In this paper we extend soft neutrosophic rings and soft neutrosophic fields to soft neutrosophic birings, soft neutrosophic N-rings and soft neutrosophic bifields and soft neutrosophic N-fields. We also extend soft neutrosophic ideal theory to form soft neutrosophic biideal and soft neutrosophic N-ideals over a neutrosophic biring and soft neutrosophic N-ring . We have given examples to illustrate the theory of soft neutrosophic birings, soft neutrosophic N-rings (...) and soft neutrosophic fields and soft neutrosophic N-fields and display many properties of these. (shrink)

In this paper we present the generalization of neutrosophic rings and neutrosophic fields. We also extend the neutrosophic ideal to neutrosophic biideal and neutrosophic N-ideal. We also find some new type of notions which are related to the strong or pure part of neutrosophy. We have given sufficient amount of examples to illustrate the theory of neutrosophic birings, neutrosophic N-rings with neutrosophic bifields and neutrosophic N-fields and display many properties of them (...) in this paper. (shrink)

Study on Budhist Pramāṇa-vāda (doctrine of proof: an epistemological study of the nature of knowledge) and Hetu-vidya (science of causes: a system of logic).

In the same spirit with the theme of last issue of this SGJ journal (“Ongoing creation”), this paper shortly reviews a plausible mechanism from Aether to become ordinary matter from the perspective of Neutrosophic Logic. We also discuss two other possible applications of Neutrosophic Logic, including a resolution of conflicting paradigms in medicine. We hope that some ideas as outlined herein will be proved useful in the near future.

Recent excavations in Macedonia have provided an analogy to the pillaging of the Palace at Persepolis. In plundered tombs at Aiani the excavators found a number of small gold discs with impressed rosettes and of gilded silver ivy leaves; at Katerini some thirty-five gold discs with impressed rosettes, a gold double pin, a gold ring from a sword-hilt, a bit of a gilded pectoral, gilded silver fittings once attached to a leather cuirass, many buttons and other fragments; and at (...) Palatitsia bits of a gilded bronze wreath and of a gold necklace, and an ivory fitting. It was suggested that some of these objects had been dropped when ornamental facings were being torn away from a wooden funerary couch and from clothing by the robbers, who were probably working at speed and dared not return. In the antechamber of the tomb at Katerini many of the objects I have mentioned were found inside a burnt layer, and M. Andronikos has provided the explanation that they had been burnt on the pyre outside the tomb and then brought inside with the debris of the pyre itself. Nothing else was associated with burnt material. (shrink)

In this paper, we use PCR5 in order to fusion the information of two sources providing subjective probabilities of an event A to occur in the following form: chance that A occurs, indeterminate chance of occurrence of A, chance that A does not occur. -/- .

The ratio of index- and ring-finger lengths is thought to be related to prenatal androgen exposure, and in many, though not all, populations, men have a lower average digit ratio than do women. In many studies an inverse relationship has been observed, among both men and women, between 2D:4D ratio and measures of athletic ability. It has been further suggested that, in hunter-gatherer populations, 2D:4D ratio might also be negatively correlated with hunting ability, itself assumed to be contingent on (...) athleticism. This hypothesis has been tested using endurance running performance among runners from a Western, educated, and industrialized population as a proximate measure of hunting ability. However, it has not previously been tested among actual hunter-gatherers using more ecologically valid measures of hunting ability and success. The current study addresses this question among Tanzanian Hadza hunter-gatherers. I employ a novel method of assessing hunting reputation that, unlike previous methods, allows granular distinctions to be made between hunters at all levels of perceived ability. I find no statistically significant relationship between digit ratio and either hunting reputation or two important hunting skills. I confirm that Hadza men have higher mean 2D:4D ratios than men in many Western populations. I discuss the notion that 2D:4D ratio may be the consequence of an allometric scaling relationship between relative and absolute finger lengths. Although it is difficult to draw clear conclusions from these results, the current study provides no support for the theorized relationship between 2D:4D ratio and hunting skill. (shrink)

This book presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding. The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies (...) in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras. There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text. (shrink)

