Case-based reasoning is a recognized paradigm and has been explored in both applied and methodological directions. In the several phases of CBR, the adaptation phase is certainly the most problematic whereas the most characteristic and interesting phase. We propose to view this task through a fuzzy analogical scheme. The adaptation is realized by focusing on the relation existing between the pr...

In the present paper, we introduce the fuzzy Nehring axiom, fuzzy Sen axiom and weaker form of the weak fuzzycongruence axiom. We establish interrelations between these axioms and their relation with fuzzy Chernoff axiom. Weexpress full rationality of a fuzzy choice function using these axioms along with the fuzzy Chernoff axiom.

Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy binary relation on a crisp topological space.

As international corporate activities increase, their staffing involves more strategic concerns. However, foreign assignments have many differences, and dissatisfaction with the host country is a known cause of expatriate failure. From the point of view of an expatriate candidate, the decision of whether to take an expatriate assignment can be regarded as a FMCDM (fuzzy multiple criteria decisi...

Fuzzy planar graph is an important subclass of fuzzy graph. Fuzzy planar graphs and its several properties are presented. A very close association of fuzzy planar graph is fuzzy dual graph. This is also defined and several properties of it are studied. Isomorphism on fuzzy graphs are well defined in literature. Isomorphic relation between fuzzy planar graph and its dual graph are established.

In this article we introduce μ-filtered fuzzy module with a family of fuzzy submodules. It shows the relation between μ-filtered fuzzy modules and crisp filtered modules by level sets. We investigate fuzzy topology on the μ-filtered fuzzy module and apply that to introduce fuzzy completion. Finally we extend Krull’s intersection theorem of fuzzy ideals by using concept μ-adic completion.

Introducing rough sets in hesitant fuzzy set domain and using it for the various applications would open up new possibilities in rough set theory. For this purpose the notion of hesitant fuzzy relations is introduced. The foundation of equivalence hesitant fuzzy relation is laid. Definition of anti-reflexive kernel, symmetric kernel etc. is proposed and the formulae to evaluate them are derived...

In this paper, we introduce the concept of interval valued (α, β)-fuzzy subnear-rings and ideal of near-rings, where α, β any two of the {∈, q,∈ ∨q,∈ ∧q} with α 6=∈ ∧q, by using belongs to relation ∈ and quasi-coincidence with relation q between interval valued fuzzy points and interval valued fuzzy sets. We also discussed some characterizations of interval valued (α,∈ ∨q)-fuzzy ideals(subnear-...

Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by n-ary operations is considered. Namely, with the use of fuzzy...

Images of fuzzy sets under fuzzy relations have been investigated mainly in two contexts: On the one hand, mostly under the term “full image” [5], they can be regarded as very general tools for fuzzy inference, leading to the so-called “compositional rule of inference” [1, 5]. On the other hand, under the term “extensional hull”, the image of a fuzzy set under a fuzzy equivalence relation yield...