On extending generalized Bonferroni means to Atanassov orthopairs in decision making contexts

Extensions of aggregation functions to Atanassov orthopairs (often referred to as intuitionistic fuzzy sets or AIFS) usually involve replacing the standard arithmetic operations with those defined for the membership and non-membership orthopairs. One problem with such constructions is that the usual choice of operations has led to formulas which do not generalize the aggregation of ordinary fuzzy sets (where the membership and non-membership values add to 1). Previous extensions of the weighted arithmetic mean and ordered weighted averaging operator also have the absorbent element 〈1,0〉, which becomes particularly problematic in the case of the Bonferroni mean, whose generalizations are useful for modeling mandatory requirements. As well as considering the consistency and interpretability of the operations used for their construction, we hold that it is also important for aggregation functions over higher order fuzzy sets to exhibit analogous behavior to their standard definitions. After highlighting the main drawbacks of existing Bonferroni means defined for Atanassov orthopairs and interval data, we present two alternative methods for extending the generalized Bonferroni mean. Both lead to functions with properties more consistent with the original Bonferroni mean, and which coincide in the case of ordinary fuzzy values.<br /

Ranking for Objects and Attribute Reductions in Intuitionistic Fuzzy Ordered Information Systems

We aim to investigate intuitionistic fuzzy ordered information systems. The concept of intuitionistic fuzzy ordered information systems is proposed firstly by introducing an intuitionistic fuzzy relation to ordered information systems. And a ranking approach for all objects is constructed in this system. In order to simplify knowledge representation, it is necessary to reduce some dispensable attributes in the system. Theories of rough set are investigated in intuitionistic fuzzy ordered information systems by defining two approximation operators. Moreover, judgement theorems and methods of attribute reduction are discussed based on discernibility matrix in the systems, and an illustrative example is employed to show its validity. These results will be helpful for decisionmaking analysis in intuitionistic fuzzy ordered information systems

Modele otoczeniowe i topologiczne dla klasycznych i intuicjonistycznych logik modalnych

We may speak about syntax. From this point of view any logic can be considered as as the set of axioms and rules. Here we are interested in formal proofs and deduction systems. Second, we can also think about semantics, namely, about some models in which it is possible to de ne the notions of truth and falsity. As for the logical calculi, we are working with propositional logics. Thus, we are not so much interested in quanti ers. Our logics are non-classical. Of course, there are many kinds of non-classical logic and many reasons for which certain system can be considered as nonclassical. In our case, there are two main ways which are notoriously combined. On the one hand, we are interested in intuitionistic, superintuitionistic and subintuitionistic systems. This means that we narrow down the set of axioms and rules of classical logic. On the other hand, we use modal operators to de ne and analyse the ideas of necessity and possibility. As a result, we often obtain classical and intuitionistic modal logics. Our semantic models are mostly neighborhood, topological and relational. These three approaches are also combined. For this reason, we may speak about bi-relational and relational-neighborhood structures. Moreover, we go beyond the standard notion of topology in order to study its various generalizations. Finally, our aim is to investigate several non-classical calculi using all the tools mentioned above. We are interested in the issues of completeness (axiomatization), nite model property, bisimulation and decidability. Moreover, we analyse some purely topological properties of the structures in question. The philosophical aspect is also important