This paper is specialized with fuzzy random multi-objective unbalanced transportation data problems by using of fuzzy programming technique when the sources and destination parameters are fuzzy random variables in inequality type of constraints. In this paper, we focus on the solution procedure of the specified transportation data problems where the objective functions are minimization type and supplies and demands are replaced by the fuzzy random variables. We first convert the fuzzy random multi-objective unbalanced transportation problem into deterministic problem by using (...) fuzzy random chance constraints approach. By introducing the concept of linear membership function of fuzzy programming, multi-objective deterministic transportation problem is converted into single objective deterministic problem and then we solve it and we obtain the optimal compromise solution. Lastly a numerical example is provided for illustration the methodology. (shrink)

The goal of inquiry in this essay is to ascertain to what extent the Principle of Compositionality – the thesis that the meaning of a complex expression is determined by the meaning of its parts and its mode of composition – can be justifiably imposed as a constraint on semantic theories, and thereby provide information about what meanings are. Apart from the introduction and the concluding chapter the thesis is divided into five chapters addressing different questions pertaining to the overarching (...) goal of inquiry. Chapter Two is an attempt to determine whether the Principle of Compositionality is a trivial principle. It is argued that this is not the case in the context of providing the semantics of natural languages since it is an open question whether the best theories that respect available syntactic and semantic data are compositional. Chapter Three and Chapter Four ask whether there are reasons to think that the Principle of Compositionality is true. It is argued that the three most commonly cited reasons for thinking that correct semantic theories must be compositional – Linguistic Creativity, Productivity and Systematicity – in fact only give us reasons to think that the meaning of complex expressions depend on the meanings of their parts and their modes of composition, but not that the meaning of complex expressions depend ONLY on those factors. Chapter Five asks whether there are any reasons to think that the Principle of Compositionality is false. It is argued that all the phenomena that have been suggested entail non-compositionality are in fact compatible with some versions of compositionality. Even if this conclusion is reached in this chapter, the conclusion of the previous two chapters entails that we are not justified in imposing the Principle of Compositionality as an adequacy constraint on Semantic theories. Chapter Six explores the ways in which information about what meanings are can be derived by imposing constraints on semantic theories. It is argued that the distinction emphasized in Chapter Three and Chapter Four between depending on and depending ONLY on is of critical importance. It is demonstrated that the informative potential of the Principle of Compositionality goes far beyond that of the principle we are in fact justified in imposing on semantic theories. So not only is it the case that we cannot learn anything about meanings from the justified imposition of the Principle of Compositionality – since we cannot justifiably impose it as a constraint on semantic theories – what we could have learned from it had we been justified in imposing it is very different from what we can learn from the principle that we are justified in imposing. (shrink)

In this thesis, I will defend a new kind of compatibilist account of free action, indirect conscious control compatibilism (or indirect compatibilism for short), and argue that some of our actions are free according to it. My argument has three components, and involves the development of a brand new tool for experimental philosophy, and the use of cognitive neuroscience. The first component of the argument shows that compatibilism (of some kind) is a conceptual truth. Contrary to the current orthodoxy in (...) the free will literature, which is that our concept of free will is an incompatibilist concept - a concept according to which we have free will only if determinism is false - I will show that our concept of free will is in fact a compatibilist concept - a concept according to which we can have free will even if determinism is true - and I do so using a new experimental philosophy methodology inspired by two-dimensional semantics. -/- Of course, even if our concept of free will is a compatibilist concept, this does not mean that there are any free actions in the world: the current empirical evidence from the brain sciences appears to show that there might be no, or very few, free actions in the world, even on many compatibilist understandings of what it would take for there to be free will. The second component of the argument addresses this concern by extending our understanding of compatibilism. Agents act freely either when their actions are caused by compatibilistically acceptable psychological processes, or are indirectly caused by those same processes. Hence the name of my account: indirect compatibilism. -/- The final component of the argument defends my new account against some interesting objections and provides evidence from cognitive neuroscience that some of our actions count as free by the lights of indirect compatibilism. (shrink)

