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...velopment and dissemination of G-dimensional theory (GDT). K. Toshihara, from Japan, proposed the concept of a paper defining G-Dimensional theory in relation to the Smarandache quantum paradoxes. After reviewing a draft, Dr. M. L. Perez, Editor of the SNJ, suggested the inclusion of the Smarandache (FTL) Hypothesis as well. So it is hoped that a determination of parametri...

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...rom Japan, proposed the concept of a paper defining G-Dimensional theory in relation to the Smarandache quantum paradoxes. After reviewing a draft, ... ...(FTL) Hypothesis as well. So it is hoped that a determination of parametric relationships between the quantum paradoxes and GDT proves helpful in adv... ...e greater the similarity between set B and set A, the more logical is their relationship. We see then, (somewhat obviously), that these statements a... ...roportional focal length" (f), defines the general kinetic vector geometric relationship with elliptic eccentricity established in terms of (a/b); f... ...ongitudinal lengths {a 1 , a 2 }, as in accordance with the principle of equivalence, Einstein (1907), are as yet undetermined. That is, we have n... ... σ e (1 + vu) . (14) 3.5 Inertial Causality & Gravitational Equivalence We find a simple premise reveals causality of inertial motio... ...r, and thus is not contradicted by (24). 3.10 Particle Gravity Identity & Equivalence It is proposed that matter particles are extrinsic and int... ... longitudinal length contraction, and therefore does not determine relative equivalence. Given the "intrusion principle" (gravity identities 1-3) abo... ...intrusion principle" (gravity identities 1-3) above, we must infer "reverse equivalence" i.e. longitudinal length contraction in the gravitational ve...

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...ions. In the first section we just give the basic concepts or notion like equivalence relation greatest common divisor etc. Second section is devote... ...e first section we just give the basic concepts or notion like equivalence relation greatest common divisor etc. Second section is devoted to giving ... ...epts The main aim of this section is to introduce the basic concepts of equivalence relation, equivalence class and introduce some number theoreti... ...ain aim of this section is to introduce the basic concepts of equivalence relation, equivalence class and introduce some number theoretic results use... ...= c -1 ac. We denote a conjugate to b by a ~ b and we shall refer to this relation as conjugacy relation on G. 9 DEFINITION 1.2.4: Let G be a... ...properties of them. DEFINITION 1.3.1: Let A and B be non-empty sets. A relation R from A to B is a subset of A × B. Relations from A to B are cal... ...ive if for a, b, c in A, aRb and bRc imply aRc. A relation R on A is an equivalence relation if R is reflexive, symmetric and transitive. In this ... ... symmetric and transitive. In this case [a] = {b ∈ A / aRb} is called the equivalence class of a for any a ∈ A. DEFINITION 1.3.2: A relation R o... ... This problem leads to the definition of Smarandache right (left) coset equivalence sets in a loop L related to a subgroup A of L. In chapter 5 se...

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...lies to every detail and occurrence of reality, in every single world, in relation to the world Above it. ThE lAngUA gE of ThE KAbbAliSTS iS A lAngUA... ...e for these matters, being the Language of the Branches, indicating their relation to their Upper Roots. However, this language, though extremely sui... ...derstands the way the branches relate to their roots. It is because these relations are not at all clear when looking from the lower upwards. In oth... ...must ask further: How then, has the disciple grown so wise as to know the relations of branch and root through tracing the Upper Roots? The answer i... ...Torah” (Items 9,11), pleasure and sublimity are measured by the extent of equivalence of form with the Maker. And pain and intolerance are measured ... ...der, until we reach its head in the sky, which is the purposeful point of equivalence of form with our Maker. And the difference between these two f... ...our sensation of the pleasantness and gentleness that reach us due to the equivalence of form with our maker. b. We save time, for he operates to “e... ...the Creator alone, that is, from the disparity of form from the Maker, to equivalence of form with Him, which is called Dvekut (adhesion), as clarif... ...hown that when one comes to love others, he is in direct Dvekut, which is equivalence of form with the Maker, and along with 5 8 ...

