Shiv Prasad Yadav

Relative performance of academic departments using DEA with sensitivity analysis

The process of liberalization and globalization of Indian economy has brought new opportunities and challenges in all areas of human endeavor including education. Educational institutions have to adopt new strategies to make best use of the opportunities and counter the challenges. One of these challenges is how to assess the performance of academic programs based on multiple criteria. Keeping this in view, this paper attempts to evaluate the performance efficiencies of 19 academic departments of IIT Roorkee (India) through data envelopment analysis (DEA) technique. The technique has been used to assess the performance of academic institutions in a number of countries like USA, UK, Australia, etc. But we are using it first time in Indian context to the best of our knowledge. Applying DEA models, we calculate technical, pure technical and scale efficiencies and identify the reference sets for inefficient departments. Input and output projections are also suggested for inefficient departments to reach the frontier. Overall performance, research performance and teaching performance are assessed separately using sensitivity analysis.

A concept of fuzzy input mix-efficiency in fuzzy DEA and its application in banking sector

Data envelopment analysis (DEA) is a linear programming based non-parametric technique for evaluating the relative efficiency of homogeneous decision making units (DMUs) on the basis of multiple inputs and multiple outputs. There exist radial and non-radial models in DEA. Radial models only deal with proportional changes of inputs/outputs and neglect the input/output slacks. On the other hand, non-radial models directly deal with the input/output slacks. The slack-based measure (SBM) model is a non-radial model in which the SBM efficiency can be decomposed into radial, scale and mix-efficiency. The mix-efficiency is a measure to estimate how well the set of inputs are used (or outputs are produced) together. The conventional mix-efficiency measure requires crisp data which may not always be available in real world applications. In real world problems, data may be imprecise or fuzzy. In this paper, we propose (i) a concept of fuzzy input mix-efficiency and evaluate the fuzzy input mix-efficiency using @a - cut approach, (ii) a fuzzy correlation coefficient method using expected value approach which calculates the expected intervals and expected values of fuzzy correlation coefficients between fuzzy inputs and fuzzy outputs, and (iii) a new method for ranking the DMUs on the basis of fuzzy input mix-efficiency. The proposed approaches are then applied to the State Bank of Patiala in the Punjab state of India with districts as the DMUs.

Fuzzy Reliability of a Marine Power Plant Using Interval Valued Vague Sets

In conventional reliability analysis, the failure probabilities of the components of a system are treated as exact values. It is often difficult to obtain data for failure probabilities under changing environmental conditions. Hence fuzzy sets are used to analyze the fuzzy system reliability, where a fuzzy number represents the reliability of each component. Chen [14] analyzed the fuzzy system reliability using vague set theory. The values of the membership and non-membership of an element, in a vague set, are represented by a real number in [0, 1]. A specialist is always uncertain about the values of the membership and non-membership of an element in a set. Hence, it is better to represent the values of the membership and non-membership of an element in a set by intervals of possible real numbers instead of real numbers. In this paper a new method has been developed for analyzing the fuzzy system reliability of a series and parallel system using interval valued trapezoidal vague sets, where the reliability of each component of each system is represented by an interval valued trapezoidal vague set defined in the universe of discourse [0, 1].The developed method has been used to analyze the fuzzy reliability of a marine power plant. The major advantage of the proposed approach (the concept of interval valued vague sets) over the existing approaches [7, 8, 14] is that the proposed approach separates the positive and negative evidence for the membership of an element in a set. Also in the proposed approach the values of the membership and non- membership of an element in a set are intervals instead of a single real number.

A novel approach for analyzing fuzzy system reliability using different types of intuitionistic fuzzy failure rates of components.

This paper addresses the fuzzy system reliability analysis using different types of intuitionistic fuzzy numbers. Till now, in the literature, to analyze the fuzzy system reliability, it is assumed that the failure rates of all components of a system follow the same type of fuzzy set or intuitionistic fuzzy set. However, in practical problems, such type of situation rarely occurs. Therefore, in the present paper, a new algorithm has been introduced to construct the membership function and non-membership function of fuzzy reliability of a system having components following different types of intuitionistic fuzzy failure rates. Functions of intuitionistic fuzzy numbers are calculated to construct the membership function and non-membership function of fuzzy reliability via non-linear programming techniques. Using the proposed algorithm, membership functions and non-membership functions of fuzzy reliability of a series system and a parallel systems are constructed. Our study generalizes the various works of the literature. Numerical examples are given to illustrate the proposed algorithm.

Fuzzy system reliability evaluation using time-dependent intuitionistic fuzzy set

In general, fuzzy sets are used to analyse the system reliability. In this article, the concept of fuzzy set is extended by the idea of intuitionistic fuzzy set (IFS) and a new general procedure is proposed to construct the membership and non-membership functions of the fuzzy reliability using time-dependent IFS. Here, failure rate function of the system is represented by a triangular intuitionistic fuzzy number (IFN). Also, using proposed approach, membership and non-membership functions of fuzzy reliability of series and parallel systems are constructed, where the failure rate of each component is taken as a time-dependent triangular IFN. The major advantage of using IFS over fuzzy sets is that IFS separate the positive and negative evidences for membership of an element in the set. Numerical examples are given to illustrate the proposed approach.