We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context into the mathematical structure used to describe a concept, and thereby model how context influences the typicality of a single exemplar and the applicability of a single property of a concept. We introduce the notion `state of a concept' to account for this contextual influence, and show (...) that the structure of the set of contexts and of the set of properties of a concept is a complete orthocomplemented lattice. The structural study in this article is a preparation for a numerical mathematical theory of concepts in the Hilbert space of quantum mechanics that allows the description of the combination of concepts. (shrink)

Forty-two years ago, Capra published “The Tao of Physics” (Capra, 1975). In this book (page 17) he writes: “The exploration of the atomic and subatomic world in the twentieth century has …. necessitated a radical revision of many of our basic concepts” and that, unlike ‘classical’ physics, the sub-atomic and quantum “modern physics” shows resonances with Eastern thoughts and “leads us to a view of the world which is very similar to the views held by mystics of all ages and (...) traditions.“ This article stresses an analogous situation in biology with respect to a new theoretical approach for studying living systems, Integral Biomathics (IB), which also exhibits some resonances with Eastern thought. Stepping on earlier research in cybernetics1 and theoretical biology,2 IB has been developed since 2011 by over 100 scientists from a number of disciplines who have been exploring a substantial set of theoretical frameworks. From that effort, the need for a robust core model utilizing advanced mathematics and computation adequate for understanding the behavior of organisms as dynamic wholes was identified. At this end, the authors of this article have proposed WLIMES (Ehresmann and Simeonov, 2012), a formal theory for modeling living systems integrating both the Memory Evolutive Systems (Ehresmann and Vanbremeersch, 2007) and the Wandering Logic Intelligence (Simeonov, 2002b). Its principles will be recalled here with respect to their resonances to Eastern thought. (shrink)

Logical Probability (LP) is strictly distinguished from Statistical Probability (SP). To measure semantic information or confirm hypotheses, we need to use sampling distribution (conditional SP function) to test or confirm fuzzy truth function (conditional LP function). The Semantic Information Measure (SIM) proposed is compatible with Shannon’s information theory and Fisher’s likelihood method. It can ensure that the less the LP of a predicate is and the larger the true value of the proposition is, the more information there is. So the (...) SIM can be used as Popper's information criterion for falsification or test. The SIM also allows us to optimize the true-value of counterexamples or degrees of disbelief in a hypothesis to get the optimized degree of belief, i. e. Degree of Confirmation (DOC). To explain confirmation, this paper 1) provides the calculation method of the DOC of universal hypotheses; 2) discusses how to resolve Raven Paradox with new DOC and its increment; 3) derives the DOC of rapid HIV tests: DOC of “+” =1-(1-specificity)/sensitivity, which is similar to Likelihood Ratio (=sensitivity/(1-specificity)) but has the upper limit 1; 4) discusses negative DOC for excessive affirmations, wrong hypotheses, or lies; and 5) discusses the DOC of general hypotheses with GPS as example. (shrink)

Learning the basics of the logic of certain and the uncertain is presented as the result of a work of an interdisciplinary team. Our experimentation involves essentially two aspects: language comprehension of a statement and analysis of the information. The first aspect is to see how children interpret a sentence with subject and predicate, that is, if they believe that the truth values that can be assigned are those of bivalent logic, i.e. true or false, or truth-values of a multivalent (...) logic i.e. if there is the possibility/need to consider truth values intermediate between true and false such as: more true than false, more false than true, halfway between true and false. It is also required children to identify phrases not complete and therefore that are not linguistic statements. Regarding the second aspect it comes to analyzing the information on the concept expressed by a proposition, i.e. to see if it is possible to immediately assign to it a truth value, or if it is necessary to acquire a further information. Moreover we highlight the distinction between uncertainty due to incomplete information, which leads to probability assessments, and semantic uncertainty that leads to the theory of fuzzy sets. (shrink)

It is outlined the possibility to extend the quantum formalism in relation to the requirements of the general systems theory. It can be done by using a quantum semantics arising from the deep logical structure of quantum theory. It is so possible taking into account the logical openness relationship between observer and system. We are going to show how considering the truth-values of quantum propositions within the context of the fuzzy sets is here more useful for systemics. In conclusion we (...) propose an example of formal quantum coherence. (shrink)

