Search

Equilibrium distribution finds various applications in reliability, stochastic processes, repairable systems and many areas of applied probability such as renewal risk model etc. This paper deals with some of the reliability properties of reliability structures under equilibrium random variable(s). The likelihood ratio ordering for the series and parallel systems has been established under equilibrium. Further, the log-concavity properties of series and parallel systems having independently and identically distributed (i.i.d.) components under the condition of equilibrium have been studied.

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 maker's 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.

The concept of fuzzy regression model with fuzzy regression coefficients was first introduced in \cite{[1]}, \cite{[2]} and \cite{[3]}. A fuzzy number can be uniquely determined through its position and entropy as described in \cite{[4]}. 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 $R^2$ and using $F$-test. The proposed model may find applications in various areas of actuarial sciences, fuzzy time series analysis, management decision making etc.

The concept of intuitionistic fuzzy sets (IFSs) is considered as a generalization of fuzzy sets and capable of capturing the information that includes some degree of hesitation which is applicable in various fields of research. In the present communication, various existing similarity measures for intuitionistic fuzzy sets have been studied. A new similarity measure for intuitionistic fuzzy sets (IFSs) which calculate the similarity between IFSs on the basis of NTV Metric has been proposed. Further, a computational analysis for medical diagnosis has been performed on the basis of the calculation of similarity from a considered case to all considered illness and values of all symptoms. Based on the comparative analysis, we find that the proposed similarity measure is a better and more robust and gives closer results as compared to the existing similarity measures for IFSs.

The existing fuzzy information system associated with the probabilities of a number of events, does not take into account the effectiveness or importance or utility of these events. In the present communication, we propose a new mathematical model for `useful' fuzzy information system which involves fuzzy information, randomness and utility distribution. The model has been designed in order to study information in a random experiment. Based on the model, a family of fuzzy directed divergence measures has also been introduced and discussed. The parametric information improvement measure in view of fuzziness and utility has been obtained. The monotonic nature of the information measures has been studied with the help of numerical examples with certain number of experimental observations.

Reliability Engineering has an appreciable role in the design and development of a technical system which should be reliable in various applications viz. military application, space exploration etc. In the present paper, we consider the framework of Series and Parallel Systems under the usage of trapezoidal intuitionistic fuzzy sets for the evaluation. An application of the presented framework has also been provided for marine power plant.