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... man gradually correct him- self through developing the screen, thus attaining equivalence of form with the Creator, to the point of Ein Sof, meaning... ...nce or by chance discoveries. We would know nature in its perfect harmony and relationships, and learn how to use it wisely. Today, however, all sci... ...of receiving, in order to turn it into giving. Then, by reason of the law of “equivalence of form,” the Light will enter our souls. Those concealed ... ...That is why it is the most effective means to produce spiritual closeness and equivalence of form with the Creator. It only becomes the most effectiv... ...ctions do not bear any external manifestation, but rather change our personal relationship with the Creator. Hence, the concealment. We perform the ... ...nstantly receive a different sensation, a different position, and a different relationship with anything or anyone. That would immediately place us ... ...he land of Israel after the holocaust, the last era began. It was a return by equivalence of root and branch, a return to the corporeal land of Isra... ... nature and rejecting it. You are experiencing the beginning of your personal relationship with the Creator. The good and right thoughts came becaus... ...r friends. This happens naturally. There’s a law in nature called “the law of equivalence of form.” That law makes objects with similar attributes d...

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... discernments and the changes are made specifically in the receiver, with relation to how the receiver is impressed by them. However, we must discer... ...kut (Adhesion) with the Creator through one’s work, which is discerned as equivalence of form, where all of one’s deeds are in order to bestow. It i... ...sured according to one’s sensation. However, all these sensations have no relation to the Creator, as it says in the “Poem of Unification,” “As she,... ... “he and I cannot dwell in the same abode.” This is because there must be equivalence of form between the Light and the Kli (Vessel). Hence, when on... ...ment of the correction of creation, being to achieve Dvekut, discerned as equivalence of form, being that all his actions will be only to bestow. Af... ...ead, they want to be adhered to the Creator, and this can only be through equivalence of form. However, to achieve that, meaning in order for one to ... ...ve with the Creator, since the matter of Dvekut (Adhesion) is measured by equivalence of form. It is thus impossible to have pure bestowal without a... ...cernments were made in the Kli (Vessel). The first is that it developed a relation to the separated pleasures, and the work of exiting the authority... ...tal teachings of Kabbalah, and how you can use its wisdom to clarify your relationship with others and the world around you. Using language both sci...

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...comparing opposites — hot vs. cold, black vs. white. We recognize one in relation to the other. if everything were white, we wouldn’t detect anythi... ... oday the ego has evolved to such a degree that we pre- fer a more virtual relationship with others. it is not that we do or do not want others. but w... ...eek deeper contact with others, so for the time being we turn to virtual relationships. A Social Network on the Spiritual Level 3 1 in the next ph... .... A Social Network on the Spiritual Level 3 1 in the next phase, virtual relationships will not satisfy us and we will want an even deeper connecti... ... root of cre- ation. a man and a woman, or groom and bride, represent the relationship between the creator and the creature—the creature being a wom... ...on, but rather in accord with the awareness of the necessity of achieving equivalence of qual- ities with the creator (the quality of love and bestow...

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...ut issue of the intermingling of life and the media. Examples for such incestuous relationships abound: Ronald Reagan, the cinematic president wa... ... desirable and two identically-preferable courses of action. Where there is no such equivalence – there is no choice, merely the pre-ordained (given... ...bitrary environment. In contrast, a model of reality must have a direct and strong relationship to the world. It must obey the rules of physics and... ...o the world. It must obey the rules of physics and of logic. The absence of such a relationship renders it meaningless. A flight simulator is not m... ...e divorced? It is because we cannot believe in an a-causal world. Causality is a relationship (mostly between two things, or, rather, events, the... ...aling with mundane, routine, causal statements because they do not reveal an OVERT relation between the two events discussed. Moreover, in daily us...

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... from Him, with the aim of bringing contentment to the Creator, it is called “equivalence of form.” At first, one restricts oneself, saying, “I don’t... ...or created and the pleasure that He gives serve as a condition upon which the relationship with the Creator is based. Man agrees to re- ceive from th... ...ain eternal and perfect pleasure and unity with the Creator. Without attaining equivalence of attributes with the Creator, we will only be able to ex... ...om, the first of which is called “the Light of Neshama.” The entire spiritual relationship between the Creator and the crea- ture in the state of Kat... ...he Creator and the crea- ture in the state of Katnut is built exactly like the relationship in our world between mother and child. We can solve all t... ...etween mother and child. We can solve all the problems that arise in physical relationships by understanding the root relationships that exist in th... ...ppear alike on the outside, but you can see the difference only when you have equivalence of spiritual attributes, when the T H E PAT H O F K A B B... ...nge another, we climb another degree and so on. All the degrees are levels of equivalence with the Creator. The world of Ein Sof is in complete equi... ... the Upper World, we, too, feel what happens “outside us” by the principle of equivalence of attributes. In order to feel some- thing external, an or...