Knowledge representation is one of the central concepts in Artificial Intelligence. It is very common that knowledge about a field is expressed in natural language. Therefore, most of the times, knowledge representation using a logic programming language derives into a translation problem. This translation consists in the formalization of the statements, belonging to the knowledge level, which are converted into formulas of the so called symbolic level. Knowledge may be imprecise or vague and, in order to deal with vagueness using (...) declarative techniques, fuzzy logic programming amalgamates classical logic programming and fuzzy logic. Fuzzy logic programming has mainly led to programming languages that use annotations to represent vagueness. But vagueness is a linguistic phenomenon which is implicit in the statements of the knowledge level. Hence, the natural connection existing between these two levels is broken when annotations are employed, since they introduce weights in a symbolic level which are not present in the knowledge level and converts knowledge representation in a more complex, counterintuitive task. In order to overcome this problem, we propose a fuzzy linguistic logic framework which allows the treatment of imprecision through linguistic resources. This framework makes a clean separation between precise knowledge and vague knowledge. In this paper, we argue that this separation is more declarative than the one dispensed by the approach based on annotations, and can be beneficial for modeling a problem. (shrink)

“And maybe some of this stuff counts as philosophy after all. The form of a philosophical theory, often enough, is: Let’s try looking over here”- Jerry A. Fodor.

S.Haack has defended the idea that in fuzzy logic it cannot be affirmed that the true values of a statement are themselves blurry. This article analyzes Haack position in the light of some current approaches of classic philosophy of logic, and from the cognitive point of view of philosophy of logic, especially from the theory of concepts. Under the said approaches, the thesis on non-gradation of truth appears significantly weakened.

What is Computational Intelligence (CI) and what are its relations with Artificial Intelligence (AI)? A brief survey of the scope of CI journals and books with ``computational intelligence'' in their title shows that at present it is an umbrella for three core technologies (neural, fuzzy and evolutionary), their applications, and selected fashionable pattern recognition methods. At present CI has no comprehensive foundations and is more a bag of tricks than a solid branch of science. The change of focus from methods (...) to challenging problems is advocated, with CI defined as a part of computer and engineering sciences devoted to solution of non-algoritmizable problems. In this view AI is a part of CI focused on problems related to higher cognitive functions, while the rest of the CI community works on problems related to perception and control, or lower cognitive functions. Grand challenges on both sides of this spectrum are addressed. (shrink)

A critical survey of the fundamental philosophical issues in the logic and formal ontology of space, with special emphasis on the interplay between mereology (the theory of parthood relations), topology (broadly understood as a theory of qualitative spatial relations such as continuity and contiguity), and the theory of spatial location proper.

In the aftermath of a normalized Foucaultian world with an all encompassing web of biopower, one remaining hope is to cultivate nimbleness. Nimbleness is an embodied aesthetic sensitivity to the material presence. Cultivating nimbleness is a particular style of cultivation; it is to willfully gather together one’s self in the wake of a formative force far richer than the derivative web of living power relationships of human embeddness within a horizon of social, economical, political and historical subjectivating power relations; which (...) are chronicled and labeled by Michel Foucault as the normalizing practices of biopower. In other words to have freedom, one must start by rejecting the categories and labels normally internalized in order to relearn to learn from the material presence. Such a style of cultivation is a means of resisting normalizing power relations which co-opt cultivating practices to engross their own dominance which has had the by-product of an impotence to negate the gross material injustices present. This normalizing style of cultivation is a prevalent, corrupted, semblance which denies the importance of beauty for that of efficiency, rejects non-human purposiveness, and limits its measure of ethics to short term economical pragmatism. The thesis acknowledges that something is awry with the world and that giving care to beauty might help. The aim is to examine the event of Beauty as depicted by the philosopher Immanuel Kant and to apply this characterization to elective architectural spaces such that it may motivate individuals to cultivate their own nimbleness in relation to a formative force of nature. However given the revealed need for sensitivity to the particular material presence, the thesis can not be a rule book or catalog for beautiful design. Rather it is a rehabilitation for architects who are already heterospatially curious, with the desired outcome of architects cultivating their own nimbleness to reflectively judge as a ground up, multi-node, rhizomatic means of resistance to normalizing power practices as manifest in bad architecture. (shrink)

