A short note on inequalities of interval-valued intuitionistic fuzzy matrices

Abstract

Inequality, also known as inequation, but unlike equation does not have rich history. After the introduction of equation, inequation captures its popularity in different fields namely algebra, geometry, trigonometry, probability, set theory, fuzzy set theory, logic, calculus etc. Whereas inequalities used in algebra are called algebraic inequalities, the ones used in geometry are called geometric inequalities etc. However, if the same techniques used in solving an equation are used for an inequation, wrong results may be obtained. Unlike equation, it has limited applications. When two quantities or expressions are not the same, then we use inequality and it is written by cross-out equal sign ( ) or . From a logical point of view, there is a difference between  and  . Sometimes we explain inequalities in linguistic form to describe the social values. All the above discussions on inequalities have been done according to the classical sense. In view of the present situation, it is necessary to extend this concept to fuzzy sense. Many researchers and mathematicians have shown the use of inequalities in fuzzy set, intuitionistic fuzzy set, soft set, rough set etc to describe the imprecise data. In this paper, some results related to inequalities of interval-valued intuitionistic fuzzy matrices with respect to algebraic sum and algebraic product were studied and proven. Key words: Fuzzy matrix, Interval-valued intuitionistic fuzzy matrix, algebraic sum, algebraic product.