5,322 research outputs found
Black-Litterman model with intuitionistic fuzzy posterior return
The main objective is to present a some variant of the Black - Litterman
model. We consider the canonical case when priori return is determined by means
such excess return from the CAPM market portfolio which is derived using
reverse optimization method. Then the a priori return is at risk quantified
uncertainty. On the side, intensive discussion shows that the experts' views
are under knightian uncertainty. For this reason, we propose such variant of
the Black - Litterman model in which the experts' views are described as
intuitionistic fuzzy number. The existence of posterior return is proved for
this case.We show that then posterior return is an intuitionistic fuzzy
probabilistic set.Comment: SSRN Electronic Journal 201
Enhancement of dronogram aid to visual interpretation of target objects via intuitionistic fuzzy hesitant sets
In this paper, we address the hesitant information in enhancement task often caused by differences in image contrast. Enhancement approaches generally use certain filters which generate artifacts or are unable to recover all the objects details in images. Typically, the contrast of an image quantifies a unique ratio between the amounts of black and white through a single pixel. However, contrast is better represented by a group of pix- els. We have proposed a novel image enhancement scheme based on intuitionistic hesi- tant fuzzy sets (IHFSs) for drone images (dronogram) to facilitate better interpretations of target objects. First, a given dronogram is divided into foreground and background areas based on an estimated threshold from which the proposed model measures the amount of black/white intensity levels. Next, we fuzzify both of them and determine the hesitant score indicated by the distance between the two areas for each point in the fuzzy plane. Finally, a hyperbolic operator is adopted for each membership grade to improve the pho- tographic quality leading to enhanced results via defuzzification. The proposed method is tested on a large drone image database. Results demonstrate better contrast enhancement, improved visual quality, and better recognition compared to the state-of-the-art methods.Web of Science500866
Mass problems and intuitionistic higher-order logic
In this paper we study a model of intuitionistic higher-order logic which we
call \emph{the Muchnik topos}. The Muchnik topos may be defined briefly as the
category of sheaves of sets over the topological space consisting of the Turing
degrees, where the Turing cones form a base for the topology. We note that our
Muchnik topos interpretation of intuitionistic mathematics is an extension of
the well known Kolmogorov/Muchnik interpretation of intuitionistic
propositional calculus via Muchnik degrees, i.e., mass problems under weak
reducibility. We introduce a new sheaf representation of the intuitionistic
real numbers, \emph{the Muchnik reals}, which are different from the Cauchy
reals and the Dedekind reals. Within the Muchnik topos we obtain a \emph{choice
principle} and a \emph{bounding principle} where range over Muchnik
reals, ranges over functions from Muchnik reals to Muchnik reals, and
is a formula not containing or . For the convenience of the
reader, we explain all of the essential background material on intuitionism,
sheaf theory, intuitionistic higher-order logic, Turing degrees, mass problems,
Muchnik degrees, and Kolmogorov's calculus of problems. We also provide an
English translation of Muchnik's 1963 paper on Muchnik degrees.Comment: 44 page
Logic of Intuitionistic Interactive Proofs (Formal Theory of Perfect Knowledge Transfer)
We produce a decidable super-intuitionistic normal modal logic of
internalised intuitionistic (and thus disjunctive and monotonic) interactive
proofs (LIiP) from an existing classical counterpart of classical monotonic
non-disjunctive interactive proofs (LiP). Intuitionistic interactive proofs
effect a durable epistemic impact in the possibly adversarial communication
medium CM (which is imagined as a distinguished agent), and only in that, that
consists in the permanent induction of the perfect and thus disjunctive
knowledge of their proof goal by means of CM's knowledge of the proof: If CM
knew my proof then CM would persistently and also disjunctively know that my
proof goal is true. So intuitionistic interactive proofs effect a lasting
transfer of disjunctive propositional knowledge (disjunctively knowable facts)
in the communication medium of multi-agent distributed systems via the
transmission of certain individual knowledge (knowable intuitionistic proofs).
Our (necessarily) CM-centred notion of proof is also a disjunctive explicit
refinement of KD45-belief, and yields also such a refinement of standard
S5-knowledge. Monotonicity but not communality is a commonality of LiP, LIiP,
and their internalised notions of proof. As a side-effect, we offer a short
internalised proof of the Disjunction Property of Intuitionistic Logic
(originally proved by Goedel).Comment: continuation of arXiv:1201.3667; extended start of Section 1 and 2.1;
extended paragraph after Fact 1; dropped the N-rule as primitive and proved
it derivable; other, non-intuitionistic family members: arXiv:1208.1842,
arXiv:1208.591
Linear-Logic Based Analysis of Constraint Handling Rules with Disjunction
Constraint Handling Rules (CHR) is a declarative committed-choice programming
language with a strong relationship to linear logic. Its generalization CHR
with Disjunction (CHRv) is a multi-paradigm declarative programming language
that allows the embedding of horn programs. We analyse the assets and the
limitations of the classical declarative semantics of CHR before we motivate
and develop a linear-logic declarative semantics for CHR and CHRv. We show how
to apply the linear-logic semantics to decide program properties and to prove
operational equivalence of CHRv programs across the boundaries of language
paradigms
Focusing and Polarization in Intuitionistic Logic
A focused proof system provides a normal form to cut-free proofs that
structures the application of invertible and non-invertible inference rules.
The focused proof system of Andreoli for linear logic has been applied to both
the proof search and the proof normalization approaches to computation. Various
proof systems in literature exhibit characteristics of focusing to one degree
or another. We present a new, focused proof system for intuitionistic logic,
called LJF, and show how other proof systems can be mapped into the new system
by inserting logical connectives that prematurely stop focusing. We also use
LJF to design a focused proof system for classical logic. Our approach to the
design and analysis of these systems is based on the completeness of focusing
in linear logic and on the notion of polarity that appears in Girard's LC and
LU proof systems
Evaluating strategies for implementing industry 4.0: a hybrid expert oriented approach of B.W.M. and interval valued intuitionistic fuzzy T.O.D.I.M.
open access articleDeveloping and accepting industry 4.0 influences the industry structure and customer willingness. To a successful transition to industry 4.0, implementation strategies should be selected with a systematic and comprehensive view to responding to the changes flexibly. This research aims to identify and prioritise the strategies for implementing industry 4.0. For this purpose, at first, evaluation attributes of strategies and also strategies to put industry 4.0 in practice are recognised. Then, the attributes are weighted to the experts’ opinion by using the Best Worst Method (BWM). Subsequently, the strategies for implementing industry 4.0 in Fara-Sanat Company, as a case study, have been ranked based on the Interval Valued Intuitionistic Fuzzy (IVIF) of the TODIM method. The results indicated that the attributes of ‘Technology’, ‘Quality’, and ‘Operation’ have respectively the highest importance. Furthermore, the strategies for “new business models development’, ‘Improving information systems’ and ‘Human resource management’ received a higher rank. Eventually, some research and executive recommendations are provided. Having strategies for implementing industry 4.0 is a very important solution. Accordingly, multi-criteria decision-making (MCDM) methods are a useful tool for adopting and selecting appropriate strategies. In this research, a novel and hybrid combination of BWM-TODIM is presented under IVIF information
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