Non-linear neutrosophic numbers (NLNNs) are different kinds of neutrosophic numbers with at least one non-linear membership function (either of truthiness, falsity or indeterminacy part) of the ...information. Furthermore, a linear programming problem with non-linear neutrosophic numbers as coefficients/parameters is a special type of programming problem known as a non-linear linear programming problem (NLN-LPP). This paper elaborates on the concepts of non-linear neutrosophic number (NLNN) sets, different forms of non-linear neutrosophic numbers (NLNNs), alpha, beta,gamma cuts on non-linear neutrosophic numbers (NLNNs), possibility mean, possibility standard deviation, and possibility variance of non-linear neutrosophic numbers (NLNNs). In this paper, we also propose the solution technique for non-linear neutrosophic linear programming problems (NLN-LPPs) in which all coefficients/parameters are non-linear neutrosophic numbers (NLNNs). In this continuation, we suggest a new modified possibility score function for non-linear NNs in terms of possibility means and possibility standard deviations of non-linear neutrosophic numbers (NLNNs) for better use of all parts of information. This modified score function is used to convert non-linear neutrosophic number (NLNN) coefficients/parameters of non-linear neutrosophic linear programming problem (NLN-LPP) into equivalent crisp values. Thereafter, the equivalent crisp problem is solved with the usual method to obtain the optimal solution of non-linear neutrosophic linear programming problem (NLN-LPP). The proposed solution algorithm is unique and new for solving non-linear neutrosophic linear programming problems. A numerical example is solved with the proposed algorithm to legitimate the research output. A case study is also discussed to show its applicability in solving real-life problems. Keywords: Linear programming problem; Non-linear neutrosophic numbers (NLNNs), Possibility score function of Non-linear neutrosophic numbers (NLNNs), Possibility mean of Non-linear neutrosophic numbers (NLNNs), Possibility standard deviation of Non-linear neutrosophic numbers (NLNNs).
It is widely alleged that metaphysical possibility is “absolute” possibility (Kripke in Naming and necessity, Harvard University Press, Cambridge,
1980
; Lewis in On the plurality of worlds, ...Blackwell, Oxford,
1986
; van Inwagen in Philos Stud 92:68–84,
1997
; Rosen, in: Gendler and Hawthorne (eds) Conceivability and possibility, Clarendon, Oxford,
2002
, p 16; Stalnaker, in: Stalnaker (ed) Ways a world might be: metaphysical and anti-metaphysical essays, Oxford University Press, Oxford,
2003
, pp 201–215; Williamson in Can J Philos 46:453–492,
2016
). Kripke calls metaphysical necessity “necessity in the highest degree” (
1980
, p. 99). Van Inwagen claims that if P is metaphysically possible, then it is possible “tout court. Possible simpliciter. Possible period…. possib(le) without qualification (
1997
, p. 72).” And Stalnaker writes, “we can agree with Frank Jackson, David Chalmers, Saul Kripke, David Lewis, and most others who allow themselves to talk about possible worlds at all, that metaphysical necessity is necessity in the widest sense (
2003
, p. 203).” What exactly does the thesis that metaphysical possibility is absolute amount to? Is it true? In this article, I argue that, assuming that the thesis is not merely terminological, and lacking in any metaphysical interest, it is an article of faith. I conclude with the suggestion that metaphysical possibility may lack the metaphysical significance that is widely attributed to it.
On Elliptical Possibility Distributions Lesniewska-Choquet, Charles; Mauris, Gilles; Atto, Abdourrahmane M ...
IEEE transactions on fuzzy systems,
2020-Aug., 2020-8-00, 2020-08-01, Letnik:
28, Številka:
8
Journal Article
Recenzirano
Odprti dostop
This paper aims to propose two main contributions in the field of multivariate data analysis through the possibility theory. The first proposition is the definition of a generalized family of ...multivariate elliptical possibility distributions. These distributions have been derived from a consistent probability-possibility transformation over the family of so-called elliptical probability distributions. The second contribution proposed by this paper is the definition of two divergence measures between possibilistic distributions. We prove that a symmetric version of the Kullback-Leibler divergence guarantees all divergence properties when related to the space of possibility distributions. We further derive analytical expressions of the latter divergence and of the Hellinger divergence for certain possibility distributions pertaining to the elliptical family proposed, especially the normal multivariate possibility divergence in two dimensions. Finally, this paper provides an illustration of the developed possibilistic tools in an application of bi-band change detection between optical satellite images.
I present and clarify one form of the modal argument for substance dualism, and go on to state and provide defeaters for five of the major arguments raised against the modal argument as a whole. I do ...not provide an unabridged defence of the modal argument. Instead, I focus on a range
of defeaters scattered throughout the literature that are raised against the modal argument. In my view, these have not been gathered in one place and freshly evaluated. Accordingly, my limited purpose is to fill this lacuna. Thus, I present a representative version of the modal argument to
set the context for what follows. Next, I clarify and critique the five major objections directed at the modal argument in general.
