Manoranjan Kumar Singh is formerly Head and Professor at the Department of Mathematics, Magadh University, Bodh Gaya, Bihar, India. He received his D.Sc. degree in 2009, Ph.D. degree in 1986, M.Sc. degree with a gold medal (first position in first class) in 1981, and B.Sc. (Hons) degree in 1979, from Magadh University, Bodh Gaya. He received the ISCA Young Scientist Award in 1989; the Best Teacher Award by the Lions Club of Gaya in 2005; the Best Research Paper Award in 2008 by the Purvanchal Academy of Sciences, Jaunpur, Uttar Pradesh; the UGC.BSR Faculty Fellowship in 2012; Bharat Gaurav Award from India International Friendship Society, New Delhi, in 2016; the Patron Award 2016-17 from the Computer Society of India, Bombay, in 2018; the Distinguished Professor Award from Arunai International Research Foundation, Madras, in 2017; the Outstanding Faculty Award at Pattaya, Thailand, in 2018; and the Life Time Achiever Award 2020 from Infinity Education Solution, Coimbatore. His areas of interest are fuzzy abstract algebra and fuzzy mathematics. With more than 38 years of teaching experience, he has published 17 books and 140 papers. He has supervised 18 Ph.D. students. He has presented research papers at more than 94 national and international conferences and chaired sessions at 6 of them. On the editorial boards of several journals, he is Reviewer for several journals.

• 1 Fundamental of Crisp Set Theory.- 2 Fundamental Concepts of Fuzzy Sets.- 3 Generalization of Fuzzy Sets.- 4 Decomposition of a Fuzzy Set and Extension Principle.- 5 Fuzzy Set-Theoretic Operators.- 6 Arithmetic Operations and Fuzzy Mathematics.- 7 Fuzzy Relations.

Manoranjan Kumar Singh is formerly Head and Professor at the Department of Mathematics, Magadh University, Bodh Gaya, Bihar, India. He received his D.Sc. degree in 2009, Ph.D. degree in 1986, M.Sc. degree with a gold medal (first position in first class) in 1981, and B.Sc. (Hons) degree in 1979, from Magadh University, Bodh Gaya. He received the ISCA Young Scientist Award in 1989; the Best Teacher Award by the Lions Club of Gaya in 2005; the Best Research Paper Award in 2008 by the Purvanchal Academy of Sciences, Jaunpur, Uttar Pradesh; the UGC.BSR Faculty Fellowship in 2012; Bharat Gaurav Award from India International Friendship Society, New Delhi, in 2016; the Patron Award 2016-17 from the Computer Society of India, Bombay, in 2018; the Distinguished Professor Award from Arunai International Research Foundation, Madras, in 2017; the Outstanding Faculty Award at Pattaya, Thailand, in 2018; and the Life Time Achiever Award 2020 from Infinity Education Solution, Coimbatore. His areas of interest are fuzzy abstract algebra and fuzzy mathematics. With more than 38 years of teaching experience, he has published 17 books and 140 papers. He has supervised 18 Ph.D. students. He has presented research papers at more than 94 national and international conferences and chaired sessions at 6 of them. On the editorial boards of several journals, he is Reviewer for several journals.

• 1 Fundamental of Crisp Set Theory.- 2 Fundamental Concepts of Fuzzy Sets.- 3 Generalization of Fuzzy Sets.- 4 Decomposition of a Fuzzy Set and Extension Principle.- 5 Fuzzy Set-Theoretic Operators.- 6 Arithmetic Operations and Fuzzy Mathematics.- 7 Fuzzy Relations.

Manoranjan Kumar Singh is formerly Head and Professor at the Department of Mathematics, Magadh University, Bodh Gaya, Bihar, India. He received his D.Sc. degree in 2009, Ph.D. degree in 1986, M.Sc. degree with a gold medal (first position in first class) in 1981, and B.Sc. (Hons) degree in 1979, from Magadh University, Bodh Gaya. He received the ISCA Young Scientist Award in 1989; the Best Teacher Award by the Lions Club of Gaya in 2005; the Best Research Paper Award in 2008 by the Purvanchal Academy of Sciences, Jaunpur, Uttar Pradesh; the UGC.BSR Faculty Fellowship in 2012; Bharat Gaurav Award from India International Friendship Society, New Delhi, in 2016; the Patron Award 2016-17 from the Computer Society of India, Bombay, in 2018; the Distinguished Professor Award from Arunai International Research Foundation, Madras, in 2017; the Outstanding Faculty Award at Pattaya, Thailand, in 2018; and the Life Time Achiever Award 2020 from Infinity Education Solution, Coimbatore. His areas of interest are fuzzy abstract algebra and fuzzy mathematics. With more than 38 years of teaching experience, he has published 17 books and 140 papers. He has supervised 18 Ph.D. students. He has presented research papers at more than 94 national and international conferences and chaired sessions at 6 of them. On the editorial boards of several journals, he is Reviewer for several journals.

• 1 Fundamental of Crisp Set Theory.- 2 Fundamental Concepts of Fuzzy Sets.- 3 Generalization of Fuzzy Sets.- 4 Decomposition of a Fuzzy Set and Extension Principle.- 5 Fuzzy Set-Theoretic Operators.- 6 Arithmetic Operations and Fuzzy Mathematics.- 7 Fuzzy Relations.