A number of reasons, both historical and philosophical, has caused Technology and Human Sciences to be perceived as disjoint domains. Contrary to this claim, we propose as a thesis that there exists a strong methodological affinity between these apparently disconnected fields of knowledge. Our view is further corroborated by the emergence, in the setting of Information Sciences of new scientific concepts and tools such as fuzziness. Comparing the ways in which both technology and literature offer a “model of reality” we (...) shall see that their approach is mainly descriptive, in opposition to the Hard Science’s approach that is markedly Galileian and proceeds by making bold hypotheses, not necessarily linked to the surface description of reality. Moreover, we will discuss the fact that, surprisingly, fuzzy logic can be applied in a very similar way in both Technology and Human Sciences – while its eventual embodiment in Hard Sciences is of a very different nature. (shrink)

The history of Fuzziness in Italy is varied and scattered among a num- ber of research groups. As a matter of fact, “fuzziness” spread in Italy through a sort of spontaneous diffusion, and, also subsequently, no one felt the need to cre- ate some “national” common structure like an Association or similar things. Since a cohesive retelling would be next to impossible, a few members of the Italian fuzzy community have been asked to recount their experience and express their hopes (...) for the future. (shrink)

A fuzzy comprehensive evaluation of COGAG power plant performance is given by using a method of fuzzy mathematics, and multilevel fuzzy evaluation model is set up. Taking a naval ship as an example, the major parameters related to COGAG power plant performance are obtained by computer simulation, and a set of synthetic performance evaluation index system is established. The result shows that the strong fuzzy propulsion system performance indexes can be quantified by this fuzzy evaluation model in order to provide (...) the reference for choosing the optimal design of ship propulsion system. (shrink)

Decisions regarding the attribution of personhood to nonhuman animals have implications not only for the rights held by a particular species but also for the moral obligations of humans as moral agents. Since humans decide which species are accorded moral standing; thus becoming candidates for legal standing as legal persons; we need to be aware of our own vested interests in where the boundaries of duty are drawn. This paper argues that simple determination of moral standing is not sufficient to (...) induce relevant changes in moral behavior. It examines six problems that emerge for us in determining the personhood of nonhuman animals: identifying which capacities we believe to be morally relevant; separating the identification of capacities from the duty consequences; designing appropriate methodologies for assessing morally relevant capacities in nonhuman animals; identifying relevant claim rights for nonhuman animals; resolving competing moral interests among species and between nonhumans and humans; and ensuring appropriate moral behavior. The conclusion of this examination is that we have a long way to go in order to be consistent in our moral behavior. (shrink)

ABSTRACT It is well-known that Artificial Intelligence requires Logic. But its Classical version shows too many insufficiencies. So, it is very necessary to introduce more sophisticated tools, as may be Fuzzy Logic, Modal Logic, Non-Monotonic Logic, and so on. When you are searching the possible precedent of such new ideas, we may found that they are not totally new, because some ancient thinkers have suggested many centuries ago similar concepts, certainly without adequate mathematical formulation, but in the same line: against (...) the dogmatism and the dualistic vision of the world: absolutely true vs. absolutely false, black vs. white, good or bad by nature, 0 vs.1, etc. We attempt to analyze here some of these greatly unexplored, and very interesting early origins. (shrink)

While the past century of neuroscientific research has brought considerable progress in defining the boundaries of the human cerebral cortex, there are cases in which the demarcation of one area from another remains fuzzy. Despite the existence of clearly demarcated areas, examples of gradual transitions between areas are known since early cytoarchitectonic studies. Since multi-modal anatomical approaches and functional connectivity studies brought renewed attention to the topic, a better understanding of the theoretical and methodological implications of fuzzy boundaries in brain (...) science can be conceptually useful. This article provides a preliminary conceptual framework to understand this problem by applying philosophical theories of vagueness to three levels of neuroanatomical research. For the first two levels (cytoarchitectonics and fMRI studies), vagueness will be distinguished from other forms of uncertainty, such as imprecise measurement or ambiguous causal sources of activation. The article proceeds to discuss the implications of these levels for the anatomical study of connectivity between cortical areas. There, vagueness gets imported into connectivity studies since the network structure is dependent on the parcellation scheme and thresholds have to be used to delineate functional boundaries. Functional connectivity may introduce an additional form of vagueness, as it is an organizational principle of the brain. The article concludes by discussing what steps are appropriate to define areal boundaries more precisely. (shrink)

Reconstructability analysis (RA) decomposes wholes, namely data in the form either of set theoretic relations or multivariate probability distributions, into parts, namely relations or distributions involving subsets of variables. Data is modeled and compressed by variable-based decomposition, by more general state-based decomposition, or by the use of latent variables. Models, which specify the interdependencies among the variables, are selected to minimize error and complexity.

