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.

the Suppes-Sen dominance relation is a weak and widely accepted criterion of distributive justice. We propose its application to Nash bargaining theory. The Nash Bargaining Solution (NBS) is characterised by replacing the controversial Independence of Irrelevant Alternatives axiom with an axiom embodying the SuppesSen principle. More precisely, maximality in the Suppes-Sen relation is shown to ...

Suppes-Sen Dominance is a commonly accepted criterion of impartiality in distributive justice. Mariotti (1999) characterized the Nash bargaining solution using Nash (1950)’s Scale Invariance (SI) axiom and an axiom named Suppes-Sen Proofness (SSP) that embodies the Suppes-Sen principle. By adding a relative equity component to SSP, we …rst consider a stronger version of of it, the Strong Suppes...

A classical result for crisp choice functions shows the equivalence between Arrow axiom and the property of full rationality. In this paper we study a fuzzy form of Arrow axiom formulated in terms of the subsethood degree and of the degree of equality (of fuzzy sets). We prove that a fuzzy choice function verifies Fuzzy Arrow Axiom if and only if it is (fuzzy) full rational. We also show that t...

This paper is devoted to the discussion of the relationship between fuzzy rough set models and fuzzy topologies on a finite universe. The (TC) axiom for fuzzy topology is proposed. It is proved that the set of all lower approximation sets based on a reflexive and transitive fuzzy relation consists of a fuzzy topology which satisfies (TC) axiom; and conversely, a fuzzy topology which obey (TC) a...

The Archimedean axiom in fuzzy set theory is critically discussed. The axiom is brought into perspective within a measurement theoretic framework and then its validity for fuzzy set theory is questioned. The discussion sheds light into what type of vagueness fuzzy set theory models.

The ‘normalization’ axiom associated with Sen’s poverty index–and this, indeed, holds for most extant measures of poverty—entails an uncomfortable implication when we adopt a strong, or inclusive, definition the poor. This paper suggests that may not always be at liberty to weak definition. available alternative then is change form measure. Accordingly, modification his normalization which lead...

EQ-algebras introduced by Novák are algebras of truth values for a higher-order fuzzy logic (fuzzy type theory). In this paper, the compatibility of multiplication w.r.t. the fuzzy equality in an arbitrary EQ-algebra is examined. Particularly, an example indicates that the compatibility axiom does not always hold, and then a class of EQ-algebras satisfying the compatibility axiom is characteriz...

The Arrow index of a fuzzy choice function C is a measure of the degree to which C satisfies the Fuzzy Arrow Axiom, a fuzzy version of the classical Arrow Axiom. The main result of this paper shows that A(C) characterizes the degree to which C is full rational. We also obtain a method for computing A(C). The Arrow index allows to rank the fuzzy choice functions with respect to their rationality...

In the approximate fuzzy reasoning the covering over of fuzzy rule base input and rule premise of a rule determines the importance of that fuzzy rule and the rule output as well. An axiom system has been created, describing the relationship between the fuzzy rule base system, rule input and rule output. By using distance-based operators a novel reasoning method appears by the compositional rule...