A new approach for analysing the fuzzy system reliability using intuitionistic fuzzy number

In general, fuzzy sets are used to analyse the fuzzy system reliability. In this paper, a new approach is developed for analysing the fuzzy system reliability of series and parallel systems using intuitionistic fuzzy set theory. For analysing the fuzzy system reliability, the definition of trapezoidal intuitionistic fuzzy number is introduced and arithmetic operations between two trapezoidal intuitionistic fuzzy numbers are also introduced. Also by considering several cases, it is shown that definitions of triangular intuitionistic fuzzy number, trapezoidal fuzzy number and triangular fuzzy number are the particular cases of the definition of trapezoidal intuitionistic fuzzy number introduced in this paper. For evaluating the fuzzy reliability of a series system and a parallel system, formulae are derived. For numerical verification of proposed approach, the fuzzy reliability of the basement flooding has been analysed using the proposed approach.

Intuitionistic fuzzy data envelopment analysis

Extend FDEA to intuitionistic FDEA (IFDEA) for handling intuitionistic fuzzy data.Develop IFDEA models and ranking methods for optimistic and pessimistic situations.Design a hybrid performance decision process in IFDEA to study overall performance.Present numerical examples and comparison with existing approach in DEA/IFDEA.Present application to the bank branches in India with intuitionistic fuzzy inputs. Intuitionistic fuzzy set (IFS) is an extension of fuzzy set and an approach to define a fuzzy set where available information is not sufficient to define an imprecise concept by means of a conventional fuzzy set. The existing fuzzy DEA (FDEA) models for measuring relative fuzzy efficiencies of decision making units (DMUs) are limited to fuzzy input/output data. However, in real life applications, some inputs and outputs of subjective, linguistic and vague forms may possess intuitionistic fuzzy essence instead of fuzziness. Therefore, in the present study, we extend FDEA to intuitionistic fuzzy DEA (IFDEA) in which the input/output data are represented by intuitionistic fuzzy numbers (IFNs), in particular triangular IFNs (TIFNs). This is the first study in analysing optimistic and pessimistic efficiencies with intuitionistic fuzzy input/output data in DEA. In this study, we develop models to measure optimistic and pessimistic efficiencies of each DMU in intuitionistic fuzzy environment (IFE). By using super-efficiency technique, we develop algorithms to obtain the complete ranking of the DMUs when optimistic and pessimistic situations are considered separately. Further, to rank the DMUs when both optimistic and pessimistic situations are taken simultaneously as hybrid approach, we propose two alternate ranking methods based on levels of inefficiencies and efficiencies respectively. To address the overall performance using optimistic and pessimistic situations together in IFEs, we propose a hybrid IFDEA performance decision model. To validate the proposed methodology and proposed ranking methods, we illustrate different numerical examples and then compare the results with an existing ranking approach based on geometric average efficiency index. Moreover, we present an application of the proposed approach to the banking sector in which two inputs, namely, labour and operating expenses possess intuitionistic fuzzy essence at branch level, and are represented as TIFNs.

Application of a Multi-objective Genetic Algorithm to Solve Reliability Optimization Problem

Presence of multiple objectives in a problem, in principle, gives rise to a set of optimal solution (largely known as Pareto-optimal solution), instead of single optimal solution. This type of problem is known as multi-objective optimization problem (MOP). In general a MOP has been solved using weighted sums or decision-making schemes. An alternative way is to look for the Pareto-optimal front. Many evolutionary algorithms (EAs) like genetic algorithm (GA) have been suggested to solve a MOP, hence termed as multi-objective evolutionary algorithms (MOEAs). Nondominated sorting genetic algorithm (NSGA-II) is one such MOEA which demonstrates the ability to indentify a Pareto-optimal front efficiently. Thus, it provides the decision maker (DM) a complete picture of the optimal solution space. This paper presents an application of NSGA-II in order to solve a multi-objective series system reliability optimization problem. Here, conflicting objectives such as maximization of system reliability and minimization of the system cost have been considered. Supremacy of the approach over the existing approach have been depicted and discussed through the results obtained.

A new approach for solving intuitionistic fuzzy transportation problem of type-2

In solving real life transportation problem, we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. In this paper, we formulate a transportation problem in which costs are triangular intuitionistic fuzzy numbers. We have defined accuracy function using score functions for membership and non membership functions of triangular intuitionistic fuzzy numbers. Then ordering of triangular intuitionistic fuzzy numbers using accuracy function has been proposed. We have utilized this ordering to develop methods for finding starting basic feasible solution in terms of triangular intuitionistic fuzzy numbers. Also the same ordering is utilized to develop intuitionistic fuzzy modified distribution method for finding the optimal solution. Finally the method is illustrated by a numerical example which is followed by graphical representation and discussion of the finding.

Efficient approach for solving type-1 intuitionistic fuzzy transportation problem

In today’s real world problems such as in corporate or in industrial, the experts and the decision makers have to suffer with uncertainty as well as with hesitation usually, due to the complexity of the situations. The main reasons behind these complexities are lack of good communications with all involved persons, error in data’s, understanding of markets, unawareness of customers etc. So, In this paper, we consider a transportation problem having uncertainty and hesitation in supply and demand. We formulate the problem and utilize triangular intuitionistic fuzzy numbers (TIFNs) to deal with uncertainty and hesitation. We propose intuitionistic fuzzy methods to find starting basic feasible solution in terms of TIFNs. Intuitionistic fuzzy modified distribution method has been proposed to find optimal solution. The shortcomings of the existing methods have been pointed out. The proposed method is illustrated by numerical examples.