Philosophers, linguists and others interested in problems concerning natural language frequently employ tools from logic and model theory. The question arises as to the proper interpretation of the formal methods employed—of the relationship between, on the one hand, the formal languages and their set-theoretic models and, on the other hand, the objects of ultimate interest: natural language and the meanings and truth conditions of its constituent words, phrases and sentences. Two familiar answers to this question are descriptivism and instrumentalism. More (...) recently, a third answer has been proposed: the logic as modelling view. This paper seeks to clarify and assess this view of logic. The conclusion is that we can successfully adopt the modelling perspective on a given piece of logical machinery only if we have to hand some other machinery to which we take the descriptive attitude. Thus, logic as modelling is not a full-fledged alternative to the descriptive view— for it cannot stand alone: it can at best be an addition to the descriptive perspective. The paper first presents the argument in a general, abstract form, before working through a detailed case study. The case examined is the one with respect to which the logic as modelling view has been developed in the greatest detail in the literature: the case of fuzzy model theory as an account of vagueness in natural language. (shrink)

This paper's goal is very simple, that of trying to look at the broad and multifaceted concept of uncertainty from a typically scientific point of view, namely, that consisting in representing concepts through numerical quantities. For the goal, it is supposed that the universe of discourse is amorphe, and that the basic treats of the meaning shown by the mother-predicate ‘uncertain’, from which it comes the concept of uncertainty, can be empirically captured in, at least, for what concerns its variability (...) between the elements of the universe of discourse. Once ‘measures of uncertainty’ are defined in the same way as measures of length, area, volume, randomness, electrical intensity, etc., were introduced, there are analyzed the two cases in which ‘uncertain’ is confused with ‘probable’ and ‘possible’, to see which restrictions they mean in the use of ‘uncertain’. What it is just attempted is to open a window towards a new, and more general way, of considering the term ‘uncertainty’. (shrink)

This paper contains some reflections going from pinpointing one of the main goals of fuzzy logic, that of representing linguistic terms whose use is gradable in a given context, to show a mathematical model able to capture what is a fuzzy set labeled P in a universe of discourse, throughout a way in which some comments on what a mathematical model is, and to what it serves, are done. It is shown that such a model for a fuzzy set is (...) but a numerical quantity coming from the so-called primary use of its linguistic label, and along the paper there are shown some hints on the design of formulas representing statements by means of fuzzy terms. All that is jointly considered along the way modern science has been following to domesticate as quantities those gradable concepts which it takes into account. Under this view, fuzzy sets appear as more typically scientific than logical or purely mathematical objects. (shrink)

ype-2 fuzzy sets and complex fuzzy sets are both three dimensional extensions of type-1 fuzzy sets. Complex fuzzy sets come in two forms, the standard form, postulated in 2002 by Ramot et al., and the 2011 innovation of pure complex fuzzy sets, proposed by Tamir et al.. In this paper we compare and contrast both forms of complex fuzzy set with type-2 fuzzy sets, as regards their rationales, applications, definitions, and structures. In addition, pure complex fuzzy sets are compared with (...) type-2 fuzzy sets in relation to their inferencing operations. Complex fuzzy sets and type-2 fuzzy sets differ in their roles and applications; complex fuzzy sets are pertinent to inferencing where there is seasonality, and type-2 fuzzy sets are applicable to reasoning under uncertainty. Their definitions differ also, though there is equivalence between those of a pure complex fuzzy set and a type-2 fuzzy set. Structural similarity is evident between these three-dimensional sets. Complex fuzzy sets are represented by a 3–D line, and type-2 fuzzy sets by a 3–D surface, but a surface is simply a generalisation of a line. This similarity is particularly apparent between pure complex fuzzy sets and type-2 fuzzy sets, which are both mappings from the domain onto the unit square. However type-2 fuzzy sets were found not to be isomorphic to pure complex fuzzy sets. The mechanisms by which complex fuzzy sets model and quantify periodicity, and type-2 fuzzy sets model and quantify uncertainty are discussed. A type-2 fuzzy set can be represented as the union of its type-2 embedded set. An embedded type-2 fuzzy set is a type-2 fuzzy set in itself, whose geometrical representation is a 3-D line. Thus, geometrically an embedded type-2 fuzzy set can be seen as equivalent to a pure complex fuzzy set and therefore a type-2 fuzzy set can be represented as the union of a collection pure complex fuzzy sets, which in turn can be regarded as embedded complex fuzzy sets of a type-2 fuzzy set. This relationship is exploited to provide a complex definition of a type-2 fuzzy set. (shrink)

