bipolar fuzzy graphs in this paper we introduce the notion of bipolar fuzzy graphs describe various methods of their construction discuss the concept of isomorphisms of these graphs and investigate some of their important properties we then introduce the notion of strong bipolar fuzzy graphs and study some of their properties we also discuss some propositions of self complementary and self weak complementary strong bipolar fuzzy graphs

types of arcs in a fuzzy graph the concept of connectivity plays an important role in both theory and applications of fuzzy graphs depending on the strength of an arc this paper classifies arcs of a fuzzy graph into three types namely a strong b strong and d arcs the advantage of this type of classification is that it helps in understanding the basic structure of a fuzzy graph completely we analyze the relation between strong paths and strongest paths in a fuzzy graph and obtain characterizations for fuzzy bridges fuzzy trees and fuzzy cycles using the concept of a strong b strong and d arcs an arc of a fuzzy tree is a strong if and only if it is an arc of its unique maximum spanning tree also we identify different types of arcs in complete fuzzy graphs

notes on bipolar fuzzy graphs in this note we show by examples that definitions 3 1 5 6 and 5 7 example 5 8 propositions 5 9 and 5 10 and partial proof of propositions 5 11 and 5 12 in a previous paper by akram muhammad akram bipolar fuzzy graphs inform sci 181 2011 5548 5564 contain some flaws and then provide the correct versions finally we introduce a generalized bipolar fuzzy graph

a fuzzy and bipolar approach to preference modeling with application to need and desire fuzziness and bipolarity allow representing human knowledge taking into account the gradual and the dialectic properties of language focusing on the meaning of concepts under this cognitive and linguistic approach we explore preference relations examining their semantic decomposition through fuzzy preference structures and the specification of meaningful opposites in particular we introduce the preference aversion p a model which allows analyzing under an independent aggregation methodology the possible gains and losses like pros and cons towards a given set of alternatives as an attractive feature of this proposal we show that the p a model allows distinguishing between need and desire contrary to common preference models where both notions are indistinguishable

on the k tuple domination of generalized de brujin and kautz digraphs a vertex u in a digraph g v a is said to dominate itself and vertices v such that u v a for a positive integer k a k tuple dominating set of g is a subset d of vertices such that every vertex in g is dominated by at least k vertices in d the k tuple domination number of g is the minimum cardinality of a k tuple dominating set of g this paper deals with the k tuple domination problem on generalized de bruijn and kautz digraphs we establish bounds on the k tuple domination number for the generalized de bruijn and kautz digraphs and we obtain some conditions for the k tuple domination number attaining the bounds

existence of maximal surfaces in asymptotically flat spacetimes we prove the existence of maximal surfaces in asymptotically flat spacetime satisfying an interior condition this uses a priori estimates which can also be applied to prescribed mean curvature surfaces in cosmological spacetimes and the dirichlet problem

distance spectra of graphs a survey abstract in 1971 graham and pollack established a relationship between the number of negative eigenvalues of the distance matrix and the addressing problem in data communication systems they also proved that the determinant of the distance matrix of a tree is a function of the number of vertices only since then several mathematicians were interested in studying the spectral properties of the distance matrix of a connected graph computing the distance characteristic polynomial and its coefficients was the first research subject of interest thereafter the eigenvalues attracted much more attention in the present paper we report on the results related to the distance matrix of a graph and its spectral properties

on fuzzification of some concepts of graphs in this paper we will be interested by the extension of the concepts of internal stability external stability not external domination and some of their combination to fuzzy graphs fuzzy sets and fuzzy logical operators are used as basis tools to model these concepts

on distance matrices and laplacians we consider distance matrices of certain graphs and of points chosen in a rectangular grid formulae for the inverse and the determinant of the distance matrix of a weighted tree are obtained results concerning the inertia and the determinant of the distance matrix of an unweighted unicyclic graph are proved if d is the distance matrix of a tree then we obtain certain results for a perturbation of d 1 as an example it is shown that if l is the laplacian matrix of an arbitrary connected graph then d 1 l 1 is an entrywise positive matrix we consider the distance matrix of a subset of a rectangular grid of points in the plane if we choose m k 1 points not containing a closed path in an m k grid then a formula for the determinant of the distance matrix of such points is obtained

