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Kim and Bishu (Fuzzy Sets and Systems 100 (1998) 343-352) proposeda modification of fuzzy linear regression analysis. Their modificationis based on a criterion of minimizing the difference of the fuzzy membershipvalues between the observed and estimated fuzzy numbers. We show that theirmethod often does not find acceptable fuzzy linear regression coefficients andto overcome this shortcoming, propose a modification. Finally, we present twonumerical examples to illustrate efficiency of the modified method.

The aim of this paper is to extend results established by H. Onoand T. Kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. The main theorem states that a residuatedlattice A is directly indecomposable if and only if its Boolean center B(A)is {0, 1}. We also prove that any linearly ordered residuated lattice and anylocal residuated lattice are directly indecomposable. We apply these results toprove some properties of the Boolean center of a residuated lattice and alsodefine the algebras on subintervals of residuated lattices.

In this paper, we dene the concepts of compatibility between twofuzzy subsets on Q, the set of states of a max- min general fuzzy automatonand transitivity in a max-min general fuzzy automaton. We then construct auniform structure on Q, and dene a topology on it. We also dene the conceptof semi-uniform structures on a nonempty set X and construct a semi-uniformstructure on the set of states of a general fuzzy automaton. We then constructa semi-uniform structure on , the set of all nite words on , the set ofinput symbols of a general fuzzy automaton and, nally, using these semi-uniform structures, we construct two topologies on Q and and discuss theirproperties.

The notion of vague ideals in pseudo MV-algebras is introduced,and several properties are investigated. Conditions for a vague set to be avague ideal are provided. Conditions for a vague ideal to be implicative aregiven. Characterizations of (implicative, prime) vague ideals are discussed.The smallest vague ideal containing a given vague set is established. Primeand implicative extension property for a vague ideal is discussed.

The aim of this paper is the study of fuzzy $Gamma$-hyperrings. In thisregard the notion of -fuzzy hyperideals of $Gamma$-hyperrings are introduced andbasic properties of them are investigated. In particular, the representationtheorem for $nu$-fuzzy hyperideals are given and it is shown that the image of a-fuzzy hyperideal of a $Gamma$-hyperring under a certain conditions is two-valued.Finally, the product of $nu$-fuzzy hyperideals are studied.

In this paper, we first define the notion of a complete general fuzzyautomaton with threshold c and construct an $H_{nu}$- group, as well as commutativehypergroups, on the set of states of a complete general fuzzy automatonwith threshold c. We then define invertible general fuzzy automata, discussthe notions of “homogeneity, “separation, “thresholdness connected, “thresholdnessinner irreducible and “principal and strongly connected, as appliedto them and use these concepts to construct a quasi-order hypergroup on aninvertible general fuzzy automaton. Finally, we derive relationships betweenthe properties of an invertible general fuzzy automaton and the induced hypergroup.

The concept of soft sets, introduced by Molodtsov [20] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. In this paper, weapply the notion of the soft sets of Molodtsov to the theory of Hilbert algebras.The notion of soft Hilbert (abysmal and deductive) algebras, soft subalgebras,soft abysms and soft deductive systems are introduced, and their basic propertiesare investigated. The relations between soft Hilbert algebras, soft Hilbertabysmal algebras and soft Hilbert deductive algebras are also derived.

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