Rakesh Kumar Bajaj

On Complex Intuitionistic Fuzzy Soft Sets with Distance Measures and Entropies

We introduce the concept of complex intuitionistic fuzzy soft sets which is parametric in nature. However, the theory of complex fuzzy sets and complex intuitionistic fuzzy sets are independent of the parametrization tools. Some real life problems, for example, multicriteria decision making problems, involve the parametrization tools. In order to get their new entropies, some important properties and operations on the complex intuitionistic fuzzy soft sets have also been discussed. On the basis of some well-known distance measures, some new distance measures for the complex intuitionistic fuzzy soft sets have also been obtained. Further, we have established correspondence between the proposed entropies and the distance measures of complex intuitionistic fuzzy soft sets.

Vendor Selection under Intuitionistic Trapezoidal Fuzzy Multiple Criteria Decision Making Model with Entropy Weights

In the present communication, we have implemented the concept of intuitionistic trapezoidal fuzzy numbers (ITFNs) to the study of multiple criteria decision making (MCDM) problem for evaluating the best vendor/supplier whose information take the form of ITFNs. We propose a new algorithm for ITF-MCDM problem where the weights of the involved attributes are supposed to be completely unknown. These weights have been calculated on the basis of the decision makers qualitative opinion to the attributes with the help of pre-defined linguistic variables and an entropy measure. Finally, the ranking of the vendors/suppliers has been determined by calculating the hamming distance between the ideal alternative and all the available alternatives.

Reliability Properties of Residual Life Time and Inactivity Time of Series and Parallel System

Reliability Properties of Residual Life Time and Inactivity Time of Series and Parallel System The concepts of residual life time and inactivity time are extensively used in reliability theory for modeling life time data. In this paper we prove some new results on stochastic comparisons of residual life time and inactivity time in series and parallel systems. These results are in addition to the existing results of Li & Zhang (2003) and Li & Lu (2003). We also present sufficient conditions for aging properties of the residual life time and inactivity life time of series and parallel systems. Some examples from Weibull and Gompertz distributions are provided to support the results as well.

Sorting of Decision Making Units in Data Envelopment Analysis with Intuitionistic Fuzzy Weighted Entropy

Analysis method used for measuring and evaluating the efficiency of decision making units is basically a linear programming based technique. It has number of inputs and outputs included in the analysis and takes account of the relationship between inputs and outputs. Analysis method has clear advantages over competing approaches such as data envelopment analysis (DEA). In the present paper, we propose a new algorithm for decision making units in context of intuitionistic fuzzy weighted entropy in order to rank decision making units in data envelopment analysis.

R-norm Intuitionistic Fuzzy Information Measures and Its Computational Applications

Atanassov introduced the concept of intuitionistic fuzzy sets (IFS), as a generalization of fuzzy sets, which is capable of capturing the information that includes some degree of hesitation. In the present communication, a new R-norm intuitionistic fuzzy entropy and a weighted R-norm intuitionistic fuzzy directed divergence measure have been proposed with their proof of validity. Further, empirical study on the proposed information measures has also been done which explains monotonic nature of the information measures with respect to R and the weight. Computational applications of these information measures in the field of pattern recognition and image thresholding has been proposed with discussion.

'Useful' fuzzy measures of information, integrated ambiguity and directed divergence

In the present paper, a new concept of ‘useful’ fuzzy information, based on utility, is introduced by considering the uncertainties of fuzziness and probabilities of random events. A ‘useful’ fuzzy measure of integrated ambiguity is obtained by integration of fuzzy and probabilistic uncertainties with utility. A new ‘useful’ measure of fuzzy-directed divergence of a fuzzy set from another fuzzy set is proposed and its validity proved. Finally, the constrained optimisation of ‘useful’ fuzzy entropy and ‘useful’ fuzzy-directed divergence is studied.

Expected value based ranking of intuitionistic fuzzy variables

In the present paper, we introduce the idea of intuitionistic fuzzy variables by means of credibility theory. The mean value of intuitionistic fuzzy variables is obtained with the help of credibility distribution. Then, we develop a more comprehensive ranking method based on mean value of intuitionistic fuzzy variable. Also, we analyze the consistency of the propose ranking method with existing ranking methods.

Preservation Properties of the Laplace Transform and Moment Generating Function Ordering of Residual Life and Inactivity Time

Abstract In the present communication, we study some preservation properties of the Laplace transform ordering and the moment generating function ordering of residual life and inactivity time under the reliability operation of convolution. These results are in addition to the existing results available in the literature.

Fuzzy Entropy on Restricted Fuzzy Linear Regression Model with Cross Validation and Applications

The concept of fuzzy regression model with fuzzy regression coefficients was first introduced in [4], [5] and [6]. A fuzzy number can be uniquely determined through its position and entropy as described in [9]. Hence, by using the concept of fuzzy entropy the estimators of the fuzzy regression coefficients may be estimated. In the present communication, we develop a newer fuzzy linear regression (FLR) model with some restrictions in the form of prior information. We have obtained the estimators of regression coefficients with the help of fuzzy entropy for the restricted FLR model. Applications on some hypothetical numerical examples are provided in order to illustrate the proposed model and the obtained estimators. Cross validation of the regression model has been done based on computation of R2 and using F-test. The proposed model may find applications in various areas of actuarial sciences, fuzzy time series analysis, management decision making etc.

On Some Reliability Properties of Mean Inactivity Time under Weighing

the present communication, we discuss some reliability properties of mean inactivity time order and study the preservation of mean inactivity time under some weight function. Weighted Distribution methods arise in the context of research related to reliability, data gathering, ecology, inference, modeling, bio-medicine and several other areas. In general, weighted distributions have wide role for the analysis of life time data.