on heterogeneous formal contexts we propose a new type of fuzzification for formal concept analysis that works with heterogeneous values in a context and illustrate this with an example we formulate and prove an appropriate counterpart to the so called basic theorem of a concept lattice we show that this is a generalization of the previous approaches it covers the so called generalized concept lattice and multi adjoint t concept lattices

ambiguity and fuzziness measures defined on the set of closed intervals in 0 1 starting from the idea of activity orders we define a family of orders on the set of closed intervals of a distributive lattice l that will allow us to set up some preorders associated to the ambiguity and fuzziness in order to measure the ambiguity and fuzziness degree of any closed interval in 0 1

hypersurfaces of prescribed mean curvature in lorentzian manifolds we give a new existence proof for closed hypersurfaces of prescribed mean curvature in lorentzian manifolds

note on generating fuzzy concept lattices via galois connections the aim of this paper is to compare an approach of creating fuzzy concept lattices proposed by popescu with several other approaches particularly we show that this approach is in some way equivalent to the approach of krajci called generalized concept lattices we also give a straightforward generalization of popescu s approach to non homogeneous cases

strong arcs in fuzzy graphs an arc of a fuzzy graph is called strong if its weight is at least as great as the strength of connectedness of its end nodes when it is deleted an arc is strong iff its weight is equal to the strength of connectedness of its end nodes a bridge is strong but a strong arc need not be a bridge an arc of maximum weight is strong but a strong arc need not have maximum weight in a connected graph there is a strong path a path consisting of strong arcs between any two nodes a fuzzy graph is a fuzzy tree iff there is a unique strong path between any two of its nodes in a fuzzy tree an arc is strong iff it is a bridge and a strong path between two nodes is a path of maximum strength between them

fuzzy end nodes in fuzzy graphs we define a fuzzy end node in a fuzzy graph and show that no node can be both a cut node and a fuzzy end node in a fuzzy tree every node is either a cut node or a fuzzy end node but the converse is not true we also show that any nontrivial fuzzy tree has at least two fuzzy end nodes and we characterize fuzzy cycles that have no cut nodes or no fuzzy end nodes

conditional edge fault tolerant hamiltonicity of dual cubes the dual cube is an interconnection network for linking a large number of nodes with a low node degree it uses low dimensional hypercubes as building blocks and keeps the main desired properties of the hypercube a dual cube dc n has n 1 links per node where n is the degree of a cluster n cube and one more link is used for connecting to a node in another cluster in this paper assuming each node is incident with at least two fault free links we show a dual cube dc n contains a fault free hamiltonian cycle even if it has up to 2n 3 link faults the result is optimal with respect to the number of tolerant edge faults

on multi adjoint concept lattices based on heterogeneous conjunctors sets of attributes and objects in fuzzy formal concept analysis are usually different and hence it might not make sense to evaluate them on the same carrier in this context the operators used to obtain the concept lattice could be defined by associating different lattices to attributes and objects several reasons exist for which we need to evaluate the sets of attributes and objects in the same carrier following this direction we introduce a new definition of a concept lattice where objects and attributes are evaluated on the same lattice l although operators evaluating objects and attributes in different carriers are used moreover we study the relationship between this new concept lattice and the alternative one which can be obtained directly by using different carriers for the sets of attributes and objects

graphs whose distance matrix has at most three negative eigenvalues abstract let d g be the distance matrix of a connected simple graph g the negative inertia of d g denoted by n d g is the number of negative eigenvalues of d g in this paper we determine all connected graphs g whose distance matrix d g has at most three negative eigenvalues

positive and negative inertia index of a graph abstract in this paper the positive and negative inertia index of trees unicyclic graphs and bicyclic graphs are discussed the methods of calculating them are obtained and an inequality about the difference between positive and negative inertia index is proved moreover a conjecture is proposed

characterizing reducts in multi adjoint concept lattices abstract the construction of reducts that is minimal sets of attributes containing the main information of a database is a fundamental task in different frameworks such as in formal concept analysis fca and rough set theory rst this paper will be focused on a general fuzzy extension of fca called multi adjoint concept lattice and we present a study about the attributes generating meet irreducible elements and on the reducts in this framework from this study we introduce interesting results on the cardinality of reducts and the consequences in the classical case

global c2 estimates for convex solutions of curvature equations we establish a c2 a priori estimate for convex hypersurfaces whose principal curvatures 1 n satisfy k x f x x the weingarten curvature equation we also obtain such an estimate for admissible 2 convex hypersurfaces in the case k 2 our estimates resolve a longstanding problem in geometric fully nonlinear elliptic equations 2015 wiley periodicals inc