Soft set developed by Smarandache in 2018 to Hypersoft set (HSS) to deal with multi argument approximate functions. The soft set cannot deal with cases when attributes are required to be further ...divided into disjoint attribute-valued sets. Neutrosophic Hypersoft Set (NHSS) is the most effective and useful method to handle the environment which involved more than one attribute. Neutrosophic Hypersoft Set introduced by combining Hypersoft Set and Neutrosophic Soft Set. In this paper, we first define the concept of Possibility Neutrosophic Hypersoft Set (PNHSS in short) which is combination of PNSS and HSS. Certain essential basic characteristics as subset, equal and complement are studied with illustrative examples. Basic operations such as: union, intersection and some properties such as commutative, associative, distributive low and De Morgan’s low are discussing. Also, we introduce AND and OR operation of PNHSS with suitable examples and some propositions.
This contribution is intended to promote possibility theory as a maturing general framework for the quantification of epistemic and aleatory uncertainties. For this purpose, we revisit Zadeh’s ...Extension Principle in the context of imprecise probabilities. Therein the aggregation of the possibility distributions is performed by the minimum-operator, corresponding to non-interactivity of the uncertain variables. Yet, this notion is not equivalent to well-established terms from probability theory such as stochastic independence. In order to use possibilistic calculus for propagating multivariate imprecise probabilities through models, we present suitable aggregation operations, corresponding to simple modifications of the Extension Principle, and we prove preservation of probability-possibility consistency, the fundamental concept in possibility theory. For the purpose of demonstration, the possibilistic solutions of two benchmark problems of uncertainty quantification are presented.
Expert knowledge is an important source of input to risk analysis. In practice, experts might be reluctant to characterize their knowledge and the related (epistemic) uncertainty using precise ...probabilities. The theory of possibility allows for imprecision in probability assignments. The associated possibilistic representation of epistemic uncertainty can be combined with, and transformed into, a probabilistic representation; in this article, we show this with reference to a simple fault tree analysis. We apply an integrated (hybrid) probabilistic‐possibilistic computational framework for the joint propagation of the epistemic uncertainty on the values of the (limiting relative frequency) probabilities of the basic events of the fault tree, and we use possibility‐probability (probability‐possibility) transformations for propagating the epistemic uncertainty within purely probabilistic and possibilistic settings. The results of the different approaches (hybrid, probabilistic, and possibilistic) are compared with respect to the representation of uncertainty about the top event (limiting relative frequency) probability. Both the rationale underpinning the approaches and the computational efforts they require are critically examined. We conclude that the approaches relevant in a given setting depend on the purpose of the risk analysis, and that further research is required to make the possibilistic approaches operational in a risk analysis context.
•Time-variant creep coefficient and shrinkage strain model is developed.•Corrosion is considered.•Epistemic uncertainty is considered to incorporate vagueness of variables.•To evaluate TDFP and TDR, ...a single-loop optimization method is applied.•Fuzzy reliability estimated by the area ratio of failure domain to the total area of MF.•Real-time data from Addis Ababa is used for the case-study.•The proposed methodology prevents the exploitation of the probability theory.
Time-dependent reliability (TDR) is the possibility that a structure or system under consideration can perform the intended function under specified service conditions over a given time instant under fuzzy uncertainty. This paper is mainly concerned to identify fuzzy variables, generate the membership function of the input variables and output quantities, analyze timedependent performance level, estimate the possibility safety index, and evaluate the TDR of the structures. To evaluate TDR by a possibilistic approach, the fuzzy uncertainty that is characterized by membership function is considered. The type of uncertainty defines the method of reliability analysis, i.e., aleatory uncertainty possesses a probabilistic approach, whereas epistemic uncertainty leads to a possibilistic approach. The TDR analysis of the structures subjected to sustained load and corrosion based on probability theory is well developed. On the contrary, the TDR of structures subjected to combined effects sustained load, corrosion, creep, and shrinkage based on possibility theory lack research. Thus, this paper is significant to evaluate the TDR of structures subjected to the aforementioned effects based on possibility theory. However, it requires a rigorous procedure, a single-loop optimization method (SLOM) is employed to evaluate the TDR of structures involving epistemic uncertainty. To enhance the validation of the proposed approach, several examples are thoroughly carried out.
RiassuntoIl presente contributo si propone di analizzare la relazione tra sostenibilità e giustizia, al fine di metterne in evidenza il carattere riflessivo. Non vi è dubbio infatti che la ...sostenibilità costituisca il focus primario del dibattito pubblico, attorno al quale si dispongono le strategie e le pratiche nazionali e sovranazionali; tuttavia, l’estensione semantica che questo termine ha subito rischia di confondere e infine dissiparne il senso. Il contributo si sofferma pertanto sulla portata significante del concetto di sostenibilità, sottolineandone il carattere “aperto”. Il riferimento all’apertura diviene così la chiave ermeneutica per accordare sostenibilità e giustizia. Se la sostenibilità, pertanto, si inscrive entro una precipua rappresentazione della giustizia, quest’ultima deve riflessivamente divenire sostenibile.
Single-valued neutrosophic numbers (SVN-numbers) are a special kind of neutrosophic set on the real number set. The concept of a SVN-number is important for quantifying an ill-known quantity and ...ranking of SVN-number is a very difficult situation in decision-making problems. The main aim of this paper is to present a new ranking methodology of SVN-numbers for solving multi-attribute decision-making problems. Therefore, we firstly define the possibility mean, variance and standard deviation of single-valued neutrosophic numbers. Using the ratio of possibility mean and standard deviation, we have developed the proposed ranking approach and applied to MADM problems. Finally, a numerical example is examined to show the applicability and embodiment of the proposed method.
PDF