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...and virtually a personal home. People find it very difficult to maintain relationships, and divorce rates are soaring. The family unit is falling a... ...wer, the power of love and giving. In Kabbalah terminology, it is called “equivalence of form,” which is a gradual process that leads to our sensing... ... come in through those five inlets in the box, which are all processed in relation to the existing information in that person’s memory, and in relat... ...at scholar, is completely irrelevant. o nly when one corrects oneself in relation to others does one actually become wise. This does not mean that ... ...cing. Yet, it is precisely this hatred that will compel us to correct our relationships. Even though we see everything as actually being in front of ... ...ve” ... and without annulling self-love, it is impossible to achieve ... equivalence of form. And since it is against our nature, we need a society... ...reforms. That light still does not permeate and fill our souls, since the equivalence of form between our souls and the light is still absent. But i... ...animate level to the human level during our lives, if we did not achieve equivalence of form—acquired the quality of love and giving and became sim... ...And with all that, they will attain strong adhesion by the force of their equivalence of form with their Maker, since they will not receive all that...

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...ddenly feel the whole of reality change, too. He recognized that egoistic relation- - ships are the cause of every form of suffering in the world. Th... ...tion, everything that will happen to her will stem from reciprocity, the “relationship” between Phases one and Two. As we’ve just shown, the new des... ...doing, help the unworkable desires correct themselves. We can picture the relationship between the worlds and Creation as a group of construction wo... ... humanity’s evolution, we will all attain the Creator in a state called “Equivalence of Form.” To reach that goal, Kabbalists carefully defined whic... ...hat we not only have the same intention, but be- - cause we have developed equivalence of form with Him, we see and perceive things we would not perc... ...ishly, we will regain 148 K abbalah for b eg Inners - p art f our equivalence of form with Him as it exists in the spiritual worlds. Deactiv... ...ves. Discovering the Creator is only possible according to the measure of equivalence of qualities with the Cre- - ator. If we could feel the Creator... ...ator, it is the end of correction. what is love? Love is a consequence of equivalence of inner traits, meaning attributes. In Kabbalah, there is onl... ...al teachings of Kabbalah, and how you can use its wisdom to clarify your relationship with others and the world around you. Using language both scie...

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... an inkling of spirituality, bringing him to prefer it to materialism. Then, in relation to his spirituality, he clarifies his desire. Accordingly, h... ...ends the sort of framework in which he should live, and what his position is in relation to other generations. In each era, mankind uses the world s... ...tion of the worlds from above to below, in order to draw the spiritual Light in relation to the material studied. This Light gradually cleanses our V... ...t language might he write the correlation between two objects? And what are the relations between spiritual objects? How can he describe the spiritu... ...0 Topics examined in this lesson: 1. The First Man (Adam HaRishon) 2. The Equivalence of Form 3. The Correction 4. Spiritual Filters To sum...

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...of Yehuda Ashlag)--provides you with a deeper understanding of the fundamental teachings of Kabbalah, and how you can use this wisdom to clarify your relationship with others and the world around you. Using language both scientific and poetic, he probes the most profound questio...

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...d into individual souls that descend in a cer- tain order. He writes about relationships between the bodies in this world, under the influence of the ... ... i o n s i n b e t w e e n All the signs combined created the code for the relation- ship between God and humankind, and at any moment things 8A WAKEN... ...the highest point of spir- itual evolution in our world, anyone can attain equivalence of form with the upper force—the Creator. We can attain the hig...

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...food, but also from knowing who is giving it to me, knowing with whom I have a relationship. The smallest portion of food I receive from a great figur... ...llives,wehavebecomeusedtonotthinking at all about ourselves, our interpersonal relationships, our families, our work, in all of the deeds we perform i... ...elievetoexistoutsideofus,infactexistonlyinrelationtous. That is, they exist in relation to one who perceives reality in this particular manner. Ifwedo... ...the spiritual Light. OtherwisetheLightcannotenterthem,accordingtotheLaw of the Equivalence of Form of Spiritual Objects. The activity of spiritual obj... ...degree that egoism has been ejected. This is in accordance with the Law of the Equivalence of Qualities Between the Light and the Vessel. We can, in f... ...n ourselves, we should try to cultivate both a sense of our own inferiority in relation to the Creator, and a sense of pride in the fact that as human... ...dies, due tothe demands of work and family. Any effort can be measured only in relation to one’s free time,andbydetermininghowmuchonesuffersbecauseofa... ...tothe lower part (the spiritual level of the seeker) and comes into a state of equivalence with the qualities of the lower part. EradicatingEgoism -12... ...D heart." This even includes those desires not required to be brought into an equivalence of form with the Creator. If we can completely suppress all...