immersed hypersurfaces with constant weingarten curvature in a recent paper korevaar 1 5 used the alexandrov reflection principle to show that closed embedded hypersurfaces in n 1 lhn 1 or the upper hemisphere of s 1 are umbilic spheres provided a certain function f of the principal curvatures t t 22 is constant he only had to assume that f is positive on the positive cone 212i 0 vi and that f is elliptic on the component f of 21 f 0 which contains here f is said to be elliptic if 0f d21 0 for all i 1 inn this generalization of earlier sphere theorems see 9 and 10 for references cannot be extended to hypersurface immersions in view of recent counterexamples 1 11 however assuming additional curvature conditions walter derived in 10 global results for hypersurface immersions in a space n l c of constant curvature c which have a constant higher mean curvature function h here h is the r th symmetric function of the principal curvatures it was shown that such hypersurfaces are of constant mean curvature h1 provided they have nonnegative sectional curvature and non negative principal curvatures as a consequence they have to be isoparametric with at most two distinct principal curvatures and can therefore be completely classified here we show that it is not necessary to assume all principal curvatures to be non negative moreover we extend waiter s result to general symmetric functions f f 2 let m be a smooth connected and compact manifold without boundary then we have the following result

fuzzy graph representation of a fuzzy concept lattice in this paper we present a new relationship between fuzzy concept lattice and fuzzy graph given a fuzzy binary relation we define an underlying fuzzy graph and establish a new relation between the set of elements of the fuzzy concept lattice built from the fuzzy relation and the set of minimal disconnections of the associated fuzzy graph this link is important from the point of view of application and computation

parabolic methods for the construction of spacelike slices of prescribed mean curvature in cosmological spacetimes spacelike hypersurfaces of prescribed mean curvature in cosmological spacetimes are constructed as asymptotic limits of a geometric evolution equation in particular an alternative constructive proof is given for the existence of maximal and constant mean curvature slices

constraint heterogeneous concept lattices and concept lattices with heterogeneous hedges the paper deals with the isomorphism between the constraint heterogeneous concept lattices and concept lattices with heterogeneous hedges the essential point of the former approach encompasses the full diversification of data structures within a formal context in particular we use a different complete lattice for diverse objects a different complete lattice for diverse attributes and a different poset for diverse matrix fields the latter framework with heterogeneous hedges results in a reduction in the size of the corresponding concept lattice we present the properties of constraint heterogeneous approach that is associated with the fixpoints of hedges and we add remarks to the related studies

the use of linguistic variables and fuzzy propositions in the l fuzzy concept theory the use of linguistic variables and fuzzy propositions in the interval valued l fuzzy contexts can be an interesting tool to extract a more complete information from them in this paper we analyze three different situations first we obtain significant relations in order to study all the objects and attributes of the interval valued l fuzzy context by means of the interval valued l fuzzy concepts after that we show how to replace the erroneous values to be able to study in a suitable way the context finally we use the linguistic labels to obtain a subcontext that represents our interest of study we also show an experimental evaluation in the paper

intuitionistic fuzzy hypergraphs with applications hypergraphs are considered a useful tool for modeling system architectures and data structures and to represent a partition covering and clustering in the area of circuit design in this paper we apply the concept of intuitionistic fuzzy set theory to generalize results concerning hypergraphs for each intuitionistic fuzzy structure defined we use cut level sets to define an associated sequence of crisp structures we determine what properties of the sequence of crisp structures characterize a given property of the intuitionistic fuzzy structure we also present applications of intuitionistic fuzzy hypergraphs

the study of the interval valued contexts the aim of this paper is to contribute to the interval valued fuzzy data analysis proposing a new method based on the formal concept analysis we develop a theoretical model that analyzes the interval valued information that arises from the opinion of a group of experts about the relationship between a set of objects and a set of attributes and we want to analyze this information from the point of view of the formal concept analysis to do this we are going to modelize a new l fuzzy concept theory using some results about multisets and expertons finally we include a simple example to illustrate it by showing its potential applications