The ratio of index- and ring-finger lengths is thought to be related to prenatal androgen exposure, and in many, though not all, populations, men have a lower average digit ratio than do women. In many studies an inverse relationship has been observed, among both men and women, between 2D:4D ratio and measures of athletic ability. It has been further suggested that, in hunter-gatherer populations, 2D:4D ratio might also be negatively correlated with hunting ability, itself assumed to be contingent on (...) athleticism. This hypothesis has been tested using endurance running performance among runners from a Western, educated, and industrialized population as a proximate measure of hunting ability. However, it has not previously been tested among actual hunter-gatherers using more ecologically valid measures of hunting ability and success. The current study addresses this question among Tanzanian Hadza hunter-gatherers. I employ a novel method of assessing hunting reputation that, unlike previous methods, allows granular distinctions to be made between hunters at all levels of perceived ability. I find no statistically significant relationship between digit ratio and either hunting reputation or two important hunting skills. I confirm that Hadza men have higher mean 2D:4D ratios than men in many Western populations. I discuss the notion that 2D:4D ratio may be the consequence of an allometric scaling relationship between relative and absolute finger lengths. Although it is difficult to draw clear conclusions from these results, the current study provides no support for the theorized relationship between 2D:4D ratio and hunting skill. (shrink)

Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, (...) single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, medicine, social science, and some more. (shrink)

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and (...) engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, by many authors around the world. (shrink)

In an almost forgotten passage of the Postenor Analytics (Bk I, ch. III) Aristotle argues against 'another school', according to which it is possible to proof things 'by each other and in a circle'. His logical refutation of this opinion became so dominant in the Western philosophical tradition, that the 'vicious circle' has always deemed a crime since. A scientific demonstration has to be built on firm premisses in order to deduce conclusions from them in a straight, ongoing proces, in (...) which one does not have to return to the premisses for a reconsideration of them on the basis of their implications. Although Aristotle does not mention names, he in fact reacts against Plato and the mainstream of Greek thought, which stresses the essential circularity of human argumentation. In the first, the historical part of the treatise the roots of this circular logic are unearthed in the work of Heraclitus and Parmenides, who both defended a ring structure of their metaphysical explication of nature. Truth is described as well-rounded, because you can follow it in a circle, passing through each of its links in turn, back to your startingpoint. The association of circular motion with thought is fully present in the work of Plato, who speeks many times about the 'periforas tès dianoias' and the essential interdependance of our ideas. Not the theory of an anonymous alternative school but Aristotle's own rectilinear formal logic was the exceptional, untraditional standpoint, which, moreover, was in conflict with his explication of divine thinking as 'noèsis noèseôs'. In modern times Hegel, Nietzsche and Heidegger were the main representatives of an anti-Aristotelian attitude. All three reject the logical prohibition of the circular argument, because it is inadequate to the life of concrete scientific thinking. The path of science always turns around towards its origins and results in a correction of its fundamental hypotheses on a higher level. Circularity is considered as a hallmark of sound logical procedure, as a characteristic of excellence in human understanding. The famous 'hermeneutic circle' is interpreted as the modern equivalent of the Hegelian 'Kreislauf and the Greek ' to par'allèlôn'. In the second, the more systematic part of the text the circular nature of our cognitive and scientific behaviour is demonstrated along three different lines. Reflection on the natural language with its finite stock of words, whose meanings are structurally connected, leads us to the so called semiotical circularity. Natural language is a complex network in which circular argumentation is not only unavoidable, but even the only means of explication. We have to work with the material contained in our dictionary, in which the items are defined by each other. The second reason is constituted by the system-orientation of science. In science we try to systematize our knowledge by means of formalisations and abstractions. The development of science can be characterised as a succession of systems, in which every element gets its meaning from the whole organisation. If we accept systematicity as the arbiter of truth, our logic is anti-fundamentalistic and the path of our thought is in fact circular (or better : spiralistic). The third adstruction of our theory is afforded by the coupling, that is realised in a rational proof. We draw conclusions from the coherence of our perceptions, from the reciprocal implications of our ideas. Never any of our ideas is without the repercussions of the movements elsewhere in the field. When we proof something, we also disproof and correct our startingpoints at the same time. The tradition of the circular nature of human thinking is very old, but not antiquated. The accusation of committing a fallacy in the case of circularity in normal and in scientific thinking is unfouded. It is now the formal logicians turn to defend his claim. (shrink)

