Soft p-ideals of soft BCI-algebras

AbstractMolodtsov [D. Molodtsov, Soft set theory–First results, Comput. Math. Appl. 37 (1999) 19–31] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties that is free from the difficulties that have troubled the usual theoretical approaches. Jun [Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl. 56 (2008) 1408–1413] applied first the notion of soft sets by Molodtsov to the theory of BCK/BCI-algebras. In this paper we introduce the notion of soft p-ideals and p-idealistic soft BCI-algebras, and then investigate their basic properties. Using soft sets, we give characterizations of (fuzzy) p-ideals in BCI-algebras. We provide relations between fuzzy p-ideals and p-idealistic soft BCI-algebras

Some views on information fusion and logic based approaches in decision making under uncertainty

Decision making under uncertainty is a key issue in information fusion and logic based reasoning approaches. The aim of this paper is to show noteworthy theoretical and applicational issues in the area of decision making under uncertainty that have been already done and raise new open research related to these topics pointing out promising and challenging research gaps that should be addressed in the coming future in order to improve the resolution of decision making problems under uncertainty

Almost structural completeness; an algebraic approach

A deductive system is structurally complete if its admissible inference rules are derivable. For several important systems, like modal logic S5, failure of structural completeness is caused only by the underivability of passive rules, i.e. rules that can not be applied to theorems of the system. Neglecting passive rules leads to the notion of almost structural completeness, that means, derivablity of admissible non-passive rules. Almost structural completeness for quasivarieties and varieties of general algebras is investigated here by purely algebraic means. The results apply to all algebraizable deductive systems. Firstly, various characterizations of almost structurally complete quasivarieties are presented. Two of them are general: expressed with finitely presented algebras, and with subdirectly irreducible algebras. One is restricted to quasivarieties with finite model property and equationally definable principal relative congruences, where the condition is verifiable on finite subdirectly irreducible algebras. Secondly, examples of almost structurally complete varieties are provided Particular emphasis is put on varieties of closure algebras, that are known to constitute adequate semantics for normal extensions of S4 modal logic. A certain infinite family of such almost structurally complete, but not structurally complete, varieties is constructed. Every variety from this family has a finitely presented unifiable algebra which does not embed into any free algebra for this variety. Hence unification in it is not unitary. This shows that almost structural completeness is strictly weaker than projective unification for varieties of closure algebras