bipolar fuzzy graph representation of concept lattice formal concept analysis fca is a mathematical framework for knowledge processing tasks fca has been successfully incorporated into fuzzy setting and its extension interval valued fuzzy set for handling vagueness and impreciseness in data however the analysis in such settings is restricted to unipolar space recently some applications of bipolar information are shown in bipolar fuzzy graph lattice theory as well as in fca the adequate analysis of bipolar information using fca requires incorporation of bipolar fuzzy set and an appropriate lattice structure for this purpose we propose an algorithm for generating the bipolar fuzzy formal concepts a method for cut of bipolar fuzzy formal context and its implications with illustrative examples

on m strong fuzzy graphs the cartesian product and disjoint sum of graphs play a prominent role and have numerous interesting algebraic properties in this note we consider operations on fuzzy graphs under which m strong property is preserved if g1 and g2 are m strong fuzzy graphs then we prove that g1 g2 g1 g2 and g1 g2 are also m strong but g1 g2 need not be m strong if g1 g2 is m strong then we show that at least one factor must be m strong we show that the product of a m strong fuzzy graph g1 with a non m strong fuzzy graph g2 remains m strong if and only if g2 satisfies special condition for any fuzzy graph g gcc is the smallest m strong fuzzy graph that contains g and g gcc if and only if g is m strong we further show that m strong fuzzy graph g is a fuzzy tree if and only if the support g is a tree

a characterization of graphs with rank 4 the rank of a graph g is defined to be the rank of its adjacency matrix in this paper we consider the following problem what is the structure of a connected graph with rank 4 this question has not yet been fully answered in the literature and only some partial results are known in this paper we resolve this question by completely characterizing graphs g whose adjacency matrix has rank 4

fuzzy graphs in the evaluation and optimization of networks abstract referring to some predecessing models the paper introduces the concept of fuzzy vertex graphs a way is shown for modeling various quantitatively featurable functional capabilities of computer communication and similar networks it is shown that functional capability of distributed hierarchical multicomponent systems networks can be described by the directed rooted tree model according to the above fuzzy graph idea the problem of optimizing the overall functional capability with given component vertex set is introduced the fuzzy formulae based on the algebraic connectives which are to be optimized are constructed in the main part of the paper a series of results are presented concerning some special however important cases also the hypotheses founded on some computer experiments are formulated finally the application of these results and hypotheses are shown by the example of a distributed communication switching system family being in development in hungary

the inertia and energy of distance matrices of complete k partite graphs abstract for a distance matrix d g its inertia is the triple of integers n d n 0 d n d where n d n 0 d n d denote the number of positive 0 negative eigenvalues of d g respectively the d energy is the sum of the absolute eigenvalues of d g in this paper we first study the inertia of distance matrices of complete k partite graphs then as applications we not only prove a conjecture proposed by caporossi et al 2009 in 5 in a different way from stevanovic et al 2013 11 but also obtain the formula of the d energy of the remaining complete k partite graphs at last we obtain the graphs with the maximum resp minimum d energy among all the complete k partite graphs with n vertices

the bipancycle connectivity of the hypercube paths and cycles are popular interconnection networks due to their simplicity and low degrees and therefore an efficient way of embedding them into an interconnection network is of particular importance many path embedding aspects and cycle embedding aspects such as hamiltonicity hamiltonian connectivity panconnectivity bipanconnectivity pancyclicity vertex pancyclicity and edge pancyclicity have been proposed and extensively studied in fact these discussions are meaningful for interconnection networks of resource allocated systems or heterogeneous computing systems in this paper we propose a new cycle embedding aspect called bipancycle connectivity that combines the concepts of vertex pancyclicity and bipanconnectivity a bipartite graph is bipancycle connected if an arbitrary pair of vertices x y is contained by common cycles called bipanconnected cycles that include a cycle of every even length ranging from minc x y to n where minc x y denotes the length of the minimum cycle that contains x and y and n is the number of vertices in this paper we introduce a new graph called the cycle of ladders we show that the hypercube is bipancycle connected by presenting algorithms to embed the cycle of ladders into the hypercube

closed weingarten hypersurfaces in semi riemannian manifolds the existence of closed hypersurfaces of prescribed curvature in semi riemannian manifolds is proved provided there are barriers

surfaces of prescribed mean curvature vector in semi riemannian manifolds abstract solving a second order quasilinear initial value problem we prove existence and uniqueness of both space like and time like immersions of prescribed mean curvature vector in general semi riemannian manifolds such surfaces arise for example as critical points of generalized area functionals as well as self similar solutions of the mean curvature flow

