Operations on complex intuitionistic fuzzy soft lattice ordered group and CIFS-COPRAS method for equipment selection process

This paper introduces some new operations on complex intuitionistic fuzzy lattice ordered groups such as sum, product, bounded product, bounded difference and disjoint sum, and verifying its pertinent properties. The research exhibits the CIFS-COPRAS algorithm in a complex intuitionistic fuzzy soft set environment. This method was furthermore applied for the equipment selection process.

Unital topology on a unital l-group

In this paper we investigate some fundamental properties of unital topology on a lattice ordered group with order unit. We show that some essential properties of order unit norm on a vector lattice with order unit, are valid for unital l-groups. For instance we show that for an Archimedean Riesz space G with order unit u, the unital topology and the strong link topology are the same.

C*-algebras generated by isometries and true representations

Let (G; P) be a quasi-lattice ordered group. In this paper we present a modied proof of Laca and Raeburn's theorem about the covariant isometric representations of amenable quasi-lattice ordered groups [7, Theorem 3.7], by following a two stage strategy. First, we construct a universal covariant representation for a given quasi-lattice ordered group (G; P) and show that it is unique. The construction of this object is new; we have not followed either Nica's approach in [10] or Laca and Raeburn's approach in [7], although all three objects are essentially the same. Our approach is a very natural one and avoids some of the intricacies of the other approaches. Then we show if (G; P) is amenable, true representations of (G; P) generate C-algebras which are canonically isomorphic to the universal object.

Lexico groups and direct products of lattice ordered groups

A lattice ordered groupThen

Structure Theorems of Specker Groups (I)

Specker groups are subgroups of group of all finite values sequences of integers. Fuchs ([5]) developed many theorems about Specker groups. Here I want to use lattice-ordered group approach to develop the lateral completion of Specker groups and Specker spaces. The main goals of this research paper are to prove theorem 2.9 and corollary 2.10.

On a type of distributivity of lattice ordered groups

Let m be an infinite cardinal. Inspired by a result of Sikorski on m-representability of Boolean algebras, we introduce the notion of r m-distributive lattice ordered group. We prove that the collection of all such lattice ordered groups is a radical class. Using the mentioned notion, we define and investigate a homogeneity condition for lattice ordered groups.

Weak relatively uniform convergences on MV-algebras

Weak relatively uniform convergences (wru-convergences, for short) in lattice ordered groups have been investigated in previous authors’ papers. In the present article, the analogous notion for MV-algebras is studied. The system s(A) of all wru-convergences on an MV-algebra A is considered; this system is partially ordered in a natural way. Assuming that the MV-algebra A is divisible, we prove that s(A) is a Brouwerian lattice and that there exists an isomorphism of s(A) into the system s(G) of all wru-convergences on the lattice ordered group G corresponding to the MV-algebra A. Under the assumption that the MV-algebra A is archimedean and divisible, we investigate atoms and dual atoms in the system s(A).

Generalized Specker lattice-ordered groups and two types of distributivity

Let A be a lattice-ordered group, B a generalized Boolean algebra. The Boolean extension A B of A has been investigated in the literature; we will refer to A B as a generalized Specker lattice-ordered group (namely, if A is the linearly ordered group of all integers, then A B is a Specker lattice-ordered group). The paper establishes that some distributivity laws extend from A B to both A and B, and (under certain circumstances) also conversely.