Recently, research on uncertainty modeling is progressing rapidly and many essential and breakthrough stud ies have already been done. There are various ways such as fuzzy, intuitionistic and neutrosophic sets to handle these uncertainties. Although these concepts can handle incomplete information in various real-world issues, they cannot address all types of uncertainty such as indeterminate and inconsistent information. Also, plithogenic sets as a generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets, which is a set whose elements are (...) characterized by many attributes’ values. In this paper, our aim is to demonstrate and review the history of fuzzy, intuitionistic and neutrosophic sets. For this purpose, we divided the paper as: section 1. History of Fuzzy Sets, section 2. History of Intuitionistic Fuzzy Sets and section 3. History of Neutrosophic Theories and Applications, section 4. History of Plithogenic Sets. (shrink)

Recognition that the Principle of Respect for Autonomy fails to work in family-centric societies such as Singapore has recently led to the promotion of relational autonomy as a suitable framework within which to place healthcare decision making. However, empirical data, relating to patient and family opinions and the practices of healthcare professionals in Confucian-inspired Singapore, demonstrate clear limitations on the ability of a relational autonomy framework to provide the anticipated compromise between prevailing family decision-making norms and adopted Western led atomistic (...) concepts of autonomy. Evidence suggests that despite a growing infusion of Western influence, there is still little to indicate any major shift to individual decision making, particularly in light of the way society and healthcare are structured. Similarly, the lack of employing a shared decision-making model and data that discredit the notion that the complex psychosocial and cultural factors that affect the decision making may be considered “content neutral” not only prevents the application of relational autonomy but questions the viability of the values behind the Principle of Respect for Autonomy. Taking into account local data and drawing upon a wider concept of personhood that extends beyond prevailing family-centric ideals along with the complex interests that are focused upon the preservation of the unique nature of personhood that arises from the Ring Theory of Personhood, we propose and “operationalize” the employing of an authoritative welfare-based approach, within the confines of best interest decision making, to better meet the current care needs within Singapore. (shrink)

Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, (...) single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, medicine, social science, and some more. (shrink)

The ternary xV2O5–(40 − x)Li2O–60B2O3 glass system, where x = 1, 2, 3, 4 and 6 mol%, was prepared by normal quenching. Ultrasonic velocities and attenuation were measured at room temperature using a pulse-echo technique. Various parameters, such as elastic moduli, micro-hardness, Poisson's ratio and Debye temperature, were determined from the measured densities and velocities. The composition dependence of these parameters, in addition to the glass-transition temperature, suggested that vanadium ions were incorporated into these glasses as a network modifier, resulting (...) in the reconversion of BO4 tetrahedra to BO3 triangles by the breaking of B–O–B linkages and the formation of nonbridging oxygens (NBOs). The outcome was a reduction in network connectivity and rigidity with increasing V2O5 content. The results are explained quantitatively in terms of fractal bond connectivity, average atomic volume, network dimensionality, packing density, number of network bonds per unit volume, cross-link density and atomic ring size. The Makishima and Mackenzie model appears to be valid for the studied glasses when the fate of BO4 tetrahedra and creation of NBOs are taken into account. (shrink)

The ratio of index- and ring-finger lengths is thought to be related to prenatal androgen exposure, and in many, though not all, populations, men have a lower average digit ratio than do women. In many studies an inverse relationship has been observed, among both men and women, between 2D:4D ratio and measures of athletic ability. It has been further suggested that, in hunter-gatherer populations, 2D:4D ratio might also be negatively correlated with hunting ability, itself assumed to be contingent on (...) athleticism. This hypothesis has been tested using endurance running performance among runners from a Western, educated, and industrialized population as a proximate measure of hunting ability. However, it has not previously been tested among actual hunter-gatherers using more ecologically valid measures of hunting ability and success. The current study addresses this question among Tanzanian Hadza hunter-gatherers. I employ a novel method of assessing hunting reputation that, unlike previous methods, allows granular distinctions to be made between hunters at all levels of perceived ability. I find no statistically significant relationship between digit ratio and either hunting reputation or two important hunting skills. I confirm that Hadza men have higher mean 2D:4D ratios than men in many Western populations. I discuss the notion that 2D:4D ratio may be the consequence of an allometric scaling relationship between relative and absolute finger lengths. Although it is difficult to draw clear conclusions from these results, the current study provides no support for the theorized relationship between 2D:4D ratio and hunting skill. (shrink)

Soft neutrosophic group and soft neutrosophic subgroup are generalized to soft neutrosophic bigroup and soft neutrosophic N-group respectively in this paper. Different kinds of soft neutrosophic bigroup and soft neutrosophic N-group are given. The structural properties and theorems have been discussed with a lot of examples to disclose many aspects of this beautiful man made structure.

Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. In this paper we introduced soft neutrosophic biLA-semigroup,soft neutosophic sub bi-LA-semigroup, soft neutrosophic N -LA-semigroup with the discuission of some of their characteristics. We also introduced a new type of soft neutrophic bi-LAsemigroup, the so called soft strong neutrosophic bi-LAsemigoup which is of pure neutrosophic character. This is also extend to soft neutrosophic strong N-LA-semigroup. We also given some (...) of their properties of this newly born soft structure related to the strong part of neutrosophic theory. (shrink)

In this paper we define neutrosophic bi-LAsemigroup and neutrosophic N-LA-semigroup. Infact this paper is an extension of our previous paper neutrosophic left almost semigroup shortly neutrosophic LAsemigroup. We also extend the neutrosophic ideal to neutrosophic biideal and neutrosophic N-ideal. We also find some new type of neutrosophic ideal which is related to the strong or pure part of neutrosophy. We have given sufficient amount of examples to illustrate the theory of neutrosophic (...) bi-LA-semigroup, neutrosophic N-LAsemigroup and display many properties of them this paper. (shrink)

Neutrosophic LA-semigroup is a midway structure between a neutrosophic groupoid and a commutative neutrosophic semigroup. Rings are the old concept in algebraic structures. We combine the neutrosophic LA-semigroup and ring together to form the notion of neutrosophic LA-semigroup ring. Neutrosophic LAsemigroup ring is defined analogously to neutrosophic group ring and neutrosophic semigroup ring.

In this paper we extend the theory of neutrosophic rings and neutrosophic fields to soft sets and construct soft neutrosophic rings and soft neutrosophic fields. We also extend neutrosophic ideal theory to form soft neutrosophic ideal over a neutrosophic ring and soft neutrosophic ideal of a soft neutrosophic ring . We have given many examples to illustrate the theory of soft neutrosophic rings and soft neutrosophic fields and (...) display many properties of of these. At the end of this paper we gave soft neutrosophic ring homomorphism. (shrink)

The objective of this study is to incorporate topological space into the realm of n-Cylindrical Fuzzy Neutrosophic Sets (n-CyFNS), which are the most novel type of fuzzy neutrosophic sets. In this paper, we introduce n-Cylindrical Fuzzy Neutrosophic Topological Spaces (n-CyFNTS), n-Cylindrical Fuzzy Neutrosophic (n-CyFN) open sets, and n-CyFN closed sets. We also defined the n-CyFN base, n-CyFN subbase, and some related theorems here.

This article introduces the notion of duplex elements of the finite rings and corresponding neutrosophic rings. The authors establish duplex ring Dup(R) and neutrosophic duplex ring Dup(R)I)) by way of various illustrations. The tables of different duplicities are constructed to reveal the comparison between rings Dup(Zn), Dup(Dup(Zn)) and Dup(Dup(Dup(Zn ))) for the cyclic ring Zn . The proposed duplicity structures have several algebraic systems with dissimilar consequences. Author’s characterize finite rings with R + R is (...) different from the duplex ring Dup(R). However, this characterization supports that R + R = Dup(R) for some well known rings, namely zero rings and finite fields. (shrink)

We show that all QE rings of prime power characteristic are constructed in a straightforward way out of three components: a filtered Boolean power of a finite field, a nilpotent Jacobson radical, and the ring Z p n or the Witt ring W 2 (F 4 ) (which is the characteristic four analogue of the Galois field with four elements).

Name der Zeitschrift: Nietzscheforschung Jahrgang: 24 Heft: 1 Seiten: 418-424.