Switzerland is renowned for many things: the mountains, Heidi, chocolate, bank accounts, the punctuality of public transport and, of course, high quality watches. However, Switzerland is probably most famous for exactness and accuracy, influencing Swiss mentalities and everyday life. Legend has it, that is to say, that in Switzerland you can set the watch by the trains – something unheard of in any other European country. Perhaps for this reason, in Switzerland it was especially difficult to take up concepts such (...) as the fuzzy set theory developed by Lotfi Zadeh. Nevertheless, fuzzy set theory found its way into Swiss computer sciences, too, jolting the beliefs and convictions of Swiss scientists. The slightly belated gradual arrival of fuzziness in Switzerland is the topic of this article. (shrink)

Our research aims to address the difficulties faced by small online retailers trying to provide meaningful recommendations to their customers. We hypothesize that fuzzy technology can be used to produce meaningful recommendations even in an environment with extremely sparse data. To set up our test, we found a small to mid-sized e-shop with no repetition, an online travel agency. In other words, our test subject was an e-shop operating in a crowded market that it did not dominate selling a product (...) where individual purchases were highly infrequent, often only annual. Its lack of dominance meant that it could not require pre-purchase registration, depriving it of one type of user-identifiable data. The purchase infrequency meant it could not assume cookie survival, depriving it of another source of user identifiable data. The only user identifiable data available was thus information mined using scripts or other time volatile techniques. To test our hypothesis, we first use fuzzy sets interpreted as user preference degree - preference indicators. Next we evaluated user-item data behavior using fuzzy preference indicators designed to build a rating for each new user. Next, we used content-based preference learning to expand this rating and so it could be used to infer preferences for yet unvisited items. Finally, we tuned the attribute preferences using the parametric families of t-conorms so that calculated user specific preference ordering could be extended to all available items. The quality of the solution was measured on top-k in several order sensitive metrics. To evaluate the effectiveness of our approach, we developed an off-line experimental framework that allowed us to test the results of our hypothesis against the actual data collected by the SMEnR´s web site. Based on our testing, we can conclude that a significant improvement in recommendation was achieved. (shrink)

We sketch the development of fuzzy sets and fuzzy logic in Austria during the last 50 years which started, after some early traces, in 1976 in Linz with my own work and in Vienna with Klaus-Peter Adlassnig’s work. Therefore we first discuss the history of our research group at the Johannes Kepler University Linz and at the JKU-Softwarepark Hagenberg. Next we have a closer look at the developments at the Vienna University Medical School, at the logic group at the Vienna (...) University of Technology, and at the work of Reinhard Viertl in statis- tics. Finally we present some achievements made at the University of Innsbruck. (shrink)

Computer science educators observed that in the present way of teaching computing, only 2% of students can easily handle computational concepts -- and, as a result, only 2% of the students specialize in computer science. With the increasing role of computers in the modern world, and the increasing need for computer-related jobs, this 2% barrier creates a shortage of computer scientists. We notice that the current way of teaching computer science is based on easiness of using two-valued logic, on easiness (...) of dividing all situations, with respect to each property, into three classes: yes, no, and unknown. The fact that the number of people for whom such a division is natural is approximately 2% provides a natural explanation of the 2% barrier -- and a natural idea of how to overcome this barrier: to tailor our teaching to students for whom division into more than three classes is much more natural. This means, in particular, emphasizing fuzzy logic, in which for each property, we divide the objects into several classes corresponding to different degrees with which the given property is satisfied. We also analyze which are the best ways to implement the corresponding fuzzy ideas. (shrink)

