IOSR Journal of Mathematics (IOSR-JM) e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 17, Issue 3 Ser. III (May – June 2021), PP 58-61 www.iosrjournals.org DOI: 10.9790/5728-1703035861 www.iosrjournals.org 58 | Page Some Algebraic Theoritic Properties on Gamma 1 Non Deranged Permutation 1 Ibrahim Aminu Alhaji 2. Garba Abor Isah, 3. Alhassan Mufassir Jega, 4. Hassan Aliyu 1.Department of Mathematics, Usmanu Danfodiyo University, Sokoto 2.Department of Mathematics, Usmanu Danfodiyo University, Sokoto 3. Department of mathematics, Kebbi state university of science and technology, aliero 4. Department of Mathematics, Usmanu Danfodiyo University, Sokoto Abstract This paper investigated some algebraic theoretic properties of fuzzy set on    using constructed membership function of fuzzy set on    and established the result for algebraic operators of fuzzy sets on    which are algebraic sum, algebraic product, bounded sum and bounded difference, then constructed a relationship between the operators of fuzzy sets on    , and came about some propositions. Keywords Fuzzy set, Algebraic Sum, Algebraic Product, Bounded Sum, Bounded Difference, Membership function --------------------------------------------------------------------------------------------------------------------------------------- Date of Submission: 08-06-2021 Date of Acceptance: 21-06-2021 --------------------------------------------------------------------------------------------------------------------------------------- I. Introduction Zadeh (1965) introduced the concept of Fuzzy sets by defining them in terms of mapping from a set into a unit interval. Permutation pattern have been used in the past decade to study mathematical structures. For instance Audu (1986), Ibrahim (2006) studied the concept of permutation pattern using some elaborate scheme to determine the order of precedence and the position of each of the elements in a finite set of prime size. Similarly an idea of an embedment as an algebraic structure has yielded some interesting results by Ibrahim (2005). Garba and Ibrahim (2010), studied the structure and developed a scheme for the range of such cycles and use it to investigate further number theoretic and algebraic properties of   . Furthermore, a group theoretical properties of    was also investigated by Garba and Abubakar (2015), the concept of fuzzy nature and of    alpha-level cut has also been studied by Aremu, Ejima and Abdullahi (2017), Garba, Zakari and Hassan (2019) investigated the fuzzy nature and modified fuzzy membership function on   and established that the α-cut level of the   is the domain     and the support (supp) of the   is the entire structure  . II. Preliminaries 2.1 FUZZY SET If X is a Collection of objects and A X  , then the fuzzy set Ă  X is a set of ordered pairs      ()):    Where   () is a measure taking values in the unit interval [0,1] called the membership of x in A. 2.2 ALGEBRAIC SUM Let A and B be Two fuzzy sets, then the Algebraic Sum of two fuzzy Sets is given by     [       – [      ] Where   is equal to the difference between the addition and product of measures of two fuzzy sets. 2.3 ALGEBRAIC PRODUCT The algebraic product of two fuzzy Sets is given by            Where    is equal to the product of measures of two fuzzy sets. 2.4 BOUNDED SUM The bounded sum of two fuzzy sets is given by   min[1, (     Where   is equal to the minimum value between 1 and the addition of measures of two fuzzy sets.