In this book we define some new notions of soft neutrosophic algebraic structures over neutrosophic algebraic structures. We define some different soft neutrosophic algebraic structures but the main motivation is two-fold. Firstly the classes of soft neutrosophic group ring and soft neutrosophic semigroup ring defined in this book is basically the generalization of two classes of rings: neutrosophic group rings and neutrosophic semigroup rings. These soft neutrosophic group rings and soft (...) neutrosophic semigroup rings are defined over neutrosophic group rings and neutrosophic semigroup rings respectively. This is basically the collection of parameterized subneutrosophic group ring and subneutrosophic semigroup ring of a neutrosophic group ring and neutrosophic semigroup ring respectively. These soft neutrosophic algebraic structures are even bigger than the corresponding classical algebraic structures. It is interesting to see that it wider the area of research for the researcher of algebraic structures. (shrink)

Soft set theory is a general mathematical tool for dealing with uncertain, fuzzy, not clearly defined objects. In this paper we introduced soft neutrosophic loop,soft neutosophic biloop, soft neutrosophic N -loop with the discuission of some of their characteristics. We also introduced a new type of soft neutrophic loop, the so called soft strong neutrosophic loop which is of pure neutrosophic character. This notion also found in all the other corresponding notions of soft neutrosophic thoery. (...) We also given some of their properties of this newly born soft structure related to the strong part of neutrosophic theory. (shrink)

In this paper we present the concept of neutrosophic quadruple algebraic structures. Specially, we study neutrosophic quadruple rings and we present their elementary properties.

In this paper, we firstly review the neutrosophic set, and then construct two new concepts called neutrosophic implication of type 1 and of type 2 for neutrosophic sets. Furthermore, some of their basic properties and some results associated with the two neutrosophic implications are proven.

In this book the authors introduced the notions of soft neutrosophic algebraic structures. These soft neutrosophic algebraic structures are basically defined over the neutrosophic algebraic structures which means a parameterized collection of subsets of the neutrosophic algebraic structure. For instance, the existence of a soft neutrosophic group over a neutrosophic group or a soft neutrosophic semigroup over a neutrosophic semigroup, or a soft neutrosophic field over a neutrosophic field, or a (...) soft neutrosophic LA-semigroup over a neutrosophic LAsemigroup, or a soft neutosophic loop over a neutrosophic loop. It is interesting to note that these notions are defined over finite and infinite neutrosophic algebraic structures. These structures are even bigger than the classical algebraic structures. This book contains five chapters. Chapter one is about the introductory concepts. In chapter two the notions of soft neutrosophic group, soft neutrosophic bigroup and soft neutrosophic N-group are introduced and many fantastic properties are given with illustrative examples. (shrink)

We say that a ring admits elimination of quantifiers, if in the language of rings, {0, 1, +, ·}, the complete theory of R admits elimination of quantifiers. Theorem 1. Let D be a division ring. Then D admits elimination of quantifiers if and only if D is an algebraically closed or finite field. A ring is prime if it satisfies the sentence: ∀ x ∀ y ∃ z (x = 0 ∨ y = 0 ∨ xzy (...) ≠ 0). Theorem 2. If R is a prime ring with an infinite center and R admits elimination of quantifiers, then R is an algebraically closed field. Let A be the class of finite fields. Let B be the class of 2 × 2 matrix rings over a field with a prime number of elements. Let C be the class of rings of the form $GF(p^n) \bigoplus GF(p^k)$ such that either n = k or g.c.d. (n, k) = 1. Let D be the set of ordered pairs (f, Q) where Q is a finite set of primes and f: Q → A ∪ B ∪ C such that the characteristic of the ring f(q) is q. Finally, let E be the class of rings of the form $\bigoplus_{q \in Q}f(q)$ for some (f, Q) in D. Theorem 3. Let R be a finite ring without nonzero trivial ideals. Then R admits elimination of quantifiers if and only if R belongs to E. Theorem 4. Let R be a ring with the descending chain condition of left ideals and without nonzero trivial ideals. Then R admits elimination of quantifiers if and only if R is an algebraically closed field or R belongs to E. In contrast to Theorems 2 and 4, we have Theorem 5. If R is an atomless p-ring, then R is finite, commutative, has no nonzero trivial ideals and admits elimination of quantifiers, but is not prime and does not have the descending chain condition. We also generalize Theorems 1, 2 and 4 to alternative rings. (shrink)