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Algebraic Structures Using Natural Class Of Intervals, Florentin Smarandache, W.B. Vasantha Kandasamy
Algebraic Structures Using Natural Class Of Intervals, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
Authors in this book introduce a new class of intervals called the natural class of intervals, also known as the special class of intervals or as natural intervals. These intervals are built using increasing intervals, decreasing intervals and degenerate intervals. We say an interval [a, b] is an increasing interval if a < b for any a, b in the field of reals R. An interval [a, b] is a decreasing interval if a > b and the interval [a, b] is a degenerate interval if a = b for a, b in the field of reals R. The natural class of intervals consists of the collection of increasing intervals, decreasing intervals and the degenerate intervals. Clearly R is contained in the natural …
Interval Semirings, Florentin Smarandache, W.B. Vasantha Kandasamy
Interval Semirings, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the notion of interval semirings are introduced. The authors study and analyse semirings algebraically. Methods are given for the construction of non-associative semirings using loops and interval semirings or interval loops and semirings. Another type of non-associative semirings are introduced using groupoids and interval semirings or interval groupoids and semirings. Examples using integers and modulo integers are given. Also infinite semirings which are semifields are given using interval semigroups and semirings or semigroups and interval semirings or using groups and interval semirings. Interval groups are introduced to construct interval group interval semirings, and properties related with them …
Interval Semigroups, Florentin Smarandache, W.B. Vasantha Kandasamy
Interval Semigroups, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book we introduce the notion of interval semigroups using intervals of the form [0, a], a is real. Several types of interval semigroups like fuzzy interval semigroups, interval symmetric semigroups, special symmetric interval semigroups, interval matrix semigroups and interval polynomial semigroups are defined and discussed. This book has eight chapters. The main feature of this book is that we suggest 241 problems in the eighth chapter. In this book the authors have defined 29 new concepts and illustrates them with 231 examples. Certainly this will find several applications. The authors deeply acknowledge Dr. Kandasamy for the proof reading …