The aim of the paper is the axiomatic justification of the theory of experience and chance, one of the dual halves of which is the Kolmogorov probability theory. The author’s main idea was the natural inclusion of Kolmogorov’s axiomatics of probability theory in a number of general concepts of the theory of experience and chance. The analogy between the measure of a set and the probability of an event has become clear for a long time. This analogy also allows further (...) evolution: the measure of a set is completely analogous to the believability of an event. In order to postulate the theory of experience and chance on the basis of this analogy, you just need to add to the Kolmogorov probability theory its dual reflection — the believability theory, so that the theory of experience and chance could be postulated as the certainty theory on the Cartesian product of the probability and believability spaces, and the central concept of the theory is the new notion of co~event as a measurable binary relation on the Cartesian product of sets of elementary incomes and elementary outcomes. Attempts to build the foundations of the theory of experience and chance from this general point of view are unknown to me, and the whole range of ideas presented here has not yet acquired popularity even in a narrow circle of specialists; in addition, there was still no complete system of the postulates of the theory of experience and chance free from unnecessary complications. Postulating the theory of experience and chance can be carried out in different ways, both in the choice of axioms and in the choice of basic concepts and relations. If one tries to achieve the possible simplicity of both the system of axioms and the theory constructed from it, then it is hardly possible to suggest anything other than axiomatization of concepts co~event and its certainty. The main result of this work is the axiom of co~event, intended for the sake of constructing a theory formed by dual theories of believabilities and probabilities, each of which itself is postulated by its own Kolmogorov system of axioms. Of course, other systems of postulating the theory of experience and chance can be imagined, however, in this work, a preference is given to a system of postulates that is able to describe in the most simple manner the results of what I call an experienced-random experiment. (shrink)

In this paper a novel term is introduced to cover for a parameter already investigated in a number of experiments conducted in the Democritus University, without, yet, being identified with a specific name. The aim of all those studies was to investigate the learning strategies frequency of use in correlation with the confidence of the subjects as to whether and to what extent such strategies enhance their language learning. In the specific experiment forty eight students from the first three grades (...) in a State Secondary school, in Thrace, Greece, were recruited through convenience sampling, twenty four Greek native speakers and twenty four Turkish native speakers with Greek as their second language. There were sixteen learners out of each grade, eight of low and eight of high level in English, four male, four female, forty eight learners altogether, twenty four male and twenty four female students. The students had to indicate not only the level of frequency of strategy use but also their confidence in those strategies’ effectiveness; this is the introduced term Confidence Hypothesis about Efficiency of Specific Strategies. Furthermore, the students used the Vougiouklis & Vougiouklis bar instead of the widely used Likert scale for the filling in of the questionnaires minimizing time and effort. The questionnaire used was the translated in Greek and validated SILL questionnaire with 50 items. Each of the 50 questions was followed by two bars: on the first bar the students had to specify the frequency of use of each strategy and on the second their confidence about each strategy’s effectiveness. (shrink)

Vougiouklis & Vougiouklis have proposed the replacement of Likert scales, usually used in questionnaires, with a bar. With this proposal a discrete situation is replaced by a fuzzy one. There are identified certain advantages concerning the use of the bar as compared to that of a scale during both the stages of filling-in as well as processing a questionnaire. The main advantage is the fact that it is much quicker to fill in and much easier to explain to participants. The (...) bar provides the potential for different types of processing Likert scales cannot offer. Therefore the researchers are allowed to ascertain that the given answers follow the Gauss or a parabola distribution, and they have the opportunity to ‘correct’ this tendency. In this research it is offered a possibility of choosing amongst a number of alternatives by utilizing fuzzy logic in the same way as it has already been done in industry and combining mathematical models with multivalued operations. Finally, the suggested method is applied in a Course and Teaching Evaluation process by the students of Democritus University of Thrace. (shrink)

Probability theory is the arithmetic of the real line constrained by special aleatory axioms. Fuzzy logic is also a kind of probability theory, but of considerably more mathematical and axiomatic complexity than the standard account. Fuzzy logic purp orts to model the human capacity for reasoning with inexact concepts. It does this by exploring the assumption that when we argue in inexact terms and draw inferences in imprecise vocabularies, we actually make computations about the embedded imprecision s. I argue that (...) this is in fact the last thing that we do, and indeed that we do the opposite. (shrink)