Interval Algebraic Bistructures

TL;DR

This work introduces and studies various interval algebraic bistructures, including bisemigroups, bigroupoids, and n-interval structures, expanding the theoretical framework of interval algebra.

Contribution

It presents new definitions and analyses of interval bistructures and n-interval structures, along with a collection of problems for further research.

Findings

Defined new interval algebraic structures such as bisemigroups and bigroupoids.

Analyzed properties of n-interval structures and mixed algebraic systems.

Provided a comprehensive set of research problems for future exploration.

Abstract

This book has four chapters. In the first chapter interval bistructures (biinterval structures) such as interval bisemigroup, interval bigroupoid, interval bigroup and interval biloops are introduced. Throughout this book we work only with the intervals of the form [0, a] where a \in Zn or Z+ \cup {0} or R+ \cup {0} or Q+ \cup {0} unless otherwise specified. Also interval bistructures of the form interval loop-group, interval groupgroupoid so on are introduced and studied. In chapter two n-interval structures are introduced. n-interval groupoids, n-interval semigroups, n-interval loops and so on are introduced and analysed. Using these notions n-interval mixed algebraic structure are defined and described. Some probable applications are discussed. Only in due course of time several applications would be evolved by researchers as per their need. The final chapter suggests around 295 problems of which some are simple exercises, some are difficult and some of them are research problems.