In this paper, several new algebraic mathematics for positive fuzzy numbers of type (a,a,a,a) are devised and do not need the computation of α-cut of the fuzzy number. Direct mathematical expressions to evaluate exponential, square root, logarithms, inverse exponential etc. of positive fuzzy numbers of type (a,a,a,a) are obtained using the basic analytical principles of algebraic mathematics an...

We extend the concept of fuzzy integral based on ⊕-decomposable measure from nonnegative fuzzy measurable function to extended real-valued fuzzy measurable function. Further investigations of fuzzy integrals based on pseudo-additive decomposable measure are carried out. Meanwhile, the space (S(μ),σ(·,·)) of all fuzzy measurable function will be proved to be a pseudo-metric space. Finally, as an...

After introducing and developing fuzzy set theory, a lot of studies have been done in this field and then a result appeared as a Fuzzy Graph (Combination of graph theory and fuzzy set theory). This is now known as Fuzzy graph theory. In this article we review essential works on different types of fuzzy graph and fuzzy hyper graph. Mathematics Subject Classification (2010): 03E72, 05C72

This model presents the invention scheduling difficulty in industry with different operational constraints, as well as strategic plan of the business, revenue purpose, and limit on finishing. In this article, we have studied an inventory model for deteriorating items with shortages under partially backlogging. The aim of present study is to minimize the total cost function in fuzzy environment....

*Correspondence: [email protected] School of Mathematics Science, Liaocheng University, Liaocheng, Shandong 252059, China Abstract In order to generalize the notions of a (∈,∈ ∨q)-fuzzy subring and various (∈,∈ ∨q)-fuzzy ideals of a ring, a (λ,μ)-fuzzy subring and a (λ,μ)-fuzzy ideal of a ring are defined. The concepts of (λ,μ)-fuzzy semiprime, prime, semiprimary and primary ideals are introdu...

The notions of intuitionistic fuzzy h-ideal and normal intuitionistic fuzzy h-ideal in Γ-hemiring are introduced and some of the basic properties of these ideals are investigated. Cartesian product of intuitionistic fuzzy h-ideals is also defined. Finally a characterization of intuitionistic fuzzy h-ideals in terms of fuzzy relations is obtained. Keywords—Γ-hemiring, fuzzy h-ideal, normal, cart...

Based on features of distance education and its disadvantages in terms of learning evaluation, this study uses Analytic Hierarchy Process (AHP) and fuzzy mathematics theory to study distance education. First, an electric file is generated for each learner. Then a practical multi-hierarchy evaluation model is built based on AHP. Finally, evaluation of on-line education is done based on informati...

In this paper ,we fuzzify the new class of algebraic structure introduced by Kim[5].In this fuzzification(called fuzzy KS-semigroups),we introduce the notions of fuzzy sub KS-semigroups,fuzzy KS-ideal,fuzzy KS-p-ideal and investigate some of their related properties.The purpose of this study is to implement the fuzzy set theory and ideal theory in the KS-semigroups.This fuzzification leads to d...

In nature as well as otherwise there are what we can call deterministic and non-deterministic phenomena. Non-deterministic ones attract more challenges in scientific study. When the patterns of occurrence of non-deterministic phenomena are stable in their occurrence, their study was taken up in statistics. However, in real world, there is a large variety of vague phenomena, imprecise concepts a...