbers have numerous advantages over triangular fuzzy numbers as they have more
generalized form. In this paper, two sample statistical test of hypothesis for means in normal population with interval data
is given. The decision rules whether to accept or reject the null hypothesis or alternative hypothesis are given. Using
numerical example, the test procedure is illustrated. The proposed test procedure has been extended to fuzzy valued
statistical hypothesis testing for trapezoidal interval data.

Trapezoidal fuzzy numbers have many advantages over triangular fuzzy numbers as they have more ge... more Trapezoidal fuzzy numbers have many
advantages over triangular fuzzy numbers as they have
more generalized form. In this paper, we have
approached a new method where trapezoidal fuzzy
numbers are defined in terms of α - level of
trapezoidal interval data based on this approach, the
test of hypothesis is performed.

This paper deals with the problem of two factor ANOVA test using Trapezoidal Fuzzy Numbers (TFNs)... more This paper deals with the problem of two factor ANOVA test using Trapezoidal Fuzzy Numbers (TFNs). The proposed ANOVA test is analysed under various types of trapezoidal fuzzy models such as Alpha Cut Interval, Membership Function, Ranking
Function, Total Integral Value and Graded Mean Integration Representation. Finally a comparative view of the conclusions obtained from various test is given. Moreover, two numerical examples having different conclusions have been given for a concrete comparative study.

Most of our traditional tools in descriptive and inferential statistics is based on crispness (pr... more Most of our traditional tools in descriptive and inferential statistics is based on crispness (preciseness) of data, measurements, random variable, hypotheses, and so on.
By crisp we mean dichotomous that is, yes-or-no type rather than more-or-less type. But there are many situations in which the above assumptions are rather non-realistic such that we need some new tools to characterize and analyze the problem. By introducing
fuzzy set theory, different branches of mathematics are recently studied. But probability and statistics attracted more attention in this regard because of their random nature. Mathematical statistics does not have methods to analyze the problems in which random
variables are vague (fuzzy).
In this regard, a simple and new technique for testing the hypotheses under the fuzzy environments is proposed. Here, the employed data are in terms of trapezoidal
fuzzy numbers (TFN) which have been transformed into interval data using α-cut interval method and on the grounds of the transformed fuzzy data, the one-factor ANOVA test is executed and decisions are concluded. This concept has been illustrated
by giving two numerical examples.

Most of our traditional tools in descriptive and inferential statistics is based on crispness (pr... more Most of our traditional tools in descriptive and inferential statistics is based on crispness (preciseness) of data, measurements, random variable, hypotheses, and so on.
By crisp we mean dichotomous that is, yes-or-no type rather than more-or-less type. But
there are many situations in which the above assumptions are rather non-realistic such that we need some new tools to characterize and analyze the problem. By introducing
fuzzy set theory, different branches of mathematics are recently studied. But probability and statistics attracted more attention in this regard because of their random nature. Mathematical statistics does not have methods to analyze the problems in which random variables are vague (fuzzy).
In this regard, a simple and new technique for testing the hypotheses under the
fuzzy environments is proposed. Here, the employed data are in terms of trapezoidal fuzzy numbers (TFN) which have been transformed into interval data using α-cut
interval method and on the grounds of the transformed fuzzy data, the one-factor ANOVA test is executed and decisions are concluded. This concept has been illustrated by giving two numerical examples.