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...like the whole of the Torah, speaks exclusively of man (creation) and his relationship with the Creator. The Torah attaches worldly appellations to ... ...t, and El—the Creator. Thus, Israel is the property of aspiring to attain equivalence of form with the Creator. The “nations of the world” are the a... ...Ima (mother), for the subsequent transfer to the children (ZON). The same relationships of ABA (see below) and PBP also transpire between their child... ...o Partzuf Ima (Bina), and if Ima also does not want to receive it, such a relationship between them is called back to back. The same relationship ca... ... receive the Creator’s Light). One can draw near the Creator only through equivalence of desires. The Creator is incorporeal, and can only be sensed... ...A. Malchut (to the extent of her corrected properties) merges with ZA via equivalence of form (desires), and receives this Light. Keter, Hochma, and ... ...HSUT is ZAT de Bina and the Light of Hochma is found only in YESHSUT, the relationship between Malchut and ZA works along the same principle, and th... ...and Sefirot B-ZA-M that separated (in their properties) and descended (by equivalence in properties) to a lower Partzuf are called ELEH. 1 0 6 ... ...he reception of more spiritual properties as an ascent, the attainment of equivalence of form as a union, and the emergence of a new property as sep...

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... who wishes to make himself familiar with the teachings of Pyrrhonism. The aim has been, accordingly, to give a concise presentation of Pyrrhonism in relation to its historical development and the Scepticism of the Academy, with critical references to the French and German works existing on the subject. The time and manner of the connection of Sextus Empiricus with the Pyr...

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...n the study of the power and limitations of human thought. There is a common desire to investigate the phenomena of sense-perception, and the genetic relations of man to the lower animals, and a common interest in the theory of human knowledge. While, however, some of the pages of Sextus' works would form a possible introduction to certain lines of modern philosophical th...

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...The Historical Relations Of Sextus Empiricus-Introductory paragraph.—The name of Sextus Empiricus. His profession.—The time when he lived.—The place of his birth.—The seat of the Sceptical School while Sextus was at its head.—The character ...

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... aim has been, accordingly, to give a concise presentation of Pyrrhonism in relation to its historical development and the Scepticism of the Academy,... ...ofessor of Philosophy in the University of Bern, for valuable assistance in relation to the plan of the work and advice in regard to the best author... ...erning the translation. CONTENTS CHAPTER I. PAGE THE HISTORICAL RELATIONS OF SEXTUS EMPIRICUS 1 Introductory paragraph.—The... ...IRICUS, TRANSLATED FROM THE GREEK 101 CHAPTER I. The Historical Relations of Sextus Empiricus. Interest has revived in the works of Sext... ...on desire to investigate the phenomena of sense- perception, and the genetic relations of man to the lower animals, and a common interest in the theo... ...νξία is used to describe his conduct . [3] He founded his Scepticism on the equivalence of opposing arguments. [4] [1] Diog. IX. 11, 61. [2] Diog...

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... Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitational fields; Mathemati...

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... how the Zagreb indices, a particular case of Smarandache-Zagreb index of a graph changes with these operators and extended these results to obtain a relation connecting the Zagreb index on operators. Key Words: Subdivision graph, ladder graph, Smarandache-Zagreb index, Zagreb index, graph operators. ...

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...SI Hypergraph Partitioning Using Taguchi Methods BY P.SUBBARAJ, S.SARAVANASANKAR and S.ANAND . . . . . . . . . . . . . . . . 69 Negation Switching Equivalence in Signed Graphs BY P.SIVA KOTA REDDY, K.SHIVASHANKARA and K.V.MADHUSUDHAN. . . . . . 85 Weak and Strong Reinforcement Number For a Graph BY PINAR DUNDAR, TUFAN TURACI and DERYA DOGAN. . . . . . . . . . . . . ....

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... Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitational fields; Mathemati...

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.... . . . . . . . 70 Entire Semitotal-Point Domination in Graphs BY B.BASAVANAGOUD, S.M.HOSAMANI and S.H.MALGHAN. . . . . . . . . . . . . . .79 On k-Equivalence Domination in Graphs BY S.ARUMUGAM and M.SUNDARAKANNAN. . . . . . . . . . . . . . . . . . . . . . . 86 On Near Mean Graphs BY A.NAGARAJAN, A.NELLAI MURUGAN and S.NAVANEETHA KRISHNAN. . . . . . 94 On Pathos Lic...