from fuzzy data analysis and fuzzy regression to granular fuzzy data analysis this note offers some personal views on the two pioneers of fuzzy sets late professors hideo tanaka and kiyoji asai the intent is to share some personal memories about these remarkable researchers and humans highlight their long lasting research accomplishments and stress a visible impact on the fuzzy set community the note elaborates on new and promising research avenues initiated by fuzzy regression and identifies future developments of these models emerging within the realm of granular computing and giving rise to a plethora of granular fuzzy models and higher order and higher type granular constructs

finite automata theory with membership values in lattices in this paper we study finite automata with membership values in a lattice which are called lattice valued finite automata the extended subset construction of lattice valued finite automata is introduced then the equivalences between lattice valued finite automata lattice valued deterministic finite automata and lattice valued finite automata with e moves are proved a simple characterization of lattice valued languages recognized by lattice valued finite automata is given then it is proved that the kleene theorem holds in the frame of lattice setting a minimization algorithm of lattice valued deterministic finite automata is presented in particular the role of the distributive law for the truth valued domain of finite automata is analyzed the distributive law is not necessary to many constructions of lattice valued finite automata but it indeed provides some convenience in simply processing lattice valued finite automata

node connectivity and arc connectivity of a fuzzy graph the fuzzy graph approach is more powerful in cluster analysis than the usual graph theoretic approach due to its ability to handle the strengths of arcs effectively the concept of node strength sequence is introduced and is studied in a complete fuzzy graph two new connectivity parameters in fuzzy graphs namely fuzzy node connectivity k and fuzzy arc connectivity k are introduced and obtained the fuzzy analogue of whitney s theorem fuzzy node cut fuzzy arc cut and fuzzy bond are defined fuzzy bond is a special type of a fuzzy bridge it is proved that at least one of the end nodes of a fuzzy bond is a fuzzy cutnode it is shown that k k for a fuzzy tree and it is the minimum of the strengths of its strong arcs the relationships of the new parameters with already existing vertex and edge connectivity parameters are studied and is shown that the value of all these parameters are equal in a compete fuzzy graph also a new clustering technique based on fuzzy arc connectivity is introduced

cycles and cocycles of fuzzy graphs abstract in this paper we show that if the fuzzy graph is a cycle then it is a fuzzy cycle if and only if is not a fuzzy tree we also examine the relationship between fuzzy bridges and cycles we introduce and examine the concepts of chords twigs 1 chains with boundary zero cycle vectors coboundary and cocycles for fuzzy graphs we show that although the set of cycle vectors fuzzy cycle vectors cocycles and fuzzy cocycles do not necessarily form vector spaces over the field z 2 of integers modulo 2 they nearly do thisallows us to introduce the concepts of fuzzy cycle rank and fuzzy cocycle rank for fuzzy graphs in a meaningful way

the inertia and energy of the distance matrix of a connected graph abstract let g be a connected graph and d g be the distance matrix of g suppose that 1 d 2 d n d are the d eigenvalues of g in this paper we show that the distance matrix of a clique tree is non singular moreover we also prove that the distance matrix of a clique tree has exactly one positive d eigenvalue in addition we determine the extremal graphs with maximum and minimum distance energy among all clique trees

discussion from imprecise to granular probabilities gert de cooman s work is an important contribution to a better understanding of how to deal with imprecise probabilities but there is an important issue which is not addressed how can imprecise probabilites be dealt with not in isolation but in the broader context of imprecise probability distributions imprecise events and imprecise relations what is needed for this purpose is the concept of granular probability a probability which is defined in terms of a generalized constraint of the form x isr r where x is the constrained variable r is a constraining realtion of r is an indexing variable which defines the modality of the constraint that is its semantics a few examples are used as illustrations

operations on fuzzy graphs abstract we define the operations of cartesian product composition union and join on fuzzy subgraphs of graphs g1 and g2 if the graph g is formed from g1 and g2 by one of these operations we determine necessary and sufficient conditions for an arbitrary fuzzy subgraph of g also to be formed by the same operation from fuzzy subgraphs of g1 and g2

