This chapter may look like a glossary of the fusion rules and we also introduce new ones presenting their formulas and examples: Conjunctive, Disjunctive, Exclusive Disjunctive, Mixed Conjunctive-Disjunctive rules, Conditional rule, Dempster’s, Yager’s, Smets’ TBM rule, Dubois-Prade’s, DezertSmarandache classical and hybrid rules, Murphy’s average rule, Inagaki-LefevreColot-Vannoorenberghe Unif...

Information fusion is an advanced research area which can assist decision makers in enhancing their decisions. This paper aims at designing a new multi-layer framework that can support the process of performing decisions from the obtained beliefs using information fusion. Since it is not an easy task to cross the gap between computed beliefs of certain hypothesis and decisions, the proposed fra...

s of Papers Presented to the American Mathematical Society, 1996, v.17, no.1, issue 103, 265. 15. Smarandache F. Neutrosophy. Neutrosophic probability, set,and logic. American Research Press, Rehoboth (NM), 1998;Republished in 2000, 2003, 2005 as Smarandache F. A unifyingfield in logics: neutrosophic logic. Neutrosophy, neutrosophicset, neutrosophic probability and statistics. A...

Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B of A which is embedded with a strong structure S. In [9], Kandasamy studied the concept of Smarandache groupoids, subgroupoids, ideal of groupoids, seminormal subgroupoids, Smarandache Bol groupoids, and strong Bol groupoids and obtained many interesting resul...

We introduce the notion of Smarandache BCH-algebra and Smarandache (fresh, clean and fantastic) ideals, some example are given and related properties are investigated. Relationship between Q-Smarandache (fresh, clean and fantastic) ideals and other types of ideals are given. Extension properties for Q-Smarandache (fresh, clean and fantastic) ideals are established.

The isotopic invariance or universality of types and varieties of quasigroups and loops described by one or more equivalent identities has been of interest to researchers in loop theory in the recent past. A variety of quasigroups(loops) that are not universal have been found to be isotopic invariant relative to a special type of isotopism or the other. Presently, there are two outstanding open...

The isotopic invariance or universality of types and varieties of quasigroups and loops described by one or more equivalent identities has been of interest to researchers in loop theory in the recent past. A variety of quasigroups(loops) that are not universal have been found to be isotopic invariant relative to a special type of isotopism or the other. Presently, there are two outstanding open...

In this paper we study the notion of Smarandache semirings and semifields and obtain some interesting results about them. We show that not every semiring is a Smarandache semiring. We similarly prove that not every semifield is a Smarandache semifield. We give several examples to make the concept lucid. Further, we propose an open problem about the existence of Smarandache semiring S of finite ...

In this article we present two new results concerning the Smarandache Ceil function. The first result proposes an equation for the number of fixed-point number of the Smarandache ceil function. Based on this result we prove that the average of the Smarandache ceil function is ) (n Θ .

In his recent paper[l], Sastry defines two triangles T(a,b,c) and T(a',b',c') to be Smarandache related ifS(a) = Sea'), S(b) = S(b') and S(c) = S(c'). The function S is known as the Smarandache function and is defmed in the following way. For n any integer greater than zero, the value of the Smarandache function Sen) is the smallest integer m such that n divides m!. He closes the paper by askin...