Buy Books


Fuzzy Decision Making Tools to Sieve Out the Poor in Nalanda District, Bihar


  • Author Name: Raj Kumar
  • Book Type: E-Book & Paperback
  • Categories: Mathematics
  • ISBN: 978-81-948231-6-2
  • Language: English
  • Pages: 204
  • Published Date: 31-MAR-2021
  • Publisher: Horizon Books
  • Size: 7 X 9

The author is glad to present to the readers, the book titled “Fuzzy Decision Making Tools to Sieve out the Poor in Nalanda District, Bihar”. The book is all about ‘how to identify and how to aggregate the poor’ in any given socio-economic context or condition, using the concept of Fuzzy Logic and Fuzzy Sets. This book will serve research students in applied mathematics and it will also be helpful to those who are involved in making socio-economic decision to distribute the resources available at their disposal.

Why and How this book came into Being

Decision making over the issue of ‘how to measure poverty’ has always been the subject of contentious debate for an economist, for a government, for a statistician, for a mathematician, or for any socio-economic plan. Several Decision Methods have been adopted to decide who would be considered poor or who would not. For examples: (i) Absolute and Relative Poverty Line Method, (ii) Uni- dimension poverty Method (iii) Income-Expenditure Method (iv) Head Count Ratio (HCR), (v) Income Gap Ratio (IGR) (vi) Poverty Gap Ratio (PGR), (vii) Advance Measure Method: – Foster-Greer-Thorbecke Measure, Sen – Shorrocks – Thon measure (SST), and Sen Index (viii) Multi-dimensional Poverty Approach :- (i) Counting Multi-dimensional Poverty (ii) Multi-dimensional Poverty Index (MPI) , and (iii) Capability Approach. These above mentioned methods were used at the global level.

Identification of poor and non-poor in India is done based on Uni-dimensional model that is to say Income-consumption and expenditure model using following experts committee reports: (i) Dandekar and Rath (ii) Y.K. Alagh (iii) Lakdawala (iii) Suresh Tendulkar Committee (iv) C. Rangarajan Committee:- Modified Mixed Reference Period (MMRP),  Poverty Line Basket (PLB), and Socio-Economic and Caste Census (SECC) 2011: BPL Identification in 2015. Nevertheless, every state in India is free to set its own standard of method to scale out the poor. The state of Bihar adopted the method of A Score Based Ranking Methodology to identify the poor.  

In Mathematical Modelling context all the above mentioned methods of making decisions fall under Crisp Decision Approach based on Aristotelian logic and Crisp Sets. In response to this method of decision making approach, fuzzy decision making approach was suggested as a better alternative to the process of poverty measurement method. Andrea Cerioli and Sergio Zani were the first one to apply fuzzy logic to poverty assessment in the year 1990. Later, Chiappero Martinetti and Qizilbash added the intrinsic vagueness of being poor by using so – called membership function for the identification of the poor. As the research continued further some more methods were addressed such as Totally Fuzzy (TF), Totally Fuzzy and Relative (TFR), Integrated Fuzzy Approach (Multidimensional and Longitudinal) to apply to identify and aggregate the poor.

Key Concepts and Techniques

This book further develops and introduces a new approach suggesting Multi-Criteria Fuzzy Decision-making Tools and Fuzzy Set Theory to capture the extent of poverty of households accommodating both the quantitative and qualitative factors such as Roti (Food), Kapda (Clothing), Makaan (Housing), Kaam (Job), and Samman (Social Status) and their fourteen respective sub-criteria.

     The fuzzification process is carried out by using Pentagonal Fuzzy Numbers (PFNs) and by introducing Stratified Fuzzy Analytical Hierarchy Process (SFAHP). Fuzzy poverty categorization is carried out by introducing Fuzzy Sieve Technique (FST). The judgment and scaling of the criteria and sub-criteria are done by adopting participative decision making method (interview method based on questionnaires).Stratified Fuzzy Analytical Hierarchy Process (SFAHP) categorizes the group of the poor into five subgroups such as (i) very poor, (ii) almost very poor (iii) poor, (iv) rather poor and (v) non-poor.  Our fuzzy tools and methods are applied to the case study in Nalanda District, Bihar, India.

The book also highlights the comparative studies between three models such as Analytical Hierarchy Process (AHP), Fuzzy Analytical Hierarchy Process (FAHP) and Stratified Fuzzy Analytical Hierarchy Process (SFAHP). The final results justify that Stratified Fuzzy Analytical Hierarchy Process (SFAHP) gives better results in identifying the Poverty Status.

Special Features

     Computer Algorithmic approach via MATLAB: (Programme for 5 X 5 Matrix) is given to calculate the fuzzy centre value by using Matlab m-file which will minimize the time in carrying out the fuzzification and normalization process to measure poverty status. 

At the end the author shall ever be grateful to the inquisitive researchers and socio-economic planners for their valuable suggestions for further improvement of this book.


St. Xavier’s College of Management and Technology, Patna

Digha Ashiyan Road -11.

Affliated to AKU, Patna, Bihar, India

Raj Kumar

The author is a Jesuit Priest and a member of the Patna Province of the Society of Jesus. He was born on November 20, 1972 in a village Basanpur , Rahui Thana, Nalanda District, Bihar (India). He graduated in the year 1997 from St. Joseph’s College, Tiruchirappalli, affiliated to Bhartidasan University, Tamil Nadu, India. Post Graduated in the year 2003 from Loyola College (Autonomous) affiliated to University of Madras, Chennai, Tamil Nadu (India). He has also completed his M.Phil. In the year 2012 from Loyola College (Autonomous) affiliated to University of Madras, Chennai, Tamil Nadu (India), and was awarded PhD. Degree in the year 2016 from University of Madras, Chennai, Tamil Nadu (India). Currently the author is working as the administrator and Assistant Professor of Mathematics at St Xavier’s College of Management and Technology, Digha — Ashiyana Road, Patna, Bihar (India). He has published many articles in UGC Care list Journals. He has also presented several papers at national and international seminars. The book titled “Fuzzy Decision Making Tools to Sieve out the Poor in Nalanda District, Bihar” aims to make aware of the readers and research scholars that there is an alternative method to analyze the reality of measurement of poverty. The book suggests Stratified Fuzzy Analytical Hierarchy Process (SFAHP) as a new method to sieve out the poor. This book also gives further scope for improvement on the issue of measurement of poverty applying fuzzy sets and fuzzy logics in a more creative and reasonable manner.

Author Name

Raj Kumar

Book Type

E-Book & Paperback








Published Date




7 X 9