Abstract
The present paper contains the sufficient condition of a fuzzy semigroup to be a fuzzy group using fuzzy points. The existence of a fuzzy kernel in semigroup is explored. It has been shown that every fuzzy ideal of a semigroup contains every minimal fuzzy left and every minimal fuzzy right ideal of semigroup. The fuzzy kernel is the class sum of minimal fuzzy left (right) ideals of a semigroup. Every fuzzy left ideal of a fuzzy kernel is also a fuzzy left ideal of a semigroup. It has been shown that the product of minimal fuzzy left ideal and minimal fuzzy right ideal of a semigroup forms a group. The representation of minimal fuzzy left (right) ideals and also the representation of intersection of minimal fuzzy left ideal and minimal fuzzy right ideal are shown. The fuzzy kernel of a semigroup is basically the class sum of all the minimal fuzzy left (right) ideals of a semigroup. Finally the sufficient condition of fuzzy kernel to be completely simple semigroup has been proved.
Highlights
Zadeh in 1965 introduced the fundamental concept of a fuzzy set in his paper [1] which provides a useful mathematical tool for describing the behavior of systems that are too complex or ill-de ned to admit precise mathematical analysis by classical methods. e literature in fuzzy set theory and its practicability has been functioning quickly uptil now. e applications of these concepts can be seen in a variety of disciplines like arti cial intellegence, computer science, control engineering, expert systems, operation research, management science, and robotics
Mordeson [2] has demonstrated the basic exploration of fuzzy semigroups
Fuzzy sets are considered with respect to a nonempty set SS. e main idea is that each element xx of SS is assigned a membership grade ffffff in [0, 1], with ffffff f f corresponding to nonmembership, 0 < ffffff ff to partial membership, and ffffff f f to full membership
Summary
Zadeh in 1965 introduced the fundamental concept of a fuzzy set in his paper [1] which provides a useful mathematical tool for describing the behavior of systems that are too complex or ill-de ned to admit precise mathematical analysis by classical methods. e literature in fuzzy set theory and its practicability has been functioning quickly uptil now. e applications of these concepts can be seen in a variety of disciplines like arti cial intellegence, computer science, control engineering, expert systems, operation research, management science, and robotics.Mordeson [2] has demonstrated the basic exploration of fuzzy semigroups. If a semigroup SS contains a minimal fuzzy ideal ff of SS ff is the fuzzy kernel of SS. Let a semigroup SS contain at least one minimal le ideal every fuzzy le ideal of fuzzy kernel is a fuzzy le ideal of SS.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