mean curvature flow of spacelike graphs we prove the mean curvature flow of a spacelike graph in 1 2 g1 g2 of a map f 1 2 from a closed riemannian manifold 1 g1 with ricci1 0 to a complete riemannian manifold 2 g2 with bounded curvature tensor and derivatives and with sectional curvatures satisfying k2 k1 remains a spacelike graph exists for all time and converges to a slice at infinity we also show with no need of the assumption k2 k1 that if k1 0 or if ricci1 0 and k2 c c 0 constant any map f 1 2 is trivially homotopic provided f g2 0 and in case k2 0 this largely extends some known results for ki constant and 2 compact obtained using the riemannian structure of 1 2 and also shows how regularity theory on the mean curvature flow is simpler and more natural in pseudo riemannian setting then in the riemannian one

some properties of fuzzy reasoning in propositional fuzzy logic systems in order to analyze the logical foundation of fuzzy reasoning this paper first introduces the concept of generalized roots of theories in lukasiewicz propositional fuzzy logic luk godel propositional fuzzy logic god product propositional fuzzy logic p and nilpotent minimum logic nm the r 0 propositional fuzzy logic l next it is proved that all consequences of a theory c named d c are completely determined by its generalized root whenever c has a generalized root moreover it is proved that every finite theory c has a generalized root which can be expressed by a specific formula finally we demonstrate the existence of a non fuzzy version of fuzzy modus ponens fmp in luk god p and nm l and we provide its numerical version as a new algorithm for solving fmp

mean curvature flow of compact spacelike submanifolds in higher codimension we prove the longtime existence for mean curvature flow of a smooth n dimensional spacelike submanifold of an n m dimensional manifold whose metric satisfies the timelike curvature condition

the positive and the negative inertia index of line graphs of trees abstract the positive resp negative inertia index of g denoted by p g resp n g is defined to be the number of positive resp negative eigenvalues of its adjacency matrix the nullity of g denoted by g is defined to be the multiplicity of the eigenvalue zero in the adjacency spectrum of g in 2001 gutman and sciriha 11 proved that the nullity of the line graph of a tree is either 0 or 1 in this paper we consider the positive and the negative inertia index for the line graph l t of a tree t showing that e t 1 2 p l t e t 1 where e t denotes the number of internal non pendant edges contained in t the extremal trees for which p l t attains the upper bound and the lower bound are respectively characterized it is shown that l t is nonsingular if p l t attains the upper bound and l t is singular if p l t attains the lower bound

fuzzy morphisms between graphs a generic definition of fuzzy morphism between graphs gfm is introduced that includes classical graph related problem definitions as sub cases such as graph and subgraph isomorphism the gfm uses a pair of fuzzy relations one on the vertices and one on the edges each relation is a mapping between the elements of two graphs these two fuzzy relations are linked with constraints derived from the graph structure and the notion of association graph the theory extends the properties of fuzzy relation to the problem of generic graph correspondence we introduce two complementary interpretations of gfm from which we derive several interesting properties the first interpretation is the generalization of the notion of association compatibility the second is the new notion of edge morphism one immediate application is the introduction of several composition laws each property has a theoretical and a practical interpretation in the problem of graph correspondence that is explained throughout the paper special attention is paid to the formulation of a non algorithmical theory in order to propose a first step towards a unified theoretic framework for graph morphisms

on the use of words and fuzzy sets this paper only tries to stimulate some reflections by showing a possible way towards rethinking fuzzy sets from their roots a rethinking that does not change the view that fuzzy sets are mathematical entities giving extension to predicates in such a way that if the predicates are precise the corresponding new entities are nothing else than classical sets what perhaps is a key idea is that the use of a predicate organizes in some way the universe of discourse when this organization is a preorder the extension or l set appears once a degree numerical or not but consistent with the organization can be defined the ultimate goal of those above mentioned reflections provided they would be realized in the future is to extend the current theories of fuzzy sets to wider areas of both language and reasoning our objective is to reach a better knowledge of the links between language and its representations for the progress of computing with words and perceptions

on stability of fuzzy formal concepts over randomized one sided formal context abstract we propose a probabilistic approach to the issue of one sided fuzzy formal concepts stability the modified rice siff algorithm represents a crisp index how to select the relevant concepts from the set of all one sided fuzzy formal concepts we suggest to explore the formal concepts stability affected by the random fluctuation of values in a formal context we describe the algorithm and study the properties of the concept stability using random variables with the gaussian normal distribution in combination with the modified rice siff algorithm the gaussian probabilistic index improves the analysis of the most relevant one sided formal concepts from the original one sided formal context the connections to recent works in the related directions are presented