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In this study, the authors envisage the neutrosophic number from various distinct rational perspectives and viewpoints to give it a look of a conundrum. They focused and analysed neutrosophic fuzzy numbers when indeterminacy and falsity functions are dependent on each other, which serves an indispensable role for the uncertainty concept. Additionally, the idea of cylindrical neutrosophic single-valued number is focused here, when the indeterminacy and falsity functions are dependent to each other using an influx of different logical and innovative graphical representation. They also developed the score and accuracy function for this particular cylindrical neutrosophic single-valued number and analysed some real-life problems like networking critical path model problem and minimal spanning tree problem of operation research field when the numbers are in cylindrical neutrosophic ambiance. They also introduced a multi-criterion group decision-making problem in this cylindrical neutrosophic domain. This noble thought will help us to solve a plethora of daily life problems in the neutrosophic arena.

We describe functions of complexity one with antiderivative of the same complexity

Image segmentation is an important step in image processing application, especially for medical images. It is also a very important task in breast cancer detection. There are various stages for breast cancer detection. The first stage is extraction/segmentation of region of interest followed by detection and classification. In this paper, a new clustering procedure is proposed to extract/segment the region of interest/lesion in mammogram images using neutrosophic set (NS). A variety of image segmentation algorithms are in the literature, but accuracy is still a crucial problem. NS has an ability to handle indeterminant information thus reducing the uncertainty in the images. The image is initially converted to an NS domain, which is described using three membership sets: degree of truth (T), degree of indeterminacy (I), and degree of false (F). In our work, indeterminate degree is computed using a novel technique that uses Shannon entropy and standard deviation. Then, a neutrosophic similarity-based image is formed using neutrosophic similarity function, which is then clustered to detect lesion/tumor. In the clustering algorithm, three image features and also a second criterion function, which is an exponential entropy, are used. The proposed algorithm has been tested on different types of mammogram images along with a comparative study with existing methods both quantitatively and qualitatively. The experimental results demonstrate that the proposed method can segment the mammogram images more effectively and accurately.

Theories of verisimilitude have routinely been classified into two rival camps—the content approach and the likeness approach—and these appear to be motivated by very different sets of data and principles. The question thus naturally arises as to whether these approaches can be fruitfully combined. Recently Zwart and Franssen (Synthese 158(1): 75-92, 2007) have offered precise analyses of the content and likeness approaches, and shown that given these analyses any attempt to meld content and likeness orderings violates some basic desiderata. Unfortunately their characterizations of the approaches do not embrace the paradigm examples of those approaches. I offer somewhat different characterizations of these two approaches, as well as of the consequence approach (Schurz and Weingartner (Synthese 172(3): 415-436, 2010) which happily embrace their respective paradigms. Finally I prove that the three approaches are indeed compatible, but only just, and that the cost of combining them is too high. Any account which combines the strictures of what I call the strong likeness approach with the demands of either the content or the consequence approach suffers from precisely the same defect as Popper's—namely, it entails the trivialization of truthlikeness. The downside of eschewing the strong likeness constraints and embracing the content constraints alone is the underdetermination of the concept of truthlikeness.

The tradition descending from Frege and Russell has typically treated theories of meaning either as theories of meanings (propositions expressed), or as theories of truth conditions. However, propositions of the classical sort don't exist, and truth conditions can't provide all the information required by a theory of meaning. In this book, one of the world's leading philosophers of language offers a way out of this dilemma. Traditionally conceived, propositions are denizens of a \"third realm\" beyond mind and matter, \"grasped\" by mysterious Platonic intuition. As conceived here, they are cognitive-event types in which agents predicate properties and relations of things--in using language, in perception, and in nonlinguistic thought. Because of this, one's acquaintance with, and knowledge of, propositions is acquaintance with, and knowledge of, events of one's cognitive life. This view also solves the problem of \"the unity of the proposition\" by explaining how propositions can be genuinely representational, and therefore bearers of truth. The problem, in the traditional conception, is that sentences, utterances, and mental states are representational because of the relations they bear to inherently representational Platonic complexes of universals and particulars. Since we have no way of understanding how such structures can be representational, independent of interpretations placed on them by agents, the problem is unsolvable when so conceived. However, when propositions are taken to be cognitive-event types, the order of explanation is reversed and a natural solution emerges. Propositions are representational because they are constitutively related to inherently representational cognitive acts. Strikingly original,What Is Meaning?is a major advance.

In this book, Scott Soames defends the revolution in philosophy led by Saul Kripke, Hilary Putnam, and David Kaplan against attack from those wishing to revive descriptivism in the philosophy of language, internalism in the philosophy of mind, and conceptualism in the foundations of modality. Soames explains how, in the last twenty-five years, this attack on the anti-descriptivist revolution has coalesced around a technical development called two-dimensional modal logic that seeks to reinterpret the Kripkean categories of the necessary aposteriori and the contingent apriori in ways that drain them of their far-reaching philosophical significance. Arguing against this reinterpretation, Soames shows how the descriptivist revival has been aided by puzzles and problems ushered in by the anti-descriptivist revolution, as well as by certain errors and missteps in the anti-descriptivist classics themselves.Reference and Descriptionsorts through all this, assesses and consolidates the genuine legacy of Kripke and Kaplan, and launches a thorough and devastating critique of the two-dimensionalist revival of descriptivism. Through it all, Soames attempts to provide the outlines of a lasting, nondescriptivist perspective on meaning, and a nonconceptualist understanding of modality.

We consider two versions of truth as grounded in verification procedures: Dummett's notion of proof as an effective way to establish the truth of a statement and Hintikka's GTS notion of truth as given by the existence of a winning strategy for the game associated with a statement. Hintikka has argued that the two notions should be effective and that one should thus restrict one's attention to recursive winning strategies. In the context of arithmetic, we show that the two notions do not coincide: on the one hand, proofs in PA do not yield recursive winning strategies for the associated game; on the other hand, there is no sound and effective proof procedure that captures recursive GTS truths. We then consider a generalized version of Game Theoretical Semantics by introducing games with backward moves. In this setting, a connection is made between proofs and recursive winning strategies. We then apply this distinction between two kinds of verificationist procedures to a recent debate about how we recognize the truth of Gödelian sentences.

Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. The basic algebraic properties of this system have been studied in Dalla Chiara et al. (Foundations of Physics 39(6): 559-572, 2009), where we have introduced the notion of Shi-Aharonov quantum computational structure. In this paper we propose an algebraic abstraction from the Hilbert-space quantum computational structures, by introducing the notion of Toffoli-Hadamard algebra. From an intuitive point of view, such abstract algebras represent a natural quantum generalization of both classical and fuzzy-like structures.

The paper investigates, in the framework of branching space-times, whether an infinite EPR-like correlation which does not involve finite EPR-like correlations is possible.