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...The aim of this book is two fold. At the outset the book gives most of the available literature about Fuzzy Relational Equations (FREs) and its properties for there is no book that solely caters to FREs and its applications. Though we have a comprehensive bibliography, we do not promise to give all the possible available literature...

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... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATIONAL MAPS HEXI... ...OSOPHIC RELATIONAL MAPS HEXIS Church Rock 2004 1 FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATIONAL MAPS W. B. Vasan... ... i c a t i o n 6 P r e f a c e 7 Chapter One FUZZY RELATIONAL EQUATIONS: BASIC CONCEPTS AND PROPERTIES 1.1 Fuzzy Rel... ... Fuzzy Relational Equations and their properties 10 1.2 Properties of Fuzzy Relations 16 1.3 Fuzzy compatibility relations and composition o... ...In this section we just recollect the properties of fuzzy relations like, fuzzy equivalence relation, fuzzy compatibility relations, fuzzy ordering ... ...more about these concepts please refer [43]. Now we proceed on to define fuzzy equivalence relation. A crisp binary relation R(X, X) that is reflex... ...inary relation R(X, X) that is reflexive, symmetric and transitive is called an equivalence relation. For each element x in X, we can define a crisp... ...sp set A x , which contains all the elements of X that are related to x, by the equivalence relation. A x = {y ⏐(x, y) ∈ R (X, X)} A x is cl... ...ed to any element of X not included in A x . This set A x is referred to an as equivalence class 17 of R (X, X) with respect to x. The members...

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... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATIONAL MAPS HEXI... ...OSOPHIC RELATIONAL MAPS HEXIS Church Rock 2004 1 FUZZY RELATIONAL MAPS AND NEUTROSOPHIC RELATIONAL MAPS W. B. Vasan... ... i c a t i o n 6 P r e f a c e 7 Chapter One FUZZY RELATIONAL EQUATIONS: BASIC CONCEPTS AND PROPERTIES 1.1 Fuzzy Rel... ... Fuzzy Relational Equations and their properties 10 1.2 Properties of Fuzzy Relations 16 1.3 Fuzzy compatibility relations and composition o... ...In this section we just recollect the properties of fuzzy relations like, fuzzy equivalence relation, fuzzy compatibility relations, fuzzy ordering ... ...more about these concepts please refer [43]. Now we proceed on to define fuzzy equivalence relation. A crisp binary relation R(X, X) that is reflex... ...inary relation R(X, X) that is reflexive, symmetric and transitive is called an equivalence relation. For each element x in X, we can define a crisp... ...sp set A x , which contains all the elements of X that are related to x, by the equivalence relation. A x = {y ⏐(x, y) ∈ R (X, X)} A x is cl... ...ed to any element of X not included in A x . This set A x is referred to an as equivalence class 17 of R (X, X) with respect to x. The members...

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...× µ ) (x, y) = min {λ(x), µ (y)} for every (x, y) ∈ X × Y. A fuzzy binary relation R λ on a set X is defined as a fuzzy subset of X × X. The co... ...X is defined as a fuzzy subset of X × X. The composition of two fuzzy relations R λ and R µ is defined by (R λ o R µ )(x, y) = sup X t∈ {min R... ... y)}, for every x, y ∈ X. DEFINITION 1.1.12: Let R λ be a fuzzy binary relation on a set X. A fuzzy subset µ of the set X is said to be a pre cla... ... {µ (x), µ (y) } ≤ R λ (x, y) for every x, y ∈ X. 11 A fuzzy binary relation R λ on a set X is said to be a similarity relation on the set X i... ....2: A relation ρ on an R-module M is called a congruence on M if it is an equivalence relation on M such that (a, b) ∈ ρ and (c, d) ∈ ρ imply that (a... ...uzzy relation α on M [i.e. a mapping α : M × M → [0,1]] is called a fuzzy equivalence relation if i. z , y , x all for ) z , y ( ) x , x ( sup M ... ...α α ∈ ≥ for all x, y in M (fuzzy transitive). DEFINITION 1.8.5: A fuzzy equivalence relation α on an R-module M is called a fuzzy congruence if α ... ... [] [] ) y , z ( ), z , x ( Min sup M z µ µ ∈ α α . Thus α µ is a fuzzy equivalence relation on M. Now α µ (x + u, y + ν) = µ (x + u – ν – y... ... generates the half groupoid P. Now we introduce the notions of fuzzy equivalence relation as given by [144] and